Giant dipoles and superfluorescence in perovskite superlattices for optical transistors under ambient conditions

Giant dipoles and superfluorescence in perovskite superlattices for optical transistors under ambient conditions | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Giant dipoles and superfluorescence in perovskite superlattices for optical transistors under ambient conditions Ruotao Wang, Yixuan Dou, Bo Peng, Yuancheng Jing, Zhipeng Zhang, and 31 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7162326/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The giant dipole is a collective state of coherent dipole coupling that contributes to our understanding of macroscopic quantum transitions and offers significant potential for quantum computing. Traditionally, the creation of giant dipoles has required extreme conditions, and their detailed behavior remains underexplored. Here, we report the first giant dipole formed under ambient conditions and investigate its ultrafast formation dynamics and energy transfer mechanisms for the first time. We used an epitaxial two-dimensional halide perovskite superlattice, which confines photo-excited carriers to enhance the formation of giant dipoles. We captured superfluorescence bursts from the giant dipole, exhibiting distinct Rabi oscillations. Additionally, we found that the superfluorescence is dependent on photo-excitation polarization, which inspired the design of an innovative optical transistor. These findings advance our understanding of giant dipoles and their role in quantum systems, offering new insights that will facilitate the development of high-precision quantum logic gates and novel optical devices. Photonics/optics Materials Engineering Figures Figure 1 Figure 2 Figure 3 Figure 4 Main Text Dipoles consisting of photo-excited electron-hole pairs can interact to form a coherent giant dipole 1 , 2 , wherein the wave functions of individual dipoles share spatially and temporally synchronized phases 3 (Fig. 1 a). The formation of a giant dipole requires a sufficiently large and closely packed dipole population 4 , 5 , ensuring overlapping electromagnetic fields that increase the likelihood of interactions and thus facilitate the transition of many individual dipoles to a coherent collective state 6 . However, quantum fluctuations disrupt such interactions, especially fluctuations induced by dipole motions such as random phase variations, random emission events, and disturbances in surrounding electromagnetic fields 7 , 8 . Therefore, the formation of giant dipoles typically requires conditions such as low temperatures or strong magnetic fields to confine or align the dipoles, enhancing their interactions 9 , 10 . Here we report the first observation of a giant dipole under ambient conditions. The multi-quantum wells in the halide perovskite superlattice create natural cavities that confine dipoles, reducing quantum fluctuations, enabling effective interactions among dipoles, and facilitating giant dipole formation 11 . We also describe the formation dynamics of giant dipoles through coherent-state absorption (CSA). The collective recombination of carriers within the giant dipole results in superfluorescence, characterized by Burnham-Chiao ringing. We exploited the polarization-dependent photo-excitation required for giant dipole formation to build an optical transistor. We found that the epitaxially grown superlattice ensured the long-term stability of both the material and device under ambient conditions. Anisotropic structural and electronic properties of the superlattice We chose PEA 2 MAPb 2 I 7 -based (PEA = phenethylamine; MA = methylamine) quasi-two-dimensional perovskite as our model because PEA has better moisture resistance than other organic spacers and Pb is more stable than Sn in air 12 . The PEA 2 MAPb 2 I 7 superlattice was grown epitaxially on a single-crystal MAPbBr 3 substrate (Supplementary Figs. 1–4 and Supplementary Note 1). Bonding selectivity between growth precursors and the substrate leads to vertically aligned multi-quantum wells 13 . Cryogenic transmission electron microscopy images revealed homogeneous Pb-I slabs in the xy plane and periodic Pb-I slabs separated by PEA spacers in the xz plane (Fig. 1 b and Supplementary Fig. 5). Long-range order within the superlattice was evidenced by synchrotron-based grazing incidence wide-angle X-ray scattering, which revealed spot patterns with directional anisotropy 14 (Supplementary Figs. 6 and 7). The homogeneous Pb-I slabs in the xy plane offer dipoles a high degree of freedom 15 (Fig. 1 c, top), while the multi-quantum wells confine dipole motion along the z -direction 16 , substantially reducing quantum fluctuations and promoting giant dipole formation (Fig. 1 c, bottom and Supplementary Note 2). The cavity qualities (e.g., continuity, uniformity, and purity) can be optimized by tuning the superlattice growth parameters 13 (Supplementary Figs. 8 and 9). Additionally, the thin organic spacer enables interlayer dipole coupling between adjacent inorganic layers, further accelerating giant dipole formation 17 (Supplementary Note 2). Ab initio calculations revealed that the perovskite superlattice had anisotropic reflectivity, absorbance, and thus efficiency of photo-excitation, resulting in an excitation–polarization-dependent dipole population 18 (Fig. 1 d, Supplementary Fig. 10, and Supplementary Note 3). Under s-polarized excitation along the z -direction, the perovskite superlattice reflected less and absorbed more light, generating a larger dipole population compared to p-polarized excitation at the same fluence in the x -direction (Supplementary Fig. 10). Furthermore, the perovskite superlattice showed dipole-population-dependent electronic behavior 19 . I p xy orbitals were dominant at the valence band maximum, whereas deeper valance states (from ~ 0.4 eV below the valence band maximum) were dominated by I p z orbitals (Fig. 1 e). This variation in orbital occupation implies that larger photo-excited carrier populations change electron-hole occupancy in different anisotropic orbitals 18 . In small dipole populations, holes were mostly found at the valence band maximum of the I p xy orbitals, whereas electrons were found at the conduction band minimum of the Pb p xy orbitals (Supplementary Fig. 11). This indicated that most dipole movements were in the xy plane with a high degree of freedom 20 (Supplementary Fig. 12), resulting in large quantum fluctuations and thus no giant dipole formation. In contrast, in large dipole populations, electrons were excited from deeper valence states to higher conduction states. Although the conduction band was dominated by the same Pb p xy orbitals, the I p z orbital became dominant in the deeper valence band (Fig. 1 e and Supplementary Figs. 13 and 14). Consequently, dipole movements were primarily distributed along the z -direction (Supplementary Fig. 13), confined by the superlattice cavities 13 , 21 , thus reducing quantum fluctuations and facilitating giant dipole formation 18 , 22 (Supplementary Fig. 15). Formation dynamics of the giant dipole As individual dipoles synchronize into a giant dipole, their band structure undergoes renormalization, transitioning from the original random states to a new coherent state 5 , 6 (Supplementary Figs. 16 and 17). To investigate this process, we applied pump-probe transient absorption mapping, which achieves high temporal and energetic resolution (Supplementary Fig. 18). All measurements were conducted under ambient conditions. Under p-polarized light, only ground-state absorption (GSA) was observed, even at high fluences (Supplementary Fig. 19 and Supplementary Note 4). In contrast, under s-polarized light, at a low fluence of 3 µJ⋅cm − 2 , the dipole population was insufficient to establish strong dipole–dipole interactions, achieving only a GSA of 600 ~ 682 nm, corresponding to the original bandgap of the superlattice (Fig. 2 a). As the fluence increased to 16 µJ⋅cm − 2 , the dipole population enlarged, enhancing the intensity of the GSA as expected. Additionally, a new absorption band appeared at 717 ~ 734 nm (Fig. 2 a), indicating CSA, a new quantum state of the giant dipole 6 (Supplementary Fig. 20). CSA has a longer wavelength than GSA due to the lower energy of the giant dipole relative to random dipoles, and is narrower in bandwidth, reflecting the synchronized coherent state of the giant dipole 6 (Supplementary Note 4). This was the first evidence for the CSA of giant dipoles in any material. When the fluence was increased to 43 µJ⋅cm − 2 , the CSA became more intense and appeared as a distinct stripe in the mapping (Fig. 2 a). The energy transfer between random dipoles and the giant dipole was evidenced by the evolution of band intensities in the transient absorption spectra (Fig. 2 b). As the excitation fluence increased, so did the GSA, indicating that more electrons were excited from the ground state (Fig. 2 b). The GSA declined once the CSA appeared, suggesting that the formation of the giant dipole led to rapid electron decay, replenishing the ground state (Supplementary Fig. 20). The giant dipole exhibited a decay of ~ 20 ps due to strong synchronization (Fig. 2 c), as opposed to tens of nanoseconds for random dipoles 23 . Meanwhile, the CSA intensity increased, reflecting the transition of additional excited electrons into the giant dipole state. This behavior suggested that energy carried by excited electrons was transferred from the GSA to the CSA (Supplementary Fig. 20 and Supplementary Note 4). It took time to synchronize the random dipoles (Supplementary Fig. 16), which introduced a characteristic delay (~ 4 ps at 7 µJ⋅cm − 2 excitation fluence) following