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Physical Review A

Interference-induced optical gain without population inversion in cold, trapped atoms

John E. Kitching, Leo W. Hollberg

Published Jun 1, 1999• 76 citations
Publisher

Abstract

Continuous-wave (cw) optical gain of $1.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2} {\mathrm{cm}}^{\ensuremath{-}1}$ is obtained on a probe transition in a driven, three-level, V-type atomic system. The atoms exhibit no population inversion between the probe excited state and the dressed ground states of the combined atom-drive Hamiltonian. This gain without population inversion is interpreted as direct evidence of quantum interference, arising from coherences established in the atom by the applied optical fields. Agreement with a simple four-level theoretical model is excellent.

DOI
10.1103/physreva.59.4685

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Continuous-wave (cw) optical gain of 1.3\ifmmode×\else\texttimes\fi10\ensuremath−2cm\ensuremath−11.3\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}2} {\mathrm{cm}}^{\ensuremath{-}1}1.3\ifmmode×\else\texttimes\fi10\ensuremath−2cm\ensuremath−1 is obtained on a probe transition in a driven, three-level, V-type atomic system. The atoms exhibit no population inversion between the probe excited state and the dressed ground states of the combined atom-drive Hamiltonian. This gain without population inversion is interpreted as direct evidence of quantum interference, arising from coherences established in the atom by the applied optical fields. Agreement with a simple four-level theoretical model is excellent.
We show that continuous-wave, two colour excitation of three-level atoms opens new channels of irreversible population transfer between atomic levels. This process, which we describe as dynamically induced irreversibility, leads to unanticipated phenomena including the inversion of atomic transitions whose upper atomic level has no conventional source of irreversible population pumping. We also study the effect of excitation-field bandwidth on the gain exhibited by driven, three-level, V-type atomic systems. Gain, which may or may not be inversionless in the atomic-state basis, is produced through strong monochromatic driving of one atomic transition and weaker pumping of a coupled transition. It is found that monochromatic pumping frequently yields greater optical gain than incoherent (wide bandwidth) pumping. This is particularly true when system gain can be attributed to hidden inversions among the eigenstates (semi-classical dressed states) of the coupled atom+driving field quantum system. Last, we report the observation of continuous-wave lasing in a strongly driven barium cascade system and interpret its properties in terms of the models presented.
For a four-level atomic system with a doublet of closely spaced levels, we find that, owing to the coherence that results from the vacuum of the radiation field, population trapping at excited levels and probe gain with population inversion can be achieved with weak incoherent pumping. This gain is different from both the conventional lasing gain and gain without inversion in that there exists population inversion on probe transitions but the inversion is achieved by the vacuum-induced coherence.
In a three-level V-type atomic system without any external coherent driving, owing to the coherence that results from the vacuum of the radiation field, both the probe gain with and without population inversion can be achieved with very weak incoherent pumping. The gain is achieved in the absence of any external coherent driving field, so it is different from the gain without inversion in ordinary laser-driven schemes where a coherent driving field is necessary to create the coherence. The gain is also different from the conventional lasing gain because the population inversion is achieved via vacuum-induced coherence, which is dependent on the atomic coherence.
Light amplification without population inversion and absorption with inversion driven by quantum coherent interferences in a closed three level V-type system is studied from the point of view of two color dressed state basis. Approximate analytic time dependent solutions, for coherences and population distribution are derived, and compared with full numerical solutions. Steady state quantities are also calculated, and the conditions under which the system exhibits gain with and without inversion, in the dressed state representation are derived. It is found that for a weak probe laser field light amplification without inversion may occur, for a range of system parameters, in both the bare and the dressed state representations.
A four-level system driven by two coherent fields is considered. the probe gain at a short wavelength can be achieved due to the quantum interference in the presence of an incoherent pump. The density matrix calculation provides the conditions for probe amplification from different origin, including gain without population inversion in any state basis, gain with population inversion in the dressed-state basis, and gain with population inversion in the bare-state basis. Also, by controlling Rabi frequency of the coupling field a totally changing from non-inversion to inversion can be achieved which does not depend on the intensity of the incoherent pump.
In this paper we analyze the steady-state populations and gain lineshape of a V-type three-level atom with a closely spaced excited doublet. The atom is driven by a strong coherent field, a weak probe, and a single broadband squeezed vacuum. We focus our attention in the interplay between the quantum interference and the squeezed field on the probe gain. It is shown that the relative phases between the two coherent fields and the squeezed field play an important role in the optical properties of the atom. Specifically, we find that the probe can experience gain without population inversion for proper values of the parameters characterizing the squeezed field and in the absence of incoherent pumping. The system can be tailored to exhibit multiple dispersion regimes accompanied by negligible gain or absorption over a large bandwidth, a desirable feature for obtaining propagation of pulses with negligible distortion.