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Physical Review A

Theory of the coherent population trapping maser: A strong-field self-consistent approach

Aldo Godone, Filippo Levi, Salvatore Micalizio, Jacques Vanier

Published Oct 12, 2000• 24 citations
Publisher

Abstract

The phenomenon of coherent microwave stimulated emission in a cavity is analyzed for the case of alkali atoms such as Cs and Rb under coherent population trapping (CPT) in a \ensuremath{\Lambda} scheme. The calculations are made in transient and in continuous operation within the framework of a three level model. The coupling of the atoms to the microwave field generated inside the cavity by the atomic ensemble, is fully taken into account; it introduces radiation damping and an imbalance in the populations of the ground-state hyperfine levels, decreasing the intrinsic symmetry of the \ensuremath{\Lambda} scheme. The effect leads also to a broadening and to a frequency shift of the microwave emission profile. A comparison is made with the optically pumped alkali atom maser, allowing a deeper understanding of the CPT stimulated emission phenomenon.

DOI
10.1103/physreva.62.053402

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The phenomenon of coherent microwave stimulated emission in a cavity is analyzed for the case of alkali atoms such as Cs and Rb under coherent population trapping (CPT) in a \ensuremath{\Lambda} scheme. The calculations are made in transient and in continuous operation within the framework of a three level model. The coupling of the atoms to the microwave field generated inside the cavity by the atomic ensemble, is fully taken into account; it introduces radiation damping and an imbalance in the populations of the ground-state hyperfine levels, decreasing the intrinsic symmetry of the \ensuremath{\Lambda} scheme. The effect leads also to a broadening and to a frequency shift of the microwave emission profile. A comparison is made with the optically pumped alkali atom maser, allowing a deeper understanding of the CPT stimulated emission phenomenon.
The coherent microwave emission from an optically thick atomic ensemble in a cavity under coherent population trapping is analyzed. Transient and continuous operations are theoretically examined within the frame of a closed three-level system in the Dicke regime. The effects related to the atomic density and to the propagation in the active medium are examined with particular reference to the subnatural linewidth, the low group velocity and the shifts of the maser emission profile from the unperturbed atomic transition. The case of alkali-metal atoms submitted to a \ensuremath{\Lambda} excitation scheme is addressed in view of applications in the atomic frequency standard field. Experimental observations in agreement with the theoretical predictions are reported for the case of rubidium in a buffer gas. Apparent superluminal propagation is also reported and briefly discussed.
The paper gives an overview of our present theoretical understanding of coherent population trapping in alkali metal atoms as used in the implementation of an atomic frequency standard. Two approaches are examined: The passive approach in which the microwave hyperfine resonance is detected directly on the transmitted radiation and the maser approach in which the same resonance is observed by means of stimulated emission in a microwave cavity. The theoretical analysis reviewed is supported by experimental results.
The phenomenon of coherent population trapping in alkali-metal atoms is analyzed by means of a perturbation approach. Closed form transparent solutions are obtained for the coherences existing within the system and the populations of the ground levels and of the excited state. The presence of dark lines and coherent microwave emission from the ground state are made explicit. Experimental results that confirm the theoretical calculations are reported for the case of cesium in a buffer gas. Conclusions are drawn in connection with the application of coherent population trapping to the field of atomic frequency standards.
Microwave emission has been observed at the ground-state hyperfine transition frequency of a cesium atomic vapor driven into a nonabsorbing state by means of coherent population trapping. The coherent emission observed is due to the oscillating magnetization generated by the coherence, which is induced between the ground-state hyperfine levels when they are coupled to an excited state by means of two laser radiations via a \ensuremath{\Lambda} scheme. The experiments described were done in a quartz cell containing buffer gases such as neon and nitrogen, reducing the linewidth through the Dicke effect. The cell was placed inside a microwave cavity tuned at 9.2 GHz, the ground-state hyperfine frequency of cesium, and a power output of the order of 100 fW was measured in the case where nitrogen was used as the buffer gas.
Coherent population trapping (CPT) resonance signals have promise in a wide range of applications involving precision sensing. Generally, the CPT phenomenon occurs in a three-level Λ system with a bichromatic phase-coherent light fields. We theoretically and experimentally studied an Rb vapor-cell-based atomic system involving bichromatic CPT optical fields and an external microwave (MW) field simultaneously. In such a mixing scheme, the coherence of the ground states could be controlled either by the Rabi frequency of the microwave field or by the relative phase between the optical fields and the MW field. Moreover, we investigated the Rabi resonance in this mixing scheme. The Rabi frequency of the MW field can be measured SI (International System of Units)-traceably based on the Rabi resonance lineshape, and thus holds the potential to realize intensity stabilization of the optical field in this system. Simple theoretical models and numerical calculations are also presented to explain the experimental results. There is scope to use the proposed technique in future development of SI-traceable optical field strength standards.
The description of a new type of frequency standard based on coherent population trapping (CPT) in cesium is given. The phenomenon creates a magnetization oscillating at the hyperfine frequency. Microwave radiation emitted by such a magnetization is detected by means of a microwave cavity. The process takes place without population inversion. Results are given for continuous and pulsed operation. The possibility of using the CPT coherent microwave emission as the basis of a frequency standard is analyzed.