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Quantum and Semiclassical Optics Journal of the European Optical Society Part B

Interpretation of transient V scheme amplification without inversion

J. Mompart, C. Peters, R. Corbalán

Published Apr 1, 1998• 10 citations
Publisher

Abstract

Amplification without inversion (AWI) in a resonant V-type system is studied using a dressed basis which reduces the coherent interaction of both involved optical transitions to that of a single two-level system. The transient AWI recently reported through a numerical analysis of the density matrix equations of the V-system in the bare atom basis (Zhu Y 1996 Phys. Rev . A 53 2742) is damped Rabi nutation with transient population inversion in this dressed basis. Although the transient AWI in the bare state basis occurs both with and without an incoherent pump field, the integrated probe gain is positive only in the first case.

DOI
10.1088/1355-5111/10/2/009

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Physical Review A•May 1, 1997•38 citations
Amplification without inversion (AWI) in a resonant V-type system is studied using a dressed basis which reduces the coherent interaction of both involved optical transitions to that of a single two-level system. The transient AWI recently reported through a numerical analysis of the density matrix equations of the V-system in the bare atom basis (Zhu Y 1996 Phys. Rev . A 53 2742) is damped Rabi nutation with transient population inversion in this dressed basis. Although the transient AWI in the bare state basis occurs both with and without an incoherent pump field, the integrated probe gain is positive only in the first case.
Summary form only given.A three-level atom in the V-configuration is treated under two coherent laser fields at resonance with the two allowed transitions. The master equation for the system and full quantum mechanical Hamiltonian are derived, and equations of motion for the elements of the density matrix are obtained by projecting into the bare- and dressed-states schemes. Analysis of light amplification without population inversion in this V-type system is accomplished within the framework of the dressed-state basis. The physical content of the equations of motion for the density matrix elements, namely the coherences and the populations is provided by identifying effective decay and relaxation rates and gain/absorption constants with the appropriate composite coefficients. These depend on the Rabi frequencies of both the drive and probe coherent fields. Time-dependent solutions for both the coherences and the populations are obtained both numerically and analytically under the secular approximation. We have shown how to construct these analytical approximate time-dependent solutions for dressed-state populations and coherences. These approximate solutions, as well as the full numerical calculation quantities, exhibit oscillations at the generalized Rabi frequency.
Amplification in a V system is studied both in the framework of the density matrix formalism and using the S matrix in the usual Hilbert space of the dressed-state vector. We show that it is possible to achieve amplification without inversion both in the bare- and in the dressed-state basis. In this case there is an asymmetry between amplification and absorption because of the occurrence of interferences between Feynman diagrams that can reduce the absorption. The comparison with the two-level atom shows a close analogy with the gain observed about the central resonance of the Mollow transmission spectrum. \textcopyright{} 1996 The American Physical Society.
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 dressed-state study of lasing without population inversion from a three-level atom interacting with a bichromatic laser field in the ladder configuration is being formulated. The system is allowed to be dressed by both laser-field photons (double dressing). The temporal behavior of the system under consideration is being explored numerically. Although the use of dressed-basis density matrix equations introduces major complexity into the equations, this procedure has crucial importance to the understanding of the atomic spectrum and the underlying physics of the processes involved. The system is found to possess a gain without population inversion, as well as a regular gain with inversion for various transitions, both in the transient and steady-state regimes. Enhancement of the refractive index accompanied by vanishingly small absorption was also found. The frequency response of various transitions is explored via numerical Fourier analysis. Some transitions are found to exhibit a dispersion-like line shape, clear evidence of a quantum-coherent interference effect. The spectrum consists of two distinct quintets centered about the coupling and probe-laser frequencies. The spectral features consisting of each quintet are located symmetrically (at resonance conditions only) around the line center at positions shifted from the center by the generalized Rabi and double Rabi frequencies.
We analyze transient properties of light amplification without population inversion (LWI) in a closed three-level @sV -type system and study the system evolution from transient LWI into steady-state LWI. From the time evolution of the atomic coherence and population distribution with and without an incoherent pump field, we elucidate the light amplification mechanism and derive the conditions under which the @sV system exhibits LWI in any state basis. We derive analytical solution for the steady-state LWI and discuss other mechanisms of light amplification such as stimulated Raman scattering and population inversion in the dressed states. \textcopyright{} 1996 The American Physical Society.
Density-matrix calculations provide the steady-state conditions for probe amplification or lasing between atomic levels with an uninverted population, but additional insight into the underlying physics is given by a probability amplitude approach. In this paper we derive the gain coefficient from the Feynman diagrams for a probe-laser incident on a resonantly pumped, V-type system using time-dependent perturbation theory in a dressed basis. The connection is made to density-matrix calculations for this model, which have been used recently to describe experiments in Rb [A. S. Zibrov et al., Laser Phys. 5, 553 (1995); Phys. Rev. Lett. 75, 1499 (1995)]. In the density-matrix calculation the overall gain is possible because the pump-induced coherence of a strongly driven transition leads to probe amplification, despite the lack of inversion on the probe transition. In our amplitude approach we associate a specific physical process with each of the scattering channels for the probe and show how amplification without inversion can be achieved. The amplitude calculation reveals a distinction between stepwise and two-quantum processes. Interference is shown to result from the two-quantum processes, constructive for the amplification channels and destructive for the absorption. Terms appearing in the gain coefficient are traced to different sources in the amplitude and density-matrix approaches. The physical origin of each term is discussed and compared for both approaches. Terms that arise from coherences in the density-matrix approach are shown to correspond to noninterfering stepwise contributions in the amplitude approach. In deriving these results, we find that the Feynman rules that we construct for forming the probability amplitude for an arbitrary scattering process of the electromagnetic field from the coupled atom-strong pump system are consistent with Rayleigh-Schr\"odinger perturbation theory in the quantum dressed basis. In addition, the spontaneously emitted photons become entangled with the probe field, correlating the emission spectrum with specific scattering channels.