Transparency in two level systems using an optical frequency comb with sinusoidal phase modulation

Transparency in atoms has been conventionally realized in three and higher-level systems through interference of probability amplitudes for multiple pathways between two states. We generalize this mechanism for creating transparency to two-level systems by using a frequency comb, a sinusoidally modulated phase-locked pulse train, to create a manifold of Floquet states. The presence of strong-field effects and multiple harmonics require us to explicitly calculate the energy shifts and decay rates in the Floquet basis. A Floquet-Lindblad master equation is then derived and used to calculate the field correlation necessary to find the spectral absorption. We use linear response theory and the time averaged correlation function to define a quasi-steady state absorption spectrum over one cycle of the pulse train. To solve for the dynamics, the Van-Vleck high frequency expansion was used to derive the effective Floquet Liouvillian and micromotion operators in a rotated frame.

We observe large suppression in the absorption of radiation resonant with the transition for certain values of the pulse train and phase modulation parameters. The tunability of the spectral amplitude and phase of the sinusoidally modulated frequency comb gives us large control over the absorption spectrum and quasi-steady dynamics, even realizing the possibility of amplification of resonant light.