photo-excitation 2 (Fig. 2 d, Supplementary Fig. 21, and Supplementary Note 5). Compared to the tens of picoseconds of delay in polycrystalline perovskites 24 , the ultrashort delay in the superlattice makes it less likely that coherence will dephase due to quantum fluctuations, facilitating giant dipole formation 4 , 24 . At high excitation fluence (43 µJ⋅cm − 2 ), the delay was reduced further to less than 1 ps, indicating that a larger dipole population expedites the synchronization 5 (Fig. 2 e, top). This is because larger dipole populations enhance dipole interactions and generate a stronger collective electromagnetic field, promoting synchronization 4 . For the same reason, the decay time of the giant dipole was also reduced 25 (Fig. 2 e, bottom). Superfluorescence from the giant dipole Superfluorescence, a synchronized pulsed emission, is a distinctive feature of the giant dipole 4 , 26 . We used a streak camera under ambient conditions to capture its ultrafast characteristics 4 . Only fluorescence was detected under p-polarized excitation as expected, with peak intensity increasing linearly with excitation fluence 22 (Supplementary Fig. 22). Under s-polarized excitation at low excitation fluence, only fluorescence was observed at ~ 705 nm, associated with intensity decay on a nanosecond scale (Fig. 3 a and 3 b). At higher excitation fluences (> 16 µJ⋅cm − 2 ), we observed superfluorescence emission. This threshold was markedly lower than previously reported (Supplementary Table 1). The superfluorescence showed differences in intensity, wavelength, and decay behavior (Fig. 3 a and 3 b and Supplementary Fig. 23). Specifically, we detected stronger superfluorescence intensities at ~ 720 nm, corresponding to the giant dipole observed during transient absorption (Fig. 2 a and 2 b). The peak intensities followed the characteristic power-law dependence of superfluorescence 4 , 5 (Fig. 3 b, right inset). The intensity decayed on a picosecond scale, three orders of magnitude faster than fluorescence, reflecting the collective emission of the giant dipole 26 . This rapid decay, similar to the giant dipole behavior during transient absorption (Fig. 2 e), was even faster at higher excitation fluences 4 (Supplementary Fig. 24). Additionally, the superfluorescence exhibited distinct decay oscillations (Fig. 3 a and 3 b and Supplementary Fig. 23). As the superfluorescence propagates, it interacts coherently and exchanges energy periodically with the giant dipole 5 . This process manifests as distinct intensity oscillations, known as Burnham-Chiao ringing, an intrinsic property of superfluorescence 27 (Supplementary Note 5). Superfluorescence was always accompanied by fluorescence (Fig. 3 c), indicating remnant random dipoles even after giant dipole formation 4 . The Lorentzian-fitted 720-nm peak suggested a superfluorescence resonance mechanism, whereas the Gaussian-fitted 705-nm peak corresponded to fluorescence 4 (Supplementary Fig. 25). As the excitation fluence increased, we observed redshifts in the superfluorescence peak from ~ 718 to ~ 720 nm and in the fluorescence peak from ~ 706 to ~ 708 nm (Supplementary Fig. 26), probably due to energy dissipation via lattice vibrations at elevated temperatures under high excitation fluences 28 . The normalized superfluorescence intensity demonstrated a 180° periodicity in its emission polarization angle because it originated from the giant dipole 16 , 29 (Fig. 3 c, inset and Supplementary Note 5), whereas the fluorescence remained isotropic because it originated from random dipoles. We also studied the intensity and full width at half maximum (FWHM) of superfluorescence as a function of s-polarized excitation fluence and identified three different regimes (Fig. 3 d). First, at fluences below 12 µJ⋅cm − 2 , we detected only background fluorescence due to the small dipole population. Second, at fluences above 12 µJ⋅cm − 2 , we detected a superfluorescence peak with an FWHM of ~ 33 meV. As the fluence increased, the superfluorescence became more intense in a superlinear manner 30 , suggesting an enhanced transition of random dipoles to the coherent state 31 due to expedited dipole synchronization in larger dipole populations 5 . Concurrently, the FWHM of the superfluorescence declined to 22 meV as more dipoles transitioned into the coherent state, resulting in more coherent emission 4 . Finally, at fluences exceeding 45 µJ⋅cm − 2 , both the superfluorescence intensity and FWHM formed a plateau, indicating the gradual depletion of electrons at corresponding valence band levels. Optical transistors Artificial cavities with complicated fabrications are typically required to construct optical transistors (Supplementary Note 6) but the natural cavities in the perovskite superlattice address this issue 32 . The power-law-dependent evolution of superfluorescence intensity ensures that only signals exceeding a certain threshold are amplified 33 , 34 , similar to the transfer curve of electrical transistors 32 . Therefore, we were able to demonstrate an optical transistor based on superfluorescence for the first time. We used two s-polarized lasers with tunable power, aligned in the same incident xy plane, to excite the superlattice (Fig. 4 a). With one beam (IN1, similar to the gate voltage in electrical transistors) maintaining a certain power, the other beam (IN2, similar to the source-drain voltage in electrical transistors) modulates the superfluorescence output across the three emission regimes (Fig. 3 d), and vice versa, demonstrating collaborative regulation of superfluorescence 33 , 35 (Fig. 4 b and Supplementary Fig. 27). The substantial differences in wavelength, intensity, and decay time between the superfluorescence output and excitation input ensure their isolation 4 , 30 , 32 . We explored the potential to use this optical transistor as a logic gate 36 , with polarization serving as the binary states of logic input and fluence controlling the type of logic gates (Supplementary Note 6). Specifically, the transistor acts as an OR gate at high levels of fluence, while the s-polarization of either IN1 or IN2 alone is sufficient to trigger superfluorescence (Fig. 4 c). In contrast, the transistor acts as an AND gate at low levels of fluence, requiring both IN1 and IN2 to be s-polarized to generate superfluorescence. NOR and NAND gates can be realized by adding inverse polarizers before the superlattices 37 . The inherent binary nature of excitation polarization remains reliable during operation, thus mitigating the loss-dependent issues of logic operations commonly encountered in other optical transistors 33 , 38 . Given the strong ionic bonds between the substrate and epitaxial superlattice, the material structure remained intact even under continuous exposure to high-intensity (e.g., 40 µJ⋅cm − 2 ) laser excitation 39 . The superfluorescence also remained stable under ambient conditions without any encapsulation (Supplementary Fig. 28). Consequently, the logic gates were stable at a high extinction ratio (i.e., the ratio between the [1] and [0] levels) after at least 1.8 million test cycles (Fig. 4 d and Supplementary Note 6). Methods Materials and solvents Lead (II) bromide (PbBr 2 , 98%+) was purchased from Thermo Scientific Chemicals. Lead (II) oxide (PbO, 99.9%) was purchased from Alfa Aesar. Methylammonium bromide (MABr, 99.99%), methylammonium iodide (MAI, 99.99%), and phenethylammonium iodide (PEAI, 99.99%) were purchased from Greatcell Solar Materials. Gamma butyrolactone (GBL, 98%) was purchased from Transene Company. Methanol (MeOH, 99.8%), isopropanol (IPA, 99.5%), propylene carbonate (PC, 99%), acetone (99.5%), dimethylformamide (DMF, 99.8%), hydriodic acid (HI, 57 wt.% in H 2 O, 99.95%), and hypophosphorous acid (H 3 PO 2 , 50 wt.% in H 2 O) were purchased from Sigma-Aldrich. All reagents were used as received without further purification. Synthesis of PEA 2 MAPb 2 I 7 single-crystal flakes 7.4 mmol of PbO was added to 10 ml of pre-heated HI (57 wt.% in H 2 O) at 180 ℃, mixed with 1 ml of H 3 PO 2 (50 wt.% in H 2 O), and stirred until the precursor solution became transparent yellow. A solution of MAI (4.2 mmol)/PEAI (4.2 mmol) in MeOH was then injected into the precursor solution and stirred for 2 min. Subsequently, the beaker was transferred into a vacuum chamber for 15 s to remove dissolved air, before being returned to ambient atmosphere for crystallization. The flakes nucleated, grew, and filled the beaker within ~ 2 h. After precipitation, the crystal flakes were filtered and sequentially washed with IPA, PC, and acetone using a vacuum funnel, followed by drying in a vacuum 20 . Preparation of bulk MAPbBr 3 single crystals Bulk MAPbBr 3 single crystals were grown by slow solution evaporation 39 . MABr and PbBr 2 were dissolved in a 1:1 stoichiometric ratio in DMF at a concentration of 1.67 M. The solution was kept at room temperature to allow the solvent to evaporate slowly for growing MAPbBr 3 single crystals. The as-grown single crystals were collected and used as substrates for superlattice growth without any further treatment. Fabrication of perovskite superlattices The PEA 2 MAPb 2 I 7 single-crystal flakes were redissolved in GBL to prepare a 1 M growth solution. This growth solution was spin-coated onto the bulk MAPbBr 3 single crystal substrate at 4,000 revolutions per minute (r.p.m.) for 30 s. The coated substrate was then annealed at 180 ℃ for 2 min to form the superlattices. Ab initio calculations First-principles density functional theory calculations 40 , 41 were performed using the Vienna ab initio Simulation Package 42 , 43 . Projector-augmented wave potentials were employed with the generalized gradient approximation in the