Coherent population trapping and polarization fluctuations: The independent-modulator approximation for coherent-population-trapping line shapes

Abstract

In order to understand how stochastic processes enter and influence coherent atomic dynamics, we have studied the behavior of a \ensuremath{\Lambda} system under random polarization variations. Polarization, in addition to amplitude and phase, is a defining feature of a classical vector field. However, to date there has been little study of how quantum systems respond to temporal variations of polarization, even though this problem has practical implications. In our work, we generate a Bernoulli sequence of random polarization changes, and we then examine the average ${}^{87}$Rb coherent-population-trapping (CPT) line shape induced by this stochastic field. To quantitatively conceptualize our results, we have developed an independent-modulator approximation (IMA) theory for CPT line shapes induced by stochastic-polarization fields. The IMA theory is based on the idea that a power spectrum can be understood as a probability distribution of Fourier modulation frequencies. We compare the IMA theory with our experimental results, finding quite good agreement when the polarization correlation time is less than or equal to the CPT dephasing time, which is the regime of primary experimental and technological interest. The utility of the IMA theory lies in its intuitive nature, which we believe has merit for guiding experimentalists' general understanding of stochastic fields and quantum systems.