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Journal of Atomic Molecular Condensate and Nano Physics

Coherent Population Trapping in An Inhomogeneously Broadened \(\Lambda\)-System with Multiple Excited States

Paramjit Kaur, Ajay Wasan

Published Aug 22, 2016• 0 citations
Publisher

Abstract

We present a theoretical model using density matrix approach to study the phenomenon of coherent population trapping (CPT) in the \(\Lambda\)-type Doppler broadened system with multiple excited states. A multi-level \(\Lambda\)-system is formed by considering the closely spaced hyperfine levels in the D2 line of \(^{87}\)Rb. The presence of closely spaced hyperfine levels affects the transparency window and cause asymmetry in absorption profiles. We observe the sharp CPT dip when the frequency difference of applied fields is equal to the frequency separation between two ground levels. This dip demonstrates that the system is trapped in the dark state. By performing a thermal averaging in the Doppler-broadened \(\Lambda\)-system, we have shown that the transparency window becomes narrower and its linewidth decreases at higher temperature. This study has potential applications in precision measurements due to the small linewidth of the transparency window.

DOI
10.26713/jamcnp.v3i2.464

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Coherent Population Trapping in An Inhomogeneously Broadened Λ\LambdaΛ-System with Multiple Excited States
We present a theoretical model using density matrix approach to study the phenomenon of coherent population trapping (CPT) in the (\Lambda)-type Doppler broadened system with multiple excited states. A multi-level (\Lambda)-system is formed by considering the closely spaced hyperfine levels in the D2 line of (^{87})Rb. The presence of closely spaced hyperfine levels affects the transparency window and cause asymmetry in absorption profiles. We observe the sharp CPT dip when the frequency difference of applied fields is equal to the frequency separation between two ground levels. This dip demonstrates that the system is trapped in the dark state. By performing a thermal averaging in the Doppler-broadened (\Lambda)-system, we have shown that the transparency window becomes narrower and its linewidth decreases at higher temperature. This study has potential applications in precision measurements due to the small linewidth of the transparency window.
A theoretical model using the density matrix approach has been presented to show the influence of multiple excited states on electromagnetically induced transparency (EIT) in a cascade-type Doppler broadened medium. A five-level system has been considered that is a simple case of the 87 Rb atom. In a room temperature vapour, when the Doppler broadening is comparable with hyperfine splitting in the middle states, there is a strong reduction in EIT. By performing the thermal averaging in the five-level Doppler broadened system, we observe an asymmetric transparency that has already been shown in most of the experimental work.
We present a theoretical model using a density matrix approach to show the influence of multiple excited states on the optical properties of an inhomogeneously broadened V-system of the Rb D2 line. These closely spaced multiple excited states cause asymmetry in absorption and dispersion profiles. We observe the reduced absorption profiles, due to dressed state interactions of the applied electromagnetic fields, which results the Mollow sideband-like transparency windows. In a room temperature vapor, we obtain a narrow enhanced absorption and steep positive dispersion at the line center when the strengths of control and pump fields are equal. Here, we show how the probe transmittance varies when it passes through the atomic medium. We also discuss the transient behavior of our system which agrees well with the corresponding absorption and dispersion profiles. This study has potential applications in controllability of group velocity, and for optical and quantum information processing.
We have detected and analysed narrow high-contrast coherent population trapping (CPT) resonances, which are induced in absorption of the weak probe light beam by the counterpropagating two-frequency pumping radiation. Our experimental investigations have been carried out on example of nonclosed three level Lambda systems formed by spectral components of the Doppler broadened D2 line of cesium atoms. We have established that CPT resonances in transmission of the probe beam (in the cesium vapor), at definite conditions, may have not only more contrast but also much lesser width in comparison with well- known CPT resonances in transmission of the corresponding two-frequency pumping radiation. Thus CPT resonances, detected by the elaborated method, may be used in atomic frequency standards and sensitive magnetometers (based on the CPT phenomenon) and also in ultahigh resolution spectroscopy of atoms and molecules.
We have detected and analysed narrow high-contrast coherent population trapping (CPT) resonances, which are induced in absorption of the weak probe light beam by the counterpropagating two-frequency pumping radiation. Our experimental investigations have been carried out on example of nonclosed three level Lambda systems formed by spectral components of the Doppler broadened D2 line of cesium atoms. We have established that CPT resonances in transmission of the probe beam (in the cesium vapor), at definite conditions, may have not only more contrast but also much lesser width in comparison with well- known CPT resonances in transmission of the corresponding two-frequency pumping radiation. Thus CPT resonances, detected by the elaborated method, may be used in atomic frequency standards and sensitive magnetometers (based on the CPT phenomenon) and also in ultahigh resolution spectroscopy of atoms and molecules.
The Doppler effect is one of the dominant broadening mechanisms in thermal vapor spectroscopy. For two-photon transitions one would naively expect the Doppler effect to cause a residual broadening, proportional to the wave-vector difference. In coherent population trapping (CPT), which is a two-photon narrow-band phenomenon, such broadening was not observed experimentally. This has been commonly attributed to frequent velocity-changing collisions, known to narrow Doppler-broadened one-photon absorption lines (Dicke narrowing). Here we show theoretically that such a narrowing mechanism indeed exists for CPT resonances. The narrowing factor is the ratio between the atom's mean free path and the wavelength associated with the wave-vector difference of the two radiation fields. A possible experiment to verify the theory is suggested.
We report our study on coherent population trapping (CPT) in a $\ensuremath{\Lambda}$ configuration coupled by magnetic dipole interactions. The $\ensuremath{\Lambda}$ configuration is formed by bichromatic radio-frequency fields coupling a pair of Zeeman sublevels in one hyperfine level of an alkali-metal atom to another sublevel in the other hyperfine level. The Zeeman sublevel at the apex is coupled to a state in the nPnPnP manifold via an optical transition on one of the spectroscopic DDD lines to induce optical pumping to a dark state. The configuration is closed without leakage to other Zeeman sublevels. We use lithium atoms in an optical trap for our experimental study. The system allows independent control of the main parameters characterizing CPT, which include the upper-state decay rate and the decoherence rate as well as the Rabi frequencies. By turning off the applied fields, the system is frozen so that its quantum state can be measured precisely. We studied the line shapes and dynamics of the CPT system, and measured the phase relation of the dark superposition state to find excellent agreement with theory. The possible application of the scheme as a method to cool optically trapped atoms below the recoil limit in a manner analogous to velocity-selective coherent population trapping is discussed.