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Optics and Spectroscopy

Quantum Squeezing of the Field of a Single-Atom Laser under Conditions of a Variable Coupling Constant

V. A. Bobrikova, R. A. Khachatryan, К. А. Баранцев, Е. Н. Попов

Published Dec 1, 2019• 2 citations
Publisher

Abstract

Abstract A nonstationary regime of squeezed-light generation by a single-atom laser is investigated. Dependences of the quantum-squeezing parameter and radiation intensity on modulation frequency of the atom–field coupling constant are obtained. It is demonstrated that a resonance appears at the modulation frequency equal to twice the average coupling constant, which leads to a more efficient quantum squeezing in a nonstationary harmonic regime than in the case of a stationary regime for the same values of the relaxation and pump parameters.

DOI
10.1134/s0030400x19120051

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Abstract A nonstationary regime of squeezed-light generation by a single-atom laser is investigated. Dependences of the quantum-squeezing parameter and radiation intensity on modulation frequency of the atom–field coupling constant are obtained. It is demonstrated that a resonance appears at the modulation frequency equal to twice the average coupling constant, which leads to a more efficient quantum squeezing in a nonstationary harmonic regime than in the case of a stationary regime for the same values of the relaxation and pump parameters.
In this work we investigate unsteady regime of generation of squeezed light in a single-atom laser. Dependences of the parameter of quantum squeezing and light intensity on modulation frequency of the coupling constant between an atom and field were calculated numerically for this. We showed that at the modulation frequency equal to double coupling constant parametric resonance occurs. This regime leads to more effective quantum squeezing than regime under steady generation with the same parameters of the pumping and the relaxation.
Based on the approximation of strong correlations between an atom and an intracavity field, which implies the equal probabilities of finding the atom in the ground state and n photons in the field and of finding the atom in an excited state and n −1 photons in the field, it is shown that the conditional states of a field generated by a single-atom laser are described by the diagonal part of the generalized coherent Mittag-Leffler state. The quasi-distributions P and Q of the intracavity-field probability amplitude are found, and the boundedness of the Glauber function on a segment is shown. The possibility of inversionless lasing is demonstrated, and the absence of a lasing threshold is found for some region of parameters. The regimes of generation of the amplitude-squeezed states of the field are studied and the parameters of the system providing the maximum squeezing are determined. It is shown that the atom-field states are entangled at weak pump intensities.
The influence of injected atomic coherence on a laser's operation is discussed by analyzing the semiclassical equations of motion of this system. Both stationary-steady-state and time-dependent regimes of operation are investigated. We present the dependence of the stationary laser intensity and phase on the external parameters (population inversion, amplitude of atomic coherence, and detuning). For small cavity-field detuning and large atomic coherence, both frequency and phase locking occurs. The laser frequency is locked to the atomic frequency, and the phase is locked to a value determined primarily by the phase of the atomic coherence. Under certain conditions, in the inverted regime, the output intensity is an ssS-shaped function of the atomic coherence, leading to the possibility of a bistable behavior. However, only a portion of the bistable curve gives stable stationary operation, and in critical points (the location of which depends crucially on the external parameters) time-dependent instabilities branch away. When the detuning is larger than a critical value there is neither phase nor frequency locking. We find that the time-dependent behavior of the laser intensity in this case is oscillatory (quasiperiodic), and show that there is a stable limit cycle in the phase plane of the quadratures. There is a small parameter region where a stationary steady state and an oscillatory state may coexist. We also consider the nonlinear quantum theory of a laser with injected atomic coherence, and include the effect of pumping statistics. We derive the Fokker-Planck equation for the P representation, and express the noise in terms of moments. We find that in the steady state the intensity noise can be suppressed below the shot-noise limit but that the phase fluctuations are not affected by pump regularity. For nonzero detuning, we find that transient squeezing of the phase fluctuations is possible.
A new possibility of generating one-mode squeezed light by coupling a system of two-level atom with a bichromatic pump field in an optical cavity is suggested. The non-classical character of light in this process is caused by two-photon radiation at the central frequency of the spectrum of resonance fluorescence in the bichromatic field. The intensity of the resonance fluorescence cavity output field as well as the variance of the quadrature amplitudes and the second-order correlation function of intensity are calculated.
The dependence of squeezing on the number of atoms is discussed in the time-dependent collective resonance fluorescence of N two-level atoms, coherently driven by a strong resonant laser field. It is shown that, for strong driving field, squeezing appears only in the transient regime of resonance fluorescence. The location of squeezing in time is independent of the number of atoms and the initial atomic populations. It is found that despite the reduction in the amount of squeezing per single atom, squeezing increases in the whole resonance fluorescence field as the number of atoms increases, and attains its maximal value for moderate N. Moreover, the maximal value of squeezing is dependent on the intensity of the driving field. As the latter increases, the maximum of squeezing increases and shifts towards larger numbers of atoms. For a very large number of atoms, however, squeezing is altogether removed.