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Journal of Physics B Atomic Molecular and Optical Physics

CPT transients induced by rapid changes in laser polarization: validation of a semi-empirical model

Mao Huang, John G. Coffer, James C. Camparo

Published Jun 8, 2010• 7 citations
Publisher

Abstract

In ultraminiature atomic physics (UAP), where the goal is to perform low-power, 'chip-scale' precision spectroscopy, stochastic-field/atom interactions can play a primary role in defining the limits of sensitivity. Unfortunately, the transient responses of a quantum system to random changes in the amplitude, phase or polarization of a resonant field are not well understood, forming the basis of what has come to be known as the stochastic-field/atom interaction problem. As the first step in understanding the more complicated stochastic problem, the present work considers the response of a coherent-population-trapping (CPT) signal to a sudden, step-function change in laser polarization. We find that the transient behaviour depends on both the redistribution of atomic population among the atom's Zeeman sublevels and the regeneration of atomic coherence between these sublevels. Despite the complicated nature of the dynamics, we develop and experimentally validate a semi-empirical, reasonably intuitive model of the CPT transient and demonstrate that in the 'typical' CPT signal the polarization-induced transients are dominated by redistribution of atomic population among the Zeeman sublevels. Further, the amplitudes of the polarization-induced transients are relatively large and could potentially 'swamp' the CPT signals of interest for UAP.

DOI
10.1088/0953-4075/43/13/135001

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In ultraminiature atomic physics (UAP), where the goal is to perform low-power, 'chip-scale' precision spectroscopy, stochastic-field/atom interactions can play a primary role in defining the limits of sensitivity. Unfortunately, the transient responses of a quantum system to random changes in the amplitude, phase or polarization of a resonant field are not well understood, forming the basis of what has come to be known as the stochastic-field/atom interaction problem. As the first step in understanding the more complicated stochastic problem, the present work considers the response of a coherent-population-trapping (CPT) signal to a sudden, step-function change in laser polarization. We find that the transient behaviour depends on both the redistribution of atomic population among the atom's Zeeman sublevels and the regeneration of atomic coherence between these sublevels. Despite the complicated nature of the dynamics, we develop and experimentally validate a semi-empirical, reasonably intuitive model of the CPT transient and demonstrate that in the 'typical' CPT signal the polarization-induced transients are dominated by redistribution of atomic population among the Zeeman sublevels. Further, the amplitudes of the polarization-induced transients are relatively large and could potentially 'swamp' the CPT signals of interest for UAP.
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{}^{87}87Rb. 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.
In chip-scale atomic clocks based on coherent-population-trapping (CPT), the laser of choice is a VCSEL due to its low threshold current, very high quantum efficiency, and large dynamic bandwidth. A problem with these lasers, however, is that they suffer from polarization fluctuations, which could degrade CPT signal-to-noise ratios. In previous work we found that a rapid change in laser polarization led to a multi-exponential variation of the light intensity transmitted through a resonant Rb vapor. Here, we show that this is not a systematic effect, but is a result of atomic dynamics. Specifically, we show that the change in transmitted light intensity arises from both a change in the system's trapping state and a re-establishment of the atomic coherence that is at the heart of the CPT signal.
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{}^{87}87Rb 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.
SummaryCurrent compact atomic clock technologies rely on coherent population trapping (CPT), which employs a microwave resonance to stabilize a crystal oscillator. Standard CPT, while a simple and easy-to-implement optical preparation scheme in alkali metal atoms, suffers from low signal-to-noise ratios (SNR). The primary contributor to the low signal amplitude is the collection of atoms at the extreme ends of the Zeeman sublevels in the hyperfine levels of the alkali ground state, so-called “trap states.” Solutions to the trap-state problem have been reported previously, though the redistribution of atomic population into the CPT signal states with these methods has not yet been carefully examined. This work aims to provide an experimental basis to evaluate trap-state recovery schemes.
SummaryChip-scale atomic clocks (CSAC) are the products of a burgeoning field of miniature precise timing efforts in support of low-SWaP space-qualified timing sources. Most CSACs are based on the coherent population trapping (CPT) effect, which uses laser light to selectively pump atoms into dark states. Because of the multiple accessible and inaccessible hyperfine Zeeman states, many atoms don’t contribute to the signal leading to a low signal-to-noise ratio of the CPT resonance. In turn, clock stability is limited. While solutions to this problem have been studied previously, the examination of the redistribution of atoms through the novel pumping solutions has not been thoroughly studied. This work provides continued exploration of an experimental effort to evaluate Zeeman end-state recovery schemes.
The Coherent-Population-Trapping (CPT) vapor-cell atomic clock represents a clear break from previous vapor-cell clock technology. As such it has advantages that may result in significant frequency stability improvements. However, along with the technology's benefits come new effects that may limit the CPT clock's capabilities, and one such effect is laser polarization noise. Here, we present our first results looking at the response of a CPT signal to modulation of a laser's polarization. Our results show that the CPT clock signal undergoes a splitting when the polarization modulation is rapid, suggesting that various Fourier components of a field's stochastic polarization fluctuations will affect the CPT clock signal in qualitatively different ways.