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Laser Physics

Dressed states analysis of lasing without population inversion in a three-level ladder scheme: Approximate analytic time dependent solutions

Doron Braunstein, R. Shuker

Published Feb 1, 2009• 4 citations
Publisher

Abstract

A dressed-state study of lasing without population inversion from a three level atom interacting with a bi-chromatic laser field, in the ladder configuration, is formulated. We allow the atomic system to be dressed by both laser filed photons (double dressing). The evolution of the system under consideration is being explored both analytically and numerically, within the transient regime. Time dependent approximate analytic solutions for dressed-state populations and coherences are derived, within the so called “secular approximation,” under resonant conditions. We also present time dependent numerical solutions for population and coherences in the off-resonance regime. A spectral analysis is also performed revealing the structure of various dressed states transitions. These are shown to be composed of quintets centered about the frequencies of the coupling and probe laser fields and having sidebands located symmetrically at positions shifted from line center at the Rabi and double Rabi frequencies.

DOI
10.1134/s1054660x09020236

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•Jan 6, 1999•1 citation
A dressed-state study of lasing without population inversion from a three level atom interacting with a bi-chromatic laser field, in the ladder configuration, is formulated. We allow the atomic system to be dressed by both laser filed photons (double dressing). The evolution of the system under consideration is being explored both analytically and numerically, within the transient regime. Time dependent approximate analytic solutions for dressed-state populations and coherences are derived, within the so called “secular approximation,” under resonant conditions. We also present time dependent numerical solutions for population and coherences in the off-resonance regime. A spectral analysis is also performed revealing the structure of various dressed states transitions. These are shown to be composed of quintets centered about the frequencies of the coupling and probe laser fields and having sidebands located symmetrically at positions shifted from line center at the Rabi and double Rabi frequencies.
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.
A dressed-state study of lasing without population inversion from a three-level atom interacting with a bi-chromatic laser field in the ladder configuration is presented. In our model we allow the atom to be dressed by both of the coupling and probe fields. The system under consideration is explored both analytically and numerically within the steady-state regime. A parameter study is performed in which we explore the influence of the change of control parameters (Rabi frequencies and incoherent pump rates, etc) on the system behaviour. The parameter study also applies to situations where both coherent fields have comparable intensities. Expressions for steady-state populations and coherences are derived, from which the constraints on the system control parameters allowing gain or absorption of various types, are calculated. The system is demonstrated to possess gain without inversion (GWI), as well as regular gain with inversion, for the appropriate choice of system control parameters. Inversion without lasing (IWL) is also found. The dressed-state approach offers a different insight into the system dynamics in which Rabi oscillations and spectral features appear natural. We believe that the dressed-state approach provides a more adequate description of the system dynamics than that provided by the bare state basis.
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.
Light-induced absorption with population inversion and amplification without population inversion in a coherently prepared closed three level V-type system are investigated. This study is performed from the point of view of a two color dressed-state basis. Both of these processes are possible due to atomic coherence and quantum interference contrary to simple intuitive predictions. Merely on a physical basis, one would expect a complementary process to the amplification without inversion. We believe that absorption in the presence of population inversion found in the dressed-state picture utilized in this study, constitutes such a process. We derive approximate analytic time-dependent solutions, for coherences and populations that are compared with full numerical solutions exhibiting good agreement. Steady-state quantities are also calculated, and the conditions under which the system exhibits absorption and gain with and without inversion, in the dressed-state representation are derived. It is found that for weak input probe-laser field absorption with inversion and amplification without inversion may occur, for a range of system parameters. These take place at resonance and the generalized Rabi ac Stark-shifted frequencies, in agreement with exprimental investigations, and at beat frequencies, depending on the relevant parameters.
We study the operational properties of the lasing field generated from strongly driven two-level atoms in a ring cavity by including the field saturation to all orders. Lasing without inversion between bare atomic states can occur for both off-resonant-- and resonant-pump fields. In the case of an off-resonant--pump field, lasing occurs at one of the Rabi sidebands, for which there exists population inversion between the relevant dressed-atom--field states. In the case of a resonant-pump field, lasing can occur near either of two Rabi sidebands, for which there is no population inversion between the dressed states; here the gain is due to the atomic coherence between the dressed states. While the operation of the off-resonantly--pumped dressed-state laser is similar to that of an ordinary laser, the operation of the resonantly pumped dressed-state laser exhibits some interesting features, such as (1) mode pushing and (2) larger laser intensity coming from smaller linear gain as the detuning is changed. In order to show such features, the calculations have to go beyond the secular approximation.
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.