Perdew-Burke-Ernzerhof parametrizations for the exchange-correlation functional 44 . Van der Waals interactions were described using the DFT-D3 method of Grimme with a zero-damping function 45 , properly describing the long-range dispersion interactions between the organic molecules in the hybrid materials. Based on convergence tests, a plane-wave basis set with a kinetic energy cutoff of 800 eV and a Brillouin zone grid of 5×5×2 Γ-centered k-points were employed. Relaxation was carried out until the energy differences were converged within 10 − 6 eV, with a Hellman-Feynman force convergence threshold of 10 − 2 eV/Å. Spin-orbit coupling was included throughout all electronic structures and optical properties calculations. To calculate the bandgap of the perovskite superlattices, hybrid functionals within the Heyd–Scuseria–Ernzerhof HSE06 formalism were used. On top of the HSE06 band structures, the excitonic effects are computed from time-dependent Hartree − Fock calculations using the Casida Eq. 4 6 with a total of 24 valence and 24 conduction bands. Structure and morphology characterizations X-ray diffraction (XRD) was taken using an Anton Paar XRDynamic 500 diffractometers. Scanning electron microscopy images were captured using a Zeiss Sigma 500. Cryo-transmission electron microscope (cryo-TEM) samples were prepared with an FEI Scios DualBeam cryo-FIB/scanning electron microscope (cryo-FIB/SEM). Cryo-TEM images were acquired on a Thermofisher Talos F200X G2 cryo-S/TEM with a Gatan Elsa cryo-transfer holder. Cross-sectional electron energy loss spectroscopy mapping was performed using a Gatan Enfinium ER (977) spectrometer. Synchrotron-based grazing incidence wide-angle X-ray scattering was measured on beamline 7.3.3 at the Advanced Light Source, Lawrence Berkeley National Laboratory. The X-ray wavelength was 1.240 Å, with various grazing incident angles and scattering intensity was detected using a PILATUS 2M detector. The exposure time was 5 s per frame in single mode, with a total measurement time of 2 min. The images were sector-averaged using the Nika software package. Ultrafast pump-probe measurements Reflection mode was used for transient absorption measurements because the superlattices were epitaxially grown on a thick, non-transparent single-crystal MAPbBr 3 substrate. Pump-probe absorption was measured using a Helios system from Ultrafast Systems (Supplementary Fig. 29). The excitation source was generated by an Astrella-F-1K femtosecond amplifier with an 800 nm, 1 kHz fundamental beam. This beam was directly applied to produce the probe beam by passing through a crystal for continuum generation in the Helios system. The 515 nm pump beam was produced by an optical parametric amplifier system from Coherent. The sample was positioned on a reflection sample holder, and the chopper-modulated pump light was directed onto the sample. The detector was triggered to record every probe pulse and calculate the reflection spectrum. From the chopper sync out, the Helios software determined the chopper state (pump-on or pump-off) for each measured probe spectrum, allowing for the calculation of the differential reflection spectrum by taking the difference between pump-on and pump-off states. All measurements were conducted at room temperature in ambient air. Time-resolved photoluminescence spectra The femtosecond laser used to excite the sample was generated by a regenerative amplifier (400 nm wavelength, 100 fs pulse width, and 1 kHz repetition, Coherent Legend) seeded by a Ti: sapphire oscillator (100 fs, 80 MHz, Coherent Vitesse) (Supplementary Fig. 30). The pump laser wavelength was controlled at 515 nm by an optical parametric amplifier. Emission from the sample was collected in a backscattered geometry with a pair of lenses and directed to a monochromator (Acton, Spectra Pro 2500i) coupled to a streak camera (Hamamatsu, ultimate temporal resolution of ~ 1 ps). Superfluorescence peak intensities were extracted from the streak camera images. All measurements were performed at room temperature in ambient air. Polarization-dependent emission spectra A high-repetition-rate femtosecond laser system (Pharos, 100 kHz, Light Conversion) in a reflection geometry was used for the customized superfluorescence spectra measurement (Supplementary Fig. 31). The Pharos laser generated pulses with a center wavelength of 1030 nm and a pulse width of 160 fs, delivering a pulse energy of 100 µJ. In this work, the 1030 nm pulses were directed through a beta barium borate crystal to generate a 515 nm second harmonic excitation beam. This excitation beam was then directed through a 515 nm λ /2 waveplate to control polarization and a continuous neutral density filter to achieve tunable pulse energy. The beam was focused onto the sample surface using an NBK-7 lens with a 12.5 cm focal length. The incident angle was set at 15°. To prevent burning damage to the sample, a repetition rate of 100 Hz was used. The superfluorescence signals were dispersed by a spectrograph (Shamrock, Andor) and detected by a charge-coupled device (Newton idus, Andor). All measurements were performed at room temperature in ambient air. Optical transistors A 1030 nm femtosecond pulse (Pharos, 100 kHz, Light Conversion) was filtered through an etalon (SLS optics) to create an up-conversion pulse with a narrow bandwidth of 4 cm − 1 full width at half maximum (Supplementary Fig. 32). This pulse was then directed through a beta barium borate crystal to generate a 515 nm beam, referred to as IN1. Simultaneously, the reflection of the 1030 nm pulse from the etalon was directed through another beta barium borate crystal to generate a second 515 nm beam, referred to as IN2. Beam IN1 was focused onto the sample surface using a 10 cm focal length parabolic mirror, spatially overlapping with beam IN2, which was focused by a 12.5 cm focal length NBK-7 convex lens. The staggered distances between the lenses facilitated easier adjustment and alignment in the optical path. The incident angles were set at 15° for beam IN1 and 20° for beam IN2. The generated superfluorescence signals were collected by a 5 cm focal length NBK-7 convex lens, then dispersed by a spectrograph (Shamrock, Andor), and detected by a charge-coupled device (Newton idus, Andor). NOR and NAND gates were realized by employing inverse polarizers before the superlattices. Inverse polarizers, such as a λ /2 waveplate, invert the polarization of the light, serving as a NOT gate. For example, s-polarized light representing [1] becomes [0] after passing through the inverse polarizer. Combining a NOT gate with AND/OR gates created NAND/NOR gates. All measurements were performed at room temperature in ambient air. Declarations Data and materials availability: The data supporting the findings of this study are available in the main text or the supplementary materials. Raw data generated during this study are available from the corresponding author upon reasonable request. Acknowledgments We thank M.J. Li, Q. Wei, M.J. Feng, and Y. Hu for valuable discussions about the experiments. This work was supported by a Sloan Research Fellowship from the Alfred P. Sloan Foundation, a Lattimer Faculty Research Fellowship from the University of California San Diego, and a National Science Foundation award (NSF DMR 1848215). Author contributions R.T.W., D.Y.L., and S.X. conceived and designed the project. R.T.W., D.Y.L., and K.X.L. fabricated and characterized the halide perovskite superlattice. R.T.W., J.J.Y., B.H., and D.Y.L. prepared and analyzed samples by transmission electron microscopy. 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A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. The Journal of Chemical Physics 132 (2010). https://doi.org/10.1063/1.3382344 Sander, T. & Kresse, G. Macroscopic dielectric function within time-dependent density functional theory—Real time evolution versus the Casida approach. The Journal of Chemical Physics 146 , 064110 (2017). https://doi.org/10.1063/1.4975193 Supplementary Material Supplementary material not available with this version Additional Declarations The authors declare no competing interests. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7162326","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":487728549,"identity":"8b403eaf-3b31-4b67-807b-267d70bea48c","order_by":0,"name":"Ruotao Wang","email":"","orcid":"","institution":"UC San Diego","correspondingAuthor":false,"prefix":"","firstName":"Ruotao","middleName":"","lastName":"Wang","suffix":""},{"id":487728550,"identity":"50d197a2-5966-439a-8699-99a361c9a0da","order_by":1,"name":"Yixuan Dou","email":"","orcid":"","institution":"Virginia Polytechnic Institute and State 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Arrows represent photo-excited electron-hole pairs of a dipole and \u003cem\u003eΨ\u003c/em\u003e symbolizes the wave function. \u003cstrong\u003eb\u003c/strong\u003e, Cryogenic transmission electron microscopy images of the PEA\u003csub\u003e2\u003c/sub\u003eMAPb\u003csub\u003e2\u003c/sub\u003eI\u003csub\u003e7\u003c/sub\u003e superlattice. The \u003cem\u003exy\u003c/em\u003e plane (top) consists of homogeneous Pb-I slabs, whereas the \u003cem\u003exz\u003c/em\u003e plane (bottom) shows periodic multi-quantum wells. PEA\u003csup\u003e+\u003c/sup\u003e spacers are invisible under high-energy electron beam diffraction. The insets are fast Fourier transform patterns from the corresponding planes. Scale bars = 2.5 nm. \u003cstrong\u003ec\u003c/strong\u003e, Schematics of dipoles in the \u003cem\u003exy\u003c/em\u003e plane with high degrees of freedom (top) and those confined along the \u003cem\u003ez\u003c/em\u003e-direction by cavities (bottom). \u003cstrong\u003ed\u003c/strong\u003e, Calculated photo-excited dipole density (per unit cell) under polarized excitations. Polarization aligned in the \u003cem\u003ez\u003c/em\u003e-direction is defined as s-polarized, whereas that aligned in the \u003cem\u003ex\u003c/em\u003e-direction is p-polarized.