Coherent population trapping under periodic polarization modulation: Appearance of the CPT doublet

Abstract

In order to understand how stochastic processes might enter and influence coherent atomic dynamics, we have studied the behavior of a \ensuremath{\Lambda} system under periodic polarization modulation. Polarization, in addition to amplitude and phase, is a defining feature of a classical vector field. However, to date, there has been little study concerning the response of quantum systems to temporal variations in polarization, even though some lasers are known to exhibit stochastic polarization fluctuations. In our work, we square-wave modulate the polarization of a laser that induces coherent-population trapping (CPT) in ${}^{87}$Rb. At low-modulation frequencies, we find that the amplitude of the CPT resonance increases with modulation frequency because the polarization variations limit the number of atoms confined to the system's trapping state. Surprisingly, at higher-modulation frequencies, we find that the CPT resonance splits into a doublet. We have developed an analytical theory of CPT in the presence of polarization modulation that captures the primary features of our experimental findings and shows that the doublet is a consequence of ground-state coherence modulation in the \ensuremath{\Lambda} system. The present results lay a foundation for understanding how more complicated (i.e., stochastic) temporal variations in laser polarization could influence \ensuremath{\Lambda}-system dynamics.