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Physical Review A

Measurement of ground-state decoherence via interruption of coherent population trapping

Anil K. Patnaik, Paul S. Hsu, G. S. Agarwal, George R. Welch, Marlan O. Scully

Published Feb 6, 2007• 14 citations
Publisher

Abstract

We examine the role of ground-state coherence on the fluorescence from the excited state in a three-level $\ensuremath{\Lambda}$ system under continuous-wave excitation. When resonantly pumped, the fluorescence is strongly affected by any perturbation in the ground-state coherent population trapping. From our analytical results, we suggest how to use this strong dependence of fluorescence on the ground-state decays as a new method for the measurement of the ground-state decoherence rates. Our calculations should work well for a wide range of systems such as atomic vapors with a buffer gas, active dopants in solids, and quantum dots, etc. We present a proof of principle experiment using $^{87}\mathrm{Rb}$ vapor.

DOI
10.1103/physreva.75.023807

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We examine the role of ground-state coherence on the fluorescence from the excited state in a three-level \ensuremathΛ\ensuremath{\Lambda}\ensuremathΛ system under continuous-wave excitation. When resonantly pumped, the fluorescence is strongly affected by any perturbation in the ground-state coherent population trapping. From our analytical results, we suggest how to use this strong dependence of fluorescence on the ground-state decays as a new method for the measurement of the ground-state decoherence rates. Our calculations should work well for a wide range of systems such as atomic vapors with a buffer gas, active dopants in solids, and quantum dots, etc. We present a proof of principle experiment using 87Rb^{87}\mathrm{Rb}87Rb vapor.
Two-photon processes that involve different sublevels of the ground state of an atom, are highly sensitive to depopulation and decoherence within the ground state. For example, the spectral width of electromagnetically induced transparency resonances in a $\ensuremath{\Lambda}$-type system, are strongly affected by the ground-state depopulation and decoherence rates. We present a direct measurement of decay rates between hyperfine and Zeeman sublevels in the ground state of 87Rb^{87}\mathrm{Rb}87Rb vapor. Similar to the relaxation-in-the-dark technique, pumping lasers are used to prealign the atomic vapor in a well-defined quantum state. The free propagation of the atomic state is monitored using a Ramsey-like method. Coherence times in the range 1−−10ms1--10\phantom{\rule{0.3em}{0ex}}\mathrm{ms}1−−10ms were measured for room temperature atomic vapor. In the range of the experimental parameters used in this study, the dominant process inducing Zeeman decoherence is the spin-exchange collisions between rubidium atoms.
The resonance fluorescence spectrum of a Λ-system excited by two resonant light fields is calculated using a Markov analysis. Analytical formulas are derived in the strong-field limit within and beyond the rotating wave approximation. It is shown that the resonance fluorescence of the system does not vanish during coherent population trapping. Its spectrum consists of two multiplets which are similar to a triplet in the resonance fluorescence spectrum of a two-level atom and lie at the electronic transition frequencies, together with two triplets located at the frequencies of four-photon processes involving the optical excitation fields. The latter are fundamental in character and impose limits on the lower bound of the dephasing rate for the Raman resonance owing to the effect of radiative decay of the dipole transitions on the dynamics of the ground state. The effect of four-photon dephasing on the absorption spectrum of a Λ-system is analyzed and found to lead to a substantial reduction in the depth of a dip in the absorption spectrum which vanishes as the laser field strength is increased.
We analyze the properties of a pulsed coherent population trapping protocol that uses a controlled decay from the excited state in a Λ-level scheme. We study this problem analytically and numerically and find regimes where narrow transmission, absorption, or fluorescence spectral lines occur. We then look for optimal frequency measurements using these spectral features by computing the Allan deviation in the presence of ground state decoherence and show that the protocol is on a par with Ramsey-CPT. We discuss possible implementations with ensembles of alkali atoms and single ions and demonstrate that typical pulsed-CPT experiments that are realized on femto-second timescales can be implemented on micro-seconds timescales using this scheme.
The role played by a buffer gas in the ground-state superposition created in coherent-population-trapping experiments is investigated theoretically. The density matrix equations are solved on the basis of the coupled-noncoupled states. The velocity-changing collisions are examined in the limit of strong collisions. The relaxation rate for transfer of the ground-state superposition between atoms with different velocities is derived from a fit of available experimental results. \textcopyright{} 1996 The American Physical Society.
We discuss the phase-sensitive noise properties of fluorescence emitted by three-level atoms coherently excited by two laser fields, using both undressed and dressed uncoupled-state representations. The occurrence of steady-state squeezing is found to be highly sensitive to relaxation processes between the two-photon resonant levels. For purely radiative decay from the upper level, and no lower-state relaxation, the population is susceptible to coherent population trapping. Near two-photon resonance, the atom is optically pumped into a nonabsorbing (trapped) superposition state, which, although it reduces upper-level population, also leads to an interference cancellation of dipole moments and to suppression of squeezing. Lower-level relaxation unbalances this interference and restores the squeezing to some extent. Transient squeezing is also predicted in the time-dependent fluorescence.