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Quantum Electronics

Quantum theory of an active interferometer

Sergei N Bagayev, A. A. Kurbatov, Е. А. Титов

Published Oct 31, 1997• 1 citation
Publisher

Abstract

An investigation is reported of the influence of quantum noise of amplifying and absorbing media in an active interferometer, excited by an external signal, on its output characteristics. The amplitude and the frequency of the external signal are assumed to be constant. A quantum description of the radiation emitted by an active interferometer is provided by a method involving the use of coherent states. A quantum kinetic equation is derived for the distribution function of the amplitude and phase of the field in an active interferometer and the corresponding diffusion coefficients are found. The variances of fluctuations of the energy of the field and its phase, and also the spectral densities of the fluctuations, are calculated.

DOI
10.1070/qe1997v027n10abeh001063

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An investigation is reported of the influence of quantum noise of amplifying and absorbing media in an active interferometer, excited by an external signal, on its output characteristics. The amplitude and the frequency of the external signal are assumed to be constant. A quantum description of the radiation emitted by an active interferometer is provided by a method involving the use of coherent states. A quantum kinetic equation is derived for the distribution function of the amplitude and phase of the field in an active interferometer and the corresponding diffusion coefficients are found. The variances of fluctuations of the energy of the field and its phase, and also the spectral densities of the fluctuations, are calculated.
The behaviour of the amplitude of a saturated absorption resonance observed in laser radiation propagated through an active interferometer with nonlinear amplifying and absorbing media is studied experimentally for the first time. Upon variation of the gain in the amplifying medium and preserving a constant saturating field in the interferometer, a nonlinear increase in the amplitude of the saturated absorption resonance was observed. In this case, an increase in the detected signal exceeded an increase in the noise, i.e., the signal-to-noise ratio also increased.
A quantum-statistical description of noise in interferometers is given in terms of the Wigner distribution function. The interferometer may contain an amplifier in one of its arms. The input field can be in a variety of states such as a Fock state, a coherent state or a squeezed coherent state. The Wigner function of the output field at the detector is shown to have a general Gaussian form with non-zero complex field amplitude and with other parameters related to the characteristics of the input field, amplifier and beam splitters, etc. An explicit form of the photon-number distribution is given. Higher-order correlations of the output field can be obtained from the Gaussian property of the Wigner function.
A simple model of a traveling-wave parametric amplifier is discussed in quantum-mechanical terms. The amplifier consists of a slab of Raman-active material, illuminated on one face by an intense laser beam that serves as the pump mode; an optical-phonon oscillation serves as the idler mode, and the scattered Stokes light occupies the signal mode. With only a few simplifying assumptions, it is possible to solve the equation of motion for the signal field operator exactly. For large times, both an amplified steady signal and the quantum noise contributed by the material assume simple steady states in an amplifier of finite length. The transient and asymptotic behaviors of the signal and noise intensities are found, together with the corresponding first-order correlation functions. The quasiprobability distribution which specifies the complete density operator for the electric field strength of the amplified signal is also derived.
A quantum theory of a two-level single-mode laser with injected atomic coherence is developed by generalizing the Scully-Lamb laser theory to a form appropriate for the analysis of a coherently pumped laser. We assume that the active atoms are prepared initially in a coherent superposition of the upper and lower levels, and we derive the master equation for the field density operator by treating the interaction of the laser field with many active atoms simultaneously. It is shown that the photon-number distribution can be exactly Poissonian. The laser operation is analyzed in terms of the Fokker-Planck equation for the laser field. Both the intensity and phase diffusion coefficients are phase sensitive and, for stable laser operation, become much smaller than those of an ordinary laser. Consequently, the injected atomic coherence reduces both the photon-number noise and phase noise simultaneously. The intensity diffusion coefficient can vanish exactly, and at the same time the phase diffusion coefficient can become very small. This leads to spontaneous-emission noise quenching in the photon-number distribution, and the laser field can become very close to a coherent state. A scheme to generate the proper form of the initial atomic coherence necessary for the quantum noise quenching is proposed and analyzed.
The shape of the transmission band of an active interferometer, a resonator with amplification and absorption cells excited by an external signal, is studied. Upon tuning the external signal frequency, the narrow saturated absorption resonances can be observed in the transmission band of the interferometer. It is shown that, by varying the gain, the resonance absorption amplitude can be compensated for one order of smallness in pressure. The effect of amplitude and frequency noises of the external signal on the results obtained is studied.