\u003cstrong\u003e e\u003c/strong\u003e, Valence band structures (left) and orbital-projected density of states of I \u003cem\u003ep\u003c/em\u003e\u003csub\u003e\u003cem\u003exy\u003c/em\u003e\u003c/sub\u003e and I \u003cem\u003ep\u003c/em\u003e\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003e orbitals (right) for the PEA\u003csub\u003e2\u003c/sub\u003eMAPb\u003csub\u003e2\u003c/sub\u003eI\u003csub\u003e7\u003c/sub\u003e superlattice.\u003c/p\u003e","description":"","filename":"1.png","url":"https://assets-eu.researchsquare.com/files/rs-7162326/v1/f957a9f0b8c72eeb98c5f7e9.png"},{"id":87602906,"identity":"14b788a3-4174-4d52-a7e3-686cd773954a","added_by":"auto","created_at":"2025-07-25 17:14:51","extension":"png","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":243101,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eTransient absorption studies of giant dipole formation.\u003c/strong\u003e \u003cstrong\u003ea\u003c/strong\u003e, Transient absorption mappings under increasing s-polarized excitation fluences. ΔA/A represents relative absorption from pump-probe measurements. The absorptionbands are enclosed by dashed lines. The ground-state absorption (GSA) at 600~682 nm reflects the intrinsic bandgap of the superlattice. The new coherent-state absorption (CSA) at717~734 nm appears at stronger excitation fluences. \u003cstrong\u003eb\u003c/strong\u003e,Extracted transient absorption spectra with varying probe times for the quantitative analysis of absorptionintensities. \u003cstrong\u003ec\u003c/strong\u003e,Carrier dynamics of random dipoles (blue) and a giant dipole (red). \u003cstrong\u003ed\u003c/strong\u003e, Extracted giant dipole carrier dynamics at the CSA peak wavelength of 722 nm from transient absorption mappings with increasing excitation fluence. Clear delay stages (enclosed by a dashed box) are observed at low excitation fluence. Detailed features of the delays can be found in Supplementary Fig. 21. \u003cstrong\u003ee\u003c/strong\u003e, Extracted delay timefor the formation (top) and decay time (bottom) of a giant dipole as a function of excitation fluence. Error bars are standard deviations of the mean (n = 3).\u003c/p\u003e","description":"","filename":"2.png","url":"https://assets-eu.researchsquare.com/files/rs-7162326/v1/618bba75f07a6f18e427c5fb.png"},{"id":87602304,"identity":"c686b9cf-9784-4b11-85cb-8e061f040f7c","added_by":"auto","created_at":"2025-07-25 17:06:52","extension":"png","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":333161,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSuperfluorescence characteristics\u003c/strong\u003e.\u003cstrong\u003e a\u003c/strong\u003e, Streak camera images of emissions under increasing s-polarized excitation fluences. Distinct oscillations are labeled. \u003cstrong\u003eb\u003c/strong\u003e, Extracted emission traces at 705 nm (left) and 720 nm (right) from the streak camera images. Inset on the right shows superlinear growth in superfluorescence peak intensity \u003cem\u003eI\u003c/em\u003e\u003csub\u003eP\u003c/sub\u003e as the excitation fluence \u003cem\u003eP\u003c/em\u003e increases, following power-law dependence. \u003cem\u003eI\u003c/em\u003e\u003csub\u003eP\u003c/sub\u003e ~ \u003cem\u003eP\u003c/em\u003e\u003csup\u003eα\u003c/sup\u003e, where \u003cem\u003eα\u003c/em\u003e is the increase factor (1.83 ± 0.14), consistent with the theoretically predicted\u003csup\u003e5\u003c/sup\u003e \u003cem\u003eα\u003c/em\u003e = 2. \u003cstrong\u003ec\u003c/strong\u003e, Excitation-power-dependent emission spectra. Inset shows normalized emission intensities as a function of polarization angle. \u003cstrong\u003ed\u003c/strong\u003e, Integrated superfluorescence intensities (red) and full width at half maximum (FWHM, gray) as a function of the excitation fluence. Three regimes can be observed: (I) fluorescence emission, (II) intense superfluorescence emission, and (III) superfluorescence saturation. FWHM is absent in region I due to the absence of superfluorescence at low excitation fluences. Error bars are standard deviations of the mean (n = 3).\u003c/p\u003e","description":"","filename":"3.png","url":"https://assets-eu.researchsquare.com/files/rs-7162326/v1/03741a7fdad61b48bb993575.png"},{"id":87602299,"identity":"99d1a580-44b9-445b-b673-c1e663d5d1d9","added_by":"auto","created_at":"2025-07-25 17:06:51","extension":"png","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":228096,"visible":true,"origin":"","legend":"\u003cp\u003e\u003cstrong\u003eSuperfluorescence-inspired\u003c/strong\u003e \u003cstrong\u003eoptical transistors\u003c/strong\u003e. \u003cstrong\u003ea\u003c/strong\u003e, Schematic of the working principle for an optical transistor based on superfluorescence. Two excitation beams (IN1 and IN2) in the same incident plane of the superlattice serve as the input, and the superfluorescence is the output. The s/p-polarized excitation (aligns with the \u003cem\u003ez\u003c/em\u003e/\u003cem\u003ex\u003c/em\u003e-direction, respectively) represents the binary input, while superfluorescence on/off corresponds to the [1]/[0] output. \u003cstrong\u003eb\u003c/strong\u003e, Emission intensity mapping at 720 nm for different IN1 and IN2 fluences. Superfluorescence occurs once the sum of IN1 and IN2 surpasses the superfluorescence threshold (black dashed line). The right panels show the situation when IN1 or IN2 is fixed, and the emission transitions to superfluorescence as IN2 or IN1 increases. \u003cstrong\u003ec\u003c/strong\u003e, Superfluorescence (SF) enables binary state distinction in optical transistors. ‘S’ and ‘P’ represent s/p-polarized excitation at high fluence levels, whereas ‘½S’ and ‘½P’ represent the corresponding low fluence levels. Logic gates OR/NOR (left) and AND/NAND (right) are enabled by controlling the polarization and fluence of the input. \u003cstrong\u003ed\u003c/strong\u003e, Stability of superfluorescence intensity (red) and wavelength (gray) of the optical transistors (left). The data are measured at 1 Hz for 500 h continuously, demonstrating the stability of the optical transistor. Emission spectra of the initial state (solid) and after 1.8 M cycles of operation (dashed) of the optical transistor (right). The slight decrease in superfluorescence intensity after cycling probably reflects the chemical instability of moisture-sensitive methylamine in the superlattice. Additionally, intense laser excitations generate significant heat, causing iodine to gradually sublimate and methylamine to degrade at high temperatures\u003csup\u003e39\u003c/sup\u003e.\u003cbr\u003e\n\u003c/p\u003e","description":"","filename":"4.png","url":"https://assets-eu.researchsquare.com/files/rs-7162326/v1/0ae98407733dedf46fd7101f.png"},{"id":87602907,"identity":"5355f405-68e1-4def-812f-d5e622d63650","added_by":"auto","created_at":"2025-07-25 17:14:56","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2204428,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7162326/v1/0ff46bc2-f620-4364-a553-103e40f99d48.pdf"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003e\u003cstrong\u003eGiant dipoles and superfluorescence in perovskite superlattices for optical transistors under ambient conditions\u003c/strong\u003e\u003c/p\u003e","fulltext":[{"header":"Main Text","content":"\u003cp\u003eDipoles consisting of photo-excited electron-hole pairs can interact to form a coherent giant dipole\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e1\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e, wherein the wave functions of individual dipoles share spatially and temporally synchronized phases\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ea). The formation of a giant dipole requires a sufficiently large and closely packed dipole population\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e4\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e, ensuring overlapping electromagnetic fields that increase the likelihood of interactions and thus facilitate the transition of many individual dipoles to a coherent collective state\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e. However, quantum fluctuations disrupt such interactions, especially fluctuations induced by dipole motions such as random phase variations, random emission events, and disturbances in surrounding electromagnetic fields\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e7\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e8\u003c/span\u003e\u003c/sup\u003e. Therefore, the formation of giant dipoles typically requires conditions such as low temperatures or strong magnetic fields to confine or align the dipoles, enhancing their interactions\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e9\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e10\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eHere we report the first observation of a giant dipole under ambient conditions. The multi-quantum wells in the halide perovskite superlattice create natural cavities that confine dipoles, reducing quantum fluctuations, enabling effective interactions among dipoles, and facilitating giant dipole formation\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e11\u003c/span\u003e\u003c/sup\u003e. We also describe the formation dynamics of giant dipoles through coherent-state absorption (CSA). The collective recombination of carriers within the giant dipole results in superfluorescence, characterized by Burnham-Chiao ringing. We exploited the polarization-dependent photo-excitation required for giant dipole formation to build an optical transistor. We found that the epitaxially grown superlattice ensured the long-term stability of both the material and device under ambient conditions.