Electric and Magnetic Coherences: Analysis in a Four-Level Atomic System under a Magneto-Shaped Field

In this work, we investigate the dispersion-absorption spectra in a left handed medium under various magnetic shaped pulses. The system is a multi-level atom, in which the levels are coherently controlled by a weak and a strong field. Additionally, the ground state is related to an intermediate transition via a magneto-shaped field.We analyze the four level atom while first by considering the magnetic field as a quotient of the double exponential wave form, a difference of Gaussian and then as a continuous wave form. This enables us to study the dynamics of the coherence in the system. therefore, in contrast with the classical scenario where the magnetic field is taken as a constant, we observe a clear influence of the shaped magnetic field on the dispersion-absorption of the probe. We get an enhancement of about 2.5 times in the positive dispersion while we obtain 8 times enhancement in the negative dispersion. Lastly, with a shaped magnetic field, the probe dispersion, which is positive for a positive detuning and negative for a negative detuning, abruptly changes in the opposite direction.