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Physical Review A

Dark-state-based three-element vector model for the stimulated Raman interaction

M. S. Shahriar, Philip Hemmer, D. P. Katz, A. Lee, Mara Goff Prentiss

Published Mar 1, 1997• 66 citations
Publisher

Abstract

In this paper we develop a three-element vector model to describe the stimulated Raman interaction in a \ensuremath{\Lambda} system. This model is valid over the range of interaction energies for which the excited state follows the ground states adiabatically. We use the model to present simple physical interpretations of the generation of Raman-Ramsey fringes in a separated field excitation, the ac Stark shift in the Raman clock, the ultrahigh-resolution mapping of microwave phase using Raman probes, and the coherent transfer of population by adiabatic passage for atomic beam splitters. The expressions for observables are derived by inspection and agree quantitatively with published experimental results.

DOI
10.1103/physreva.55.2272

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In this paper we develop a three-element vector model to describe the stimulated Raman interaction in a \ensuremath{\Lambda} system. This model is valid over the range of interaction energies for which the excited state follows the ground states adiabatically. We use the model to present simple physical interpretations of the generation of Raman-Ramsey fringes in a separated field excitation, the ac Stark shift in the Raman clock, the ultrahigh-resolution mapping of microwave phase using Raman probes, and the coherent transfer of population by adiabatic passage for atomic beam splitters. The expressions for observables are derived by inspection and agree quantitatively with published experimental results.
We have measured the ac Stark effect in a two-zone stimulated Raman interaction in a sodium atomic beam. In addition, we have derived simple theoretical expressions for the ac Stark shift, based on a closed three-level system, in the Λ configuration, and have achieved qualitative agreement with the data. In particular, the magnitude and sense of the ac Stark shifts are found to depend on laser intensities as well as on the initial populations of the two low-lying levels of the Λ configuration. Specifically, the observed ac Stark shifts are smaller for larger laser intensities and also for smaller initial population differences between the two low-lying levels. The ac Stark effect must be considered for many potential applications of the Raman effect, such as a Raman clock. In this connection, we have identified conditions for the reduction of the ac Stark shift in our sodium Raman clock.
Coherent stimulated Raman adiabatic passages (STIRAP) based on a dark state have many applications in diverse quantum systems. In the case of large single-photon detuning in three-level $\ensuremath{\Lambda}$ systems, one of the bright states almost does not involve the excited state and then acts as the dark state. In this paper, we report the experimental observation of STIRAP based on the dark state, as well as b-STIRAP based on the above bright state, with the same transfer efficiency in a three-level $\ensuremath{\Lambda}$ cold atomic ensemble. Moreover, both STIRAP and b-STIRAP are found to be immune to the time-varying ac Stark shift. As for a typical example to manipulate a superposition state, we realize an inverse operation on an initial superposition state, which cannot be achieved efficiently for STIRAP based on only the dark state. Our observed double STIRAP thus provides a feasible and robust manner to manipulate quantum states.
A set of three classical coupled pendulums is used to model the stimulated resonance Raman interaction. This model provides a simple, intuitive, physical description of the resonance Raman process and can also be used to interpret experimental observations, including the dynamics of Raman-induced transparency, the physical nature of Ramsey fringes in separated-field excitation, and the effects of off-resonant laser excitation. The model has also been extended to suggest what might be observed for strong laser fields.
Precision studies of stimulated-resonance Raman interactions in a sodium atomic beam were performed with emphasis on Ramsey’s separated-field excitation. Ramsey fringes were obtained for a field separation of up to 30 cm, and the data were consistent with theoretical predictions. Possible applications of this Raman interaction to clock development also were studied by stabilizing a microwave oscillator to a Raman–Ramsey fringe. The resulting oscillator stability of 1.5 × 10−11 for a 1000-sec averaging time compares favorably with commercial cesium clocks when differences in atom transit time and transition frequency are taken into consideration. Finally, potential sources of long-term frequency error, which are important for clock applications, were also partially investigated.
It is well known that the resonant Raman interaction optically pumps atoms into a non-absorbing dressed-state.1 When this state is long-lived compared to the optical Rabi frequencies and the decay rate of the intermediate state, many interesting dynamics arise. These dynamics are significant in applications such as Raman clock AC–Stark shifts, microwave phase-sensitive optical absorption,2 and Raman cooling. By using appropriate approximations, we show that these dynamics can be well described with a Bloch-vector model, which involves only ground-state populations and coherence. This ground-state Bloch-vector model resembles the Bloch-vector model of a two-level system, but it has subtly different dynamics. Furthermore, we construct a novel dressed-state Bloch-vector that clearly shows the analogy between conventional optical pumping and coherent Raman trapping. In this model, one dressed-state is a nonabsorbing state, and the other is an absorbing state. We use the dressed-state Bloch vector to show how Raman AC–Stark shift arises and how it depends on experimental parameters. We also show how the microwave phase-sensitive optical absorption can be quantitatively calculated in a simple way.
Coherent population transfer and superposition of atomic states via a technique of stimulated Raman adiabatic passage in an excited-doublet four-level atomic system have been analyzed. It is shown that the behavior of adiabatic passage in this system depends crucially on the detunings between the laser frequencies and the corresponding atomic transition frequencies. Particularly, if both the fields are tuned to the center of the two upper levels, the four-level system has two degenerate dark states, although one of them contains the contribution from the excited atomic states. The nonadiabatic coupling of the two degenerate dark states is intrinsic, it originates from the energy difference of the two upper levels. An arbitrary superposition of atomic states can be prepared due to such nonadiabatic coupling effect.