Coherently coupled mechanical oscillators in the quantum regime

Abstract Coupled harmonic oscillators are ubiquitous in physics and play a prominent role in quantum science. They are a cornerstone of quantum mechanics and quantum field theory, where second quantization relies on harmonic oscillator operators to create and annihilate particles. Descriptions of quantum tunneling, beamsplitters, coupled potential wells, ``hopping terms'', decoherence, and many other phenomena rely on coupled harmonic oscillators. However, the ability to couple separate quantum harmonic oscillators directly, with coupling rates that substantially exceed decoherence rates, has remained elusive. Here, we realize high-fidelity coherent exchange of single motional quanta between harmonic oscillators -- in this case, spectrally separated harmonic modes of motion of a trapped ion crystal -- where the timing, strength, and phase of the coupling are controlled through an oscillating electric potential with suitable spatial variation. The coupling rate can be made much larger than the decoherence rates, enabling demonstrations of high-fidelity quantum state transfer, entanglement of motional modes, and Hong-Ou-Mandel-type interference. We also project a harmonic oscillator into its ground state by measurement and preserve that state during repetitions of the projective measurement, an important prerequisite for non-destructive syndrome measurement in continuous-variable quantum error correction. Controllable coupling between harmonic oscillators has potential applications in quantum information processing with continuous variables, quantum simulation, and precision measurements. It can also enable cooling and quantum logic spectroscopy involving motional modes of trapped ions that are not directly accessible.