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAnisotropic structural and electronic properties of the superlattice\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eWe chose PEA\u003csub\u003e2\u003c/sub\u003eMAPb\u003csub\u003e2\u003c/sub\u003eI\u003csub\u003e7\u003c/sub\u003e-based (PEA\u0026thinsp;=\u0026thinsp;phenethylamine; MA\u0026thinsp;=\u0026thinsp;methylamine) quasi-two-dimensional perovskite as our model because PEA has better moisture resistance than other organic spacers and Pb is more stable than Sn in air\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003e. The PEA\u003csub\u003e2\u003c/sub\u003eMAPb\u003csub\u003e2\u003c/sub\u003eI\u003csub\u003e7\u003c/sub\u003e superlattice was grown epitaxially on a single-crystal MAPbBr\u003csub\u003e3\u003c/sub\u003e substrate (Supplementary Figs.\u0026nbsp;1\u0026ndash;4 and Supplementary Note 1). Bonding selectivity between growth precursors and the substrate leads to vertically aligned multi-quantum wells\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e13\u003c/span\u003e\u003c/sup\u003e. Cryogenic transmission electron microscopy images revealed homogeneous Pb-I slabs in the \u003cem\u003exy\u003c/em\u003e plane and periodic Pb-I slabs separated by PEA spacers in the \u003cem\u003exz\u003c/em\u003e plane (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003eb and Supplementary Fig.\u0026nbsp;5). Long-range order within the superlattice was evidenced by synchrotron-based grazing incidence wide-angle X-ray scattering, which revealed spot patterns with directional anisotropy\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e14\u003c/span\u003e\u003c/sup\u003e (Supplementary Figs.\u0026nbsp;6 and 7).\u003c/p\u003e\n\u003cp\u003eThe homogeneous Pb-I slabs in the \u003cem\u003exy\u003c/em\u003e plane offer dipoles a high degree of freedom\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e15\u003c/span\u003e\u003c/sup\u003e (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ec, top), while the multi-quantum wells confine dipole motion along the \u003cem\u003ez\u003c/em\u003e-direction\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e, substantially reducing quantum fluctuations and promoting giant dipole formation (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ec, bottom and Supplementary Note 2). The cavity qualities (e.g., continuity, uniformity, and purity) can be optimized by tuning the superlattice growth parameters\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e13\u003c/span\u003e\u003c/sup\u003e (Supplementary Figs.\u0026nbsp;8 and 9). Additionally, the thin organic spacer enables interlayer dipole coupling between adjacent inorganic layers, further accelerating giant dipole formation\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e17\u003c/span\u003e\u003c/sup\u003e (Supplementary Note 2).\u003c/p\u003e\n\u003cp\u003e\u003cem\u003eAb initio\u003c/em\u003e calculations revealed that the perovskite superlattice had anisotropic reflectivity, absorbance, and thus efficiency of photo-excitation, resulting in an excitation\u0026ndash;polarization-dependent dipole population\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e18\u003c/span\u003e\u003c/sup\u003e (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ed, Supplementary Fig.\u0026nbsp;10, and Supplementary Note 3). Under s-polarized excitation along the \u003cem\u003ez\u003c/em\u003e-direction, the perovskite superlattice reflected less and absorbed more light, generating a larger dipole population compared to p-polarized excitation at the same fluence in the \u003cem\u003ex\u003c/em\u003e-direction (Supplementary Fig.\u0026nbsp;10). Furthermore, the perovskite superlattice showed dipole-population-dependent electronic behavior\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e. I \u003cem\u003ep\u003c/em\u003e\u003csub\u003e\u003cem\u003exy\u003c/em\u003e\u003c/sub\u003e orbitals were dominant at the valence band maximum, whereas deeper valance states (from ~\u0026thinsp;0.4 eV below the valence band maximum) were dominated by I \u003cem\u003ep\u003c/em\u003e\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003e orbitals (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ee). This variation in orbital occupation implies that larger photo-excited carrier populations change electron-hole occupancy in different anisotropic orbitals\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e18\u003c/span\u003e\u003c/sup\u003e. In small dipole populations, holes were mostly found at the valence band maximum of the I \u003cem\u003ep\u003c/em\u003e\u003csub\u003e\u003cem\u003exy\u003c/em\u003e\u003c/sub\u003e orbitals, whereas electrons were found at the conduction band minimum of the Pb \u003cem\u003ep\u003c/em\u003e\u003csub\u003e\u003cem\u003exy\u003c/em\u003e\u003c/sub\u003e orbitals (Supplementary Fig.\u0026nbsp;11). This indicated that most dipole movements were in the \u003cem\u003exy\u003c/em\u003e plane with a high degree of freedom\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e (Supplementary Fig.\u0026nbsp;12), resulting in large quantum fluctuations and thus no giant dipole formation. In contrast, in large dipole populations, electrons were excited from deeper valence states to higher conduction states. Although the conduction band was dominated by the same Pb \u003cem\u003ep\u003c/em\u003e\u003csub\u003e\u003cem\u003exy\u003c/em\u003e\u003c/sub\u003e orbitals, the I \u003cem\u003ep\u003c/em\u003e\u003csub\u003e\u003cem\u003ez\u003c/em\u003e\u003c/sub\u003e orbital became dominant in the deeper valence band (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e1\u003c/span\u003ee and Supplementary Figs.\u0026nbsp;13 and 14). Consequently, dipole movements were primarily distributed along the \u003cem\u003ez\u003c/em\u003e-direction (Supplementary Fig.\u0026nbsp;13), confined by the superlattice cavities\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e13\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e21\u003c/span\u003e\u003c/sup\u003e, thus reducing quantum fluctuations and facilitating giant dipole formation\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e18\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e22\u003c/span\u003e\u003c/sup\u003e (Supplementary Fig.\u0026nbsp;15).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFormation dynamics of the giant dipole\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eAs individual dipoles synchronize into a giant dipole, their band structure undergoes renormalization, transitioning from the original random states to a new coherent state\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e5\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e (Supplementary Figs.\u0026nbsp;16 and 17). To investigate this process, we applied pump-probe transient absorption mapping, which achieves high temporal and energetic resolution (Supplementary Fig.\u0026nbsp;18). All measurements were conducted under ambient conditions. Under p-polarized light, only ground-state absorption (GSA) was observed, even at high fluences (Supplementary Fig.\u0026nbsp;19 and Supplementary Note 4). In contrast, under s-polarized light, at a low fluence of 3 \u0026micro;J\u0026sdot;cm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e, the dipole population was insufficient to establish strong dipole\u0026ndash;dipole interactions, achieving only a GSA of 600\u0026thinsp;~\u0026thinsp;682 nm, corresponding to the original bandgap of the superlattice (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ea). As the fluence increased to 16 \u0026micro;J\u0026sdot;cm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e, the dipole population enlarged, enhancing the intensity of the GSA as expected. Additionally, a new absorption band appeared at 717\u0026thinsp;~\u0026thinsp;734 nm (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ea), indicating CSA, a new quantum state of the giant dipole\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e (Supplementary Fig.\u0026nbsp;20). CSA has a longer wavelength than GSA due to the lower energy of the giant dipole relative to random dipoles, and is narrower in bandwidth, reflecting the synchronized coherent state of the giant dipole\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e (Supplementary Note 4). This was the first evidence for the CSA of giant dipoles in any material. When the fluence was increased to 43 \u0026micro;J\u0026sdot;cm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e, the CSA became more intense and appeared as a distinct stripe in the mapping (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ea).\u003c/p\u003e\n\u003cp\u003eThe energy transfer between random dipoles and the giant dipole was evidenced by the evolution of band intensities in the transient absorption spectra (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003eb). As the excitation fluence increased, so did the GSA, indicating that more electrons were excited from the ground state (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003eb). The GSA declined once the CSA appeared, suggesting that the formation of the giant dipole led to rapid electron decay, replenishing the ground state (Supplementary Fig.