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Physical Review A

Exponential gain in resonant four-wave mixing via dressed inversions

Christoph H. Keitel

Published Feb 1, 1998• 26 citations
Publisher

Abstract

High-efficiency coherent high-frequency generation via resonant four-wave mixing is investigated in a dressed states analysis of a bichromatically driven three-level system. We propose the existence of exponential gain due to population transfer at the anticrossings of closely spaced inverted dressed states. This occurs when the Rabi frequency of the weaker detuned driving field is much smaller than the leading resonant Rabi frequency and simultaneously comparable to the largest atomic relaxation rate. The dressed population inversion and thus the exponential gain is not affected until the generated field becomes comparable in intensity to one of the two applied fields, when saturation may take place. The analysis is applied to a krypton configuration of interest to current experiments.

DOI
10.1103/physreva.57.1412

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Role of selective excitation of dressed populations in lasing without inversion

Wang Zhen-hua, Xiangming Hu, (1)华中师范大学物理系，武汉 430079; (2)华中师范大学物理系，武汉 430079;南华大学数理学院，衡阳 421001

Exemplifying the three-level systems in the V configuration, we investigate the role of selective excitation of dressed populations in lasing without inversion. Incoherent driving field transfers population from either of the dressed states to excited state when the level spacing between dressed states produced by the coherent field is much larger than the spectral width of the incoherent driving field. With atomic decay pathways，unidirectional channel of population transfer is formed and selective excitation of dressed populations is established. Employing selective excitation of dressed populations，three severe limits are relaxed. First，it is no longer required that the decay rate of the low-frequency driving transition is larger than that of high-frequency laser transition. Second，the threshold for incoherent driving rate is remarkably lowered. Third，linear gain of the laser without inversion is no longer inversely proportional to the coherent driving field intensity, and the gain is significantly enhanced.

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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.

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Time-dependent dressed-states analysis of lasing without population inversion in a three-level ladder scheme

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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.

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To coherently control a few-level quantum emitter, typically pulses with an energy resonant to the transition energy are applied, making use of the Rabi mechanism, while a single off-resonant pulse does not result in a population inversion. Surprisingly, a two-color excitation with a combination of two off-resonant pulses is able to invert the system. In this paper, we provide an in-depth analysis of two-color excitation schemes within the dressed-state picture. We show that such schemes can be understood as a driving of the transition between the dressed states. In the two-level system this allows us to derive analytic expressions for the pulse parameters yielding a population inversion. We relate our findings to the Swing-UP of quantum EmitteR population (SUPER) mechanism, where the two pulses are red detuned. Our interpretation also holds in the case where one pulse is red detuned while the other pulse is blue detuned, as in dichromatic excitation schemes. We extend our considerations of the SUPER mechanism to the three-level system, where a strong mixing between the bare states takes place. The insights gained from these results help in finding accessible regimes for further experimental realizations of two-color excitation schemes.

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Absorption with inversion and amplification without inversion in a coherently prepared V system: A dressed-state approach

Doron Braunstein, R. Shuker

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.

arXiv:quant-ph/9807014•Physical Review A•Oct 12, 2001•31 citations
High-efficiency coherent high-frequency generation via resonant four-wave mixing is investigated in a dressed states analysis of a bichromatically driven three-level system. We propose the existence of exponential gain due to population transfer at the anticrossings of closely spaced inverted dressed states. This occurs when the Rabi frequency of the weaker detuned driving field is much smaller than the leading resonant Rabi frequency and simultaneously comparable to the largest atomic relaxation rate. The dressed population inversion and thus the exponential gain is not affected until the generated field becomes comparable in intensity to one of the two applied fields, when saturation may take place. The analysis is applied to a krypton configuration of interest to current experiments.
Exemplifying the three-level systems in the V configuration, we investigate the role of selective excitation of dressed populations in lasing without inversion. Incoherent driving field transfers population from either of the dressed states to excited state when the level spacing between dressed states produced by the coherent field is much larger than the spectral width of the incoherent driving field. With atomic decay pathways，unidirectional channel of population transfer is formed and selective excitation of dressed populations is established. Employing selective excitation of dressed populations，three severe limits are relaxed. First，it is no longer required that the decay rate of the low-frequency driving transition is larger than that of high-frequency laser transition. Second，the threshold for incoherent driving rate is remarkably lowered. Third，linear gain of the laser without inversion is no longer inversely proportional to the coherent driving field intensity, and the gain is significantly enhanced.
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.
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.
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.
To coherently control a few-level quantum emitter, typically pulses with an energy resonant to the transition energy are applied, making use of the Rabi mechanism, while a single off-resonant pulse does not result in a population inversion. Surprisingly, a two-color excitation with a combination of two off-resonant pulses is able to invert the system. In this paper, we provide an in-depth analysis of two-color excitation schemes within the dressed-state picture. We show that such schemes can be understood as a driving of the transition between the dressed states. In the two-level system this allows us to derive analytic expressions for the pulse parameters yielding a population inversion. We relate our findings to the Swing-UP of quantum EmitteR population (SUPER) mechanism, where the two pulses are red detuned. Our interpretation also holds in the case where one pulse is red detuned while the other pulse is blue detuned, as in dichromatic excitation schemes. We extend our considerations of the SUPER mechanism to the three-level system, where a strong mixing between the bare states takes place. The insights gained from these results help in finding accessible regimes for further experimental realizations of two-color excitation schemes.
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.