\u0026nbsp;20). The giant dipole exhibited a decay of ~\u0026thinsp;20 ps due to strong synchronization (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ec), as opposed to tens of nanoseconds for random dipoles\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e23\u003c/span\u003e\u003c/sup\u003e. Meanwhile, the CSA intensity increased, reflecting the transition of additional excited electrons into the giant dipole state. This behavior suggested that energy carried by excited electrons was transferred from the GSA to the CSA (Supplementary Fig.\u0026nbsp;20 and Supplementary Note 4).\u003c/p\u003e\n\u003cp\u003eIt took time to synchronize the random dipoles (Supplementary Fig.\u0026nbsp;16), which introduced a characteristic delay (~\u0026thinsp;4 ps at 7 \u0026micro;J\u0026sdot;cm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e excitation fluence) following photo-excitation\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e2\u003c/span\u003e\u003c/sup\u003e (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ed, Supplementary Fig.\u0026nbsp;21, and Supplementary Note 5). Compared to the tens of picoseconds of delay in polycrystalline perovskites\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e, the ultrashort delay in the superlattice makes it less likely that coherence will dephase due to quantum fluctuations, facilitating giant dipole formation\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e4\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e. At high excitation fluence (43 \u0026micro;J\u0026sdot;cm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e), the delay was reduced further to less than 1 ps, indicating that a larger dipole population expedites the synchronization\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ee, top). This is because larger dipole populations enhance dipole interactions and generate a stronger collective electromagnetic field, promoting synchronization\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e4\u003c/span\u003e\u003c/sup\u003e. For the same reason, the decay time of the giant dipole was also reduced\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e25\u003c/span\u003e\u003c/sup\u003e (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ee, bottom).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eSuperfluorescence from the giant dipole\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eSuperfluorescence, a synchronized pulsed emission, is a distinctive feature of the giant dipole\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e4\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e26\u003c/span\u003e\u003c/sup\u003e. We used a streak camera under ambient conditions to capture its ultrafast characteristics\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e4\u003c/span\u003e\u003c/sup\u003e. Only fluorescence was detected under p-polarized excitation as expected, with peak intensity increasing linearly with excitation fluence\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e22\u003c/span\u003e\u003c/sup\u003e (Supplementary Fig.\u0026nbsp;22). Under s-polarized excitation at low excitation fluence, only fluorescence was observed at ~\u0026thinsp;705 nm, associated with intensity decay on a nanosecond scale (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003ea and \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003eb). At higher excitation fluences (\u0026gt;\u0026thinsp;16 \u0026micro;J\u0026sdot;cm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e), we observed superfluorescence emission. This threshold was markedly lower than previously reported (Supplementary Table\u0026nbsp;1). The superfluorescence showed differences in intensity, wavelength, and decay behavior (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003ea and \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003eb and Supplementary Fig.\u0026nbsp;23). Specifically, we detected stronger superfluorescence intensities at ~\u0026thinsp;720 nm, corresponding to the giant dipole observed during transient absorption (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ea and \u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003eb). The peak intensities followed the characteristic power-law dependence of superfluorescence\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e4\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003eb, right inset). The intensity decayed on a picosecond scale, three orders of magnitude faster than fluorescence, reflecting the collective emission of the giant dipole\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e26\u003c/span\u003e\u003c/sup\u003e. This rapid decay, similar to the giant dipole behavior during transient absorption (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e2\u003c/span\u003ee), was even faster at higher excitation fluences\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e4\u003c/span\u003e\u003c/sup\u003e (Supplementary Fig.\u0026nbsp;24). Additionally, the superfluorescence exhibited distinct decay oscillations (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003ea and \u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003eb and Supplementary Fig.\u0026nbsp;23). As the superfluorescence propagates, it interacts coherently and exchanges energy periodically with the giant dipole\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e. This process manifests as distinct intensity oscillations, known as Burnham-Chiao ringing, an intrinsic property of superfluorescence\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e27\u003c/span\u003e\u003c/sup\u003e (Supplementary Note 5).\u003c/p\u003e\n\u003cp\u003eSuperfluorescence was always accompanied by fluorescence (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003ec), indicating remnant random dipoles even after giant dipole formation\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e4\u003c/span\u003e\u003c/sup\u003e. The Lorentzian-fitted 720-nm peak suggested a superfluorescence resonance mechanism, whereas the Gaussian-fitted 705-nm peak corresponded to fluorescence\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e4\u003c/span\u003e\u003c/sup\u003e (Supplementary Fig.\u0026nbsp;25). As the excitation fluence increased, we observed redshifts in the superfluorescence peak from ~\u0026thinsp;718 to ~\u0026thinsp;720 nm and in the fluorescence peak from ~\u0026thinsp;706 to ~\u0026thinsp;708 nm (Supplementary Fig.\u0026nbsp;26), probably due to energy dissipation via lattice vibrations at elevated temperatures under high excitation fluences\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e28\u003c/span\u003e\u003c/sup\u003e. The normalized superfluorescence intensity demonstrated a 180\u0026deg; periodicity in its emission polarization angle because it originated from the giant dipole\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e16\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e29\u003c/span\u003e\u003c/sup\u003e (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003ec, inset and Supplementary Note 5), whereas the fluorescence remained isotropic because it originated from random dipoles.\u003c/p\u003e\n\u003cp\u003eWe also studied the intensity and full width at half maximum (FWHM) of superfluorescence as a function of s-polarized excitation fluence and identified three different regimes (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003ed). First, at fluences below 12 \u0026micro;J\u0026sdot;cm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e, we detected only background fluorescence due to the small dipole population. Second, at fluences above 12 \u0026micro;J\u0026sdot;cm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e, we detected a superfluorescence peak with an FWHM of ~\u0026thinsp;33 meV. As the fluence increased, the superfluorescence became more intense in a superlinear manner\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e30\u003c/span\u003e\u003c/sup\u003e, suggesting an enhanced transition of random dipoles to the coherent state\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e31\u003c/span\u003e\u003c/sup\u003e due to expedited dipole synchronization in larger dipole populations\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e. Concurrently, the FWHM of the superfluorescence declined to 22 meV as more dipoles transitioned into the coherent state, resulting in more coherent emission\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e4\u003c/span\u003e\u003c/sup\u003e. Finally, at fluences exceeding 45 \u0026micro;J\u0026sdot;cm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e, both the superfluorescence intensity and FWHM formed a plateau, indicating the gradual depletion of electrons at corresponding valence band levels.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eOptical transistors\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eArtificial cavities with complicated fabrications are typically required to construct optical transistors (Supplementary Note 6) but the natural cavities in the perovskite superlattice address this issue\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e32\u003c/span\u003e\u003c/sup\u003e. The power-law-dependent evolution of superfluorescence intensity ensures that only signals exceeding a certain threshold are amplified\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e33\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e34\u003c/span\u003e\u003c/sup\u003e, similar to the transfer curve of electrical transistors\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e32\u003c/span\u003e\u003c/sup\u003e. Therefore, we were able to demonstrate an optical transistor based on superfluorescence for the first time.\u003c/p\u003e\n\u003cp\u003eWe used two s-polarized lasers with tunable power, aligned in the same incident \u003cem\u003exy\u003c/em\u003e plane, to excite the superlattice (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ea). With one beam (IN1, similar to the gate voltage in electrical transistors) maintaining a certain power, the other beam (IN2, similar to the source-drain voltage in electrical transistors) modulates the superfluorescence output across the three emission regimes (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e3\u003c/span\u003ed), and vice versa, demonstrating collaborative regulation of superfluorescence\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e33\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e35\u003c/span\u003e\u003c/sup\u003e (Fig.\u0026nbsp;\u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003eb and Supplementary Fig.\u0026nbsp;27). The substantial differences in wavelength, intensity, and decay time between the superfluorescence output and excitation input ensure their isolation\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e4\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e30\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e32\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eWe explored the potential to use this optical transistor as a logic gate\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e36\u003c/span\u003e\u003c/sup\u003e, with polarization serving as the binary states of logic input and fluence controlling the type of logic gates (Supplementary Note 6). Specifically, the transistor acts as an OR gate at high levels of fluence, while the s-polarization of either IN1 or IN2 alone is sufficient to trigger superfluorescence (Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ec). In contrast, the transistor acts as an AND gate at low levels of fluence, requiring both IN1 and IN2 to be s-polarized to generate superfluorescence. NOR and NAND gates can be realized by adding inverse polarizers before the superlattices\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e37\u003c/span\u003e\u003c/sup\u003e. The inherent binary nature of excitation polarization remains reliable during operation, thus mitigating the loss-dependent issues of logic operations commonly encountered in other optical transistors\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e33\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e38\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003eGiven the strong ionic bonds between the substrate and epitaxial superlattice, the material structure remained intact even under continuous exposure to high-intensity (e.g., 40 \u0026micro;J\u0026sdot;cm\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e) laser excitation\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e39\u003c/span\u003e\u003c/sup\u003e. The superfluorescence also remained stable under ambient conditions without any encapsulation (Supplementary Fig. 28). Consequently, the logic gates were stable at a high extinction ratio (i.e., the ratio between the [1] and [0] levels) after at least 1.8 million test cycles (Fig. \u003cspan class=\"InternalRef\"\u003e4\u003c/span\u003ed and Supplementary Note 6).\u003c/p\u003e"},{"header":"Methods","content":"\u003cp\u003e\u003cstrong\u003eMaterials and solvents\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eLead (II) bromide (PbBr\u003csub\u003e2\u003c/sub\u003e, 98%+) was purchased from Thermo Scientific Chemicals. Lead (II) oxide (PbO, 99.9%) was purchased from Alfa Aesar. Methylammonium bromide (MABr, 99.99%), methylammonium iodide (MAI, 99.99%), and phenethylammonium iodide (PEAI, 99.99%) were purchased from Greatcell Solar Materials. Gamma butyrolactone (GBL, 98%) was purchased from Transene Company. Methanol (MeOH, 99.8%), isopropanol (IPA, 99.5%), propylene carbonate (PC, 99%), acetone (99.5%), dimethylformamide (DMF, 99.8%), hydriodic acid (HI, 57 wt.% in H\u003csub\u003e2\u003c/sub\u003eO, 99.95%), and hypophosphorous acid (H\u003csub\u003e3\u003c/sub\u003ePO\u003csub\u003e2\u003c/sub\u003e, 50 wt.% in H\u003csub\u003e2\u003c/sub\u003eO) were purchased from Sigma-Aldrich. All reagents were used as received without further purification.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eSynthesis of PEA\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003eMAPb\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e2\u003c/strong\u003e\u003c/sub\u003e\u003cstrong\u003eI\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e7\u003c/strong\u003e\u003c/sub\u003e \u003cstrong\u003esingle-crystal flakes\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003e7.4 mmol of PbO was added to 10 ml of pre-heated HI (57 wt.% in H\u003csub\u003e2\u003c/sub\u003eO) at 180 ℃, mixed with 1 ml of H\u003csub\u003e3\u003c/sub\u003ePO\u003csub\u003e2\u003c/sub\u003e (50 wt.% in H\u003csub\u003e2\u003c/sub\u003eO), and stirred until the precursor solution became transparent yellow. A solution of MAI (4.2 mmol)/PEAI (4.2 mmol) in MeOH was then injected into the precursor solution and stirred for 2 min. Subsequently, the beaker was transferred into a vacuum chamber for 15 s to remove dissolved air, before being returned to ambient atmosphere for crystallization. The flakes nucleated, grew, and filled the beaker within ~\u0026thinsp;2 h. After precipitation, the crystal flakes were filtered and sequentially washed with IPA, PC, and acetone using a vacuum funnel, followed by drying in a vacuum\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003ePreparation of bulk MAPbBr\u003c/strong\u003e\u003csub\u003e\u003cstrong\u003e3\u003c/strong\u003e\u003c/sub\u003e \u003cstrong\u003esingle crystals\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eBulk MAPbBr\u003csub\u003e3\u003c/sub\u003e single crystals were grown by slow solution evaporation\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e39\u003c/span\u003e\u003c/sup\u003e. MABr and PbBr\u003csub\u003e2\u003c/sub\u003e were dissolved in a 1:1 stoichiometric ratio in DMF at a concentration of 1.67 M. The solution was kept at room temperature to allow the solvent to evaporate slowly for growing MAPbBr\u003csub\u003e3\u003c/sub\u003e single crystals. The as-grown single crystals were collected and used as substrates for superlattice growth without any further treatment.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eFabrication of perovskite superlattices\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe PEA\u003csub\u003e2\u003c/sub\u003eMAPb\u003csub\u003e2\u003c/sub\u003eI\u003csub\u003e7\u003c/sub\u003e single-crystal flakes were redissolved in GBL to prepare a 1 M growth solution. This growth solution was spin-coated onto the bulk MAPbBr\u003csub\u003e3\u003c/sub\u003e single crystal substrate at 4,000 revolutions per minute (r.p.m.) for 30 s. The coated substrate was then annealed at 180 ℃ for 2 min to form the superlattices.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAb\u003c/strong\u003e \u003cstrong\u003einitio calculations\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eFirst-principles density functional theory calculations\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e40\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e41\u003c/span\u003e\u003c/sup\u003e were performed using the Vienna \u003cem\u003eab initio\u003c/em\u003e Simulation Package\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e42\u003c/span\u003e,\u003cspan class=\"CitationRef\"\u003e43\u003c/span\u003e\u003c/sup\u003e. Projector-augmented wave potentials were employed with the generalized gradient approximation in the Perdew-Burke-Ernzerhof parametrizations for the exchange-correlation functional\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e44\u003c/span\u003e\u003c/sup\u003e. Van der Waals interactions were described using the DFT-D3 method of Grimme with a zero-damping function\u003csup\u003e\u003cspan class=\"CitationRef\"\u003e45\u003c/span\u003e\u003c/sup\u003e, properly describing the long-range dispersion interactions between the organic molecules in the hybrid materials. Based on convergence tests, a plane-wave basis set with a kinetic energy cutoff of 800 eV and a Brillouin zone grid of 5\u0026times;5\u0026times;2 \u0026Gamma;-centered k-points were employed. Relaxation was carried out until the energy differences were converged within 10\u003csup\u003e\u0026minus;\u0026thinsp;6\u003c/sup\u003e eV, with a Hellman-Feynman force convergence threshold of 10\u003csup\u003e\u0026minus;\u0026thinsp;2\u003c/sup\u003e eV/\u0026Aring;. Spin-orbit coupling was included throughout all electronic structures and optical properties calculations. To calculate the bandgap of the perovskite superlattices, hybrid functionals within the Heyd\u0026ndash;Scuseria\u0026ndash;Ernzerhof HSE06 formalism were used. On top of the HSE06 band structures, the excitonic effects are computed from time-dependent Hartree\u0026thinsp;\u0026minus;\u0026thinsp;Fock calculations using the Casida Eq. 4\u003csup\u003e6\u003c/sup\u003e with a total of 24 valence and 24 conduction bands.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eStructure and morphology characterizations\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eX-ray diffraction (XRD) was taken using an Anton Paar XRDynamic 500 diffractometers. Scanning electron microscopy images were captured using a Zeiss Sigma 500. Cryo-transmission electron microscope (cryo-TEM) samples were prepared with an FEI Scios DualBeam cryo-FIB/scanning electron microscope (cryo-FIB/SEM). Cryo-TEM images were acquired on a Thermofisher Talos F200X G2 cryo-S/TEM with a Gatan Elsa cryo-transfer holder. Cross-sectional electron energy loss spectroscopy mapping was performed using a Gatan Enfinium ER (977) spectrometer. Synchrotron-based grazing incidence wide-angle X-ray scattering was measured on beamline 7.3.3 at the Advanced Light Source, Lawrence Berkeley National Laboratory. The X-ray wavelength was 1.240 \u0026Aring;, with various grazing incident angles and scattering intensity was detected using a PILATUS 2M detector. The exposure time was 5 s per frame in single mode, with a total measurement time of 2 min. The images were sector-averaged using the Nika software package.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eUltrafast pump-probe measurements\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eReflection mode was used for transient absorption measurements because the superlattices were epitaxially grown on a thick, non-transparent single-crystal MAPbBr\u003csub\u003e3\u003c/sub\u003e substrate. Pump-probe absorption was measured using a Helios system from Ultrafast Systems (Supplementary Fig. 29). The excitation source was generated by an Astrella-F-1K femtosecond amplifier with an 800 nm, 1 kHz fundamental beam. This beam was directly applied to produce the probe beam by passing through a crystal for continuum generation in the Helios system. The 515 nm pump beam was produced by an optical parametric amplifier system from Coherent. The sample was positioned on a reflection sample holder, and the chopper-modulated pump light was directed onto the sample. The detector was triggered to record every probe pulse and calculate the reflection spectrum. From the chopper sync out, the Helios software determined the chopper state (pump-on or pump-off) for each measured probe spectrum, allowing for the calculation of the differential reflection spectrum by taking the difference between pump-on and pump-off states. All measurements were conducted at room temperature in ambient air.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eTime-resolved photoluminescence spectra\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe femtosecond laser used to excite the sample was generated by a regenerative amplifier (400 nm wavelength, 100 fs pulse width, and 1 kHz repetition, Coherent Legend) seeded by a Ti: sapphire oscillator (100 fs, 80 MHz, Coherent Vitesse) (Supplementary Fig.\u0026nbsp;30). The pump laser wavelength was controlled at 515 nm by an optical parametric amplifier. Emission from the sample was collected in a backscattered geometry with a pair of lenses and directed to a monochromator (Acton, Spectra Pro 2500i) coupled to a streak camera (Hamamatsu, ultimate temporal resolution of ~\u0026thinsp;1 ps). Superfluorescence peak intensities were extracted from the streak camera images. All measurements were performed at room temperature in ambient air.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003ePolarization-dependent emission spectra\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eA high-repetition-rate femtosecond laser system (Pharos, 100 kHz, Light Conversion) in a reflection geometry was used for the customized superfluorescence spectra measurement (Supplementary Fig. 31). The Pharos laser generated pulses with a center wavelength of 1030 nm and a pulse width of 160 fs, delivering a pulse energy of 100 \u0026micro;J. In this work, the 1030 nm pulses were directed through a beta barium borate crystal to generate a 515 nm second harmonic excitation beam. This excitation beam was then directed through a 515 nm \u003cem\u003e\u0026lambda;\u003c/em\u003e/2 waveplate to control polarization and a continuous neutral density filter to achieve tunable pulse energy. The beam was focused onto the sample surface using an NBK-7 lens with a 12.5 cm focal length. The incident angle was set at 15\u0026deg;. To prevent burning damage to the sample, a repetition rate of 100 Hz was used. The superfluorescence signals were dispersed by a spectrograph (Shamrock, Andor) and detected by a charge-coupled device (Newton idus, Andor). All measurements were performed at room temperature in ambient air.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eOptical transistors\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eA 1030 nm femtosecond pulse (Pharos, 100 kHz, Light Conversion) was filtered through an etalon (SLS optics) to create an up-conversion pulse with a narrow bandwidth of 4 cm\u003csup\u003e\u0026minus;\u0026thinsp;1\u003c/sup\u003e full width at half maximum (Supplementary Fig. 32). This pulse was then directed through a beta barium borate crystal to generate a 515 nm beam, referred to as IN1. Simultaneously, the reflection of the 1030 nm pulse from the etalon was directed through another beta barium borate crystal to generate a second 515 nm beam, referred to as IN2. Beam IN1 was focused onto the sample surface using a 10 cm focal length parabolic mirror, spatially overlapping with beam IN2, which was focused by a 12.5 cm focal length NBK-7 convex lens. The staggered distances between the lenses facilitated easier adjustment and alignment in the optical path. The incident angles were set at 15\u0026deg; for beam IN1 and 20\u0026deg; for beam IN2. The generated superfluorescence signals were collected by a 5 cm focal length NBK-7 convex lens, then dispersed by a spectrograph (Shamrock, Andor), and detected by a charge-coupled device (Newton idus, Andor). NOR and NAND gates were realized by employing inverse polarizers before the superlattices. Inverse polarizers, such as a \u003cem\u003e\u0026lambda;\u003c/em\u003e/2 waveplate, invert the polarization of the light, serving as a NOT gate. For example, s-polarized light representing [1] becomes [0] after passing through the inverse polarizer. Combining a NOT gate with AND/OR gates created NAND/NOR gates. All measurements were performed at room temperature in ambient air.\u003c/p\u003e"},{"header":"Declarations","content":"\u003cp\u003e\u003cstrong\u003eData and materials availability:\u003c/strong\u003e The data supporting the findings of this study are available in the main text or the supplementary materials. Raw data generated during this study are available from the corresponding author upon reasonable request.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAcknowledgments\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eWe thank M.J. Li, Q. Wei, M.J. Feng, and Y. Hu for valuable discussions about the experiments. This work was supported by a Sloan Research Fellowship from the Alfred P. Sloan Foundation, a Lattimer Faculty Research Fellowship from the University of California San Diego, and a National Science Foundation award (NSF DMR 1848215).\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eAuthor contributions\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eR.T.W., D.Y.L., and S.X. conceived and designed the project. R.T.W., D.Y.L., and K.X.L. fabricated and characterized the halide perovskite superlattice. R.T.W., J.J.Y., B.H., and D.Y.L. prepared and analyzed samples by transmission electron microscopy. B.P. was responsible for the \u003cem\u003eab initio\u003c/em\u003e calculations. X.F.W., H.X., and Z.F. contributed to the synchrotron-based grazing incidence wide-angle X-ray scattering and analysis. Y.X.D., L.Q., D.Y.L., R.T.W., and L.H.Z. contributed to the transient absorption mappings and analysis. Z.P.Z., G.C.X., R.T.W., D.Y.L., C.W.L., and P.X. contributed to the streak camera images and analysis. Y.C.J., W.X., R.T.W., and D.Y.L. contributed to the photoluminescence measurements and optical transistor. R.T.W., D.Y.L., Y.X.D., B.P., and S.X. wrote and revised the manuscript. All authors provided constructive discussions and valuable feedback on the manuscript.\u003c/p\u003e\n\u003cp\u003e\u003cstrong\u003eCompeting interests\u003c/strong\u003e\u003c/p\u003e\n\u003cp\u003eThe authors declare that they have no competing interests.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\n \u003cli\u003eGross, M. \u0026amp; Haroche, S. Superradiance: An essay on the theory of collective spontaneous emission. \u003cem\u003ePhysics Reports\u003c/em\u003e \u003cstrong\u003e93\u003c/strong\u003e, 301-396 (1982). https://doi.org/https://doi.org/10.1016/0370-1573(82)90102-8\u003c/li\u003e\n \u003cli\u003eDicke, R. H. 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Traditionally, the creation of giant dipoles has required extreme conditions, and their detailed behavior remains underexplored. Here, we report the first giant dipole formed under ambient conditions and investigate its ultrafast formation dynamics and energy transfer mechanisms for the first time. We used an epitaxial two-dimensional halide perovskite superlattice, which confines photo-excited carriers to enhance the formation of giant dipoles. We captured superfluorescence bursts from the giant dipole, exhibiting distinct Rabi oscillations. Additionally, we found that the superfluorescence is dependent on photo-excitation polarization, which inspired the design of an innovative optical transistor. These findings advance our understanding of giant dipoles and their role in quantum systems, offering new insights that will facilitate the development of high-precision quantum logic gates and novel optical devices.\u003c/p\u003e","manuscriptTitle":"Giant dipoles and superfluorescence in perovskite superlattices for optical transistors under ambient conditions","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2025-07-25 17:06:44","doi":"10.21203/rs.3.rs-7162326/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"fd9ff905-7cb4-43ab-b58d-fb4d1c864aad","owner":[],"postedDate":"July 25th, 2025","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":51782520,"name":"Photonics/optics"},{"id":51782521,"name":"Materials Engineering"}],"tags":[],"updatedAt":"2025-07-25T17:06:44+00:00","versionOfRecord":[],"versionCreatedAt":"2025-07-25 17:06:44","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-7162326","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-7162326","identity":"rs-7162326","version":["v1"]},"buildId":"8U1c8b4HqxoKbykW_rLl7","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}