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Journal of Experimental and Theoretical Physics

Relaxation of a Quantum Oscillator in the Presence of an External Force

Boris Ya Zel'dovich, A. M. Perelomov, В. С. Попов

Published Jan 1, 1969• 2 citations
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Relaxation of a Quantum Oscillator

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We demonstrate that the stochastic resonance phenomenon can occur in a pure quantum regime for a wider class of microscopic systems described by a dissipative anharmonic oscillator driven by two periodic forces. We apply a quantum-state diffusion method, and display the synchronization of quantum trajectories by the stochastic resonance process. The model proposed is accessible for experiments, and results in the formation of quantum states of the anharmonic oscillator, namely sub- and super-Poissonian statistics for time intervals exceeding the relaxation rate. We show that stochastic resonance phenomenon can be described in terms of the minimization of the quantum von Neuman entropy, and demonstrate the possibility of controlling both the dissipative dynamics and quantum statistics of anharmonic oscillator by two external periodic forces.

Physical Review A•Jan 5, 2001•33 citations
Исследуются особенности динамики двух связанных квантовых осцилляторов в поле лазерной волны. Построена теоретическая модель этой системы, в которой учтена диссипация энергии. Особое внимание в работе уделено выявлению условий наиболее эффективного протекания процесса обмена экситонами между осцилляторами. Учёт поля лазерной волны и диссипативных сил был произведён с использованием гамильтониана Бейтмана-Кальдирола-Канаи. The forced oscillations in a system of two coupled quantum oscillators of finite Q-factor of zero temperature are considered. The subject of the study was the process of energy exchange between oscillators in this system. The presence of friction and external forces was taken into account by using the Bateman-Caldirola-Kanai Hamiltonian. Expressions are obtained for the time evolution of the average energy of each oscillator for various external forces and parameters of a quantum system.
The standard Bloch oscillation normally refers to the oscillatory tunneling dynamics of quantum particles in a periodic lattice plus a linear gradient. In this paper we theoretically investigate the generalized form of the Bloch oscillation in the presence of additional higher-order gradients and demonstrate that the higher-order gradients can significantly modify the tunneling dynamics, particularly in the spectrum of the density oscillation. The spectrum of the standard Bloch oscillation is composed of a single prime frequency and its higher harmonics, while the higher-order gradients in the external potential give rise to fine structures in the spectrum around each of these Bloch frequencies, which are composed of series of frequency peaks. Our investigation leads to a twofold consequence to the applications of Bloch oscillations for measuring external forces. For one thing, under a limited resolution of the measured spectrum, the fine structures would manifest as a blur to the spectrum and lead to intrinsic errors to the measurement. For another, given that the fine structures could be experimentally resolved, they can supply more information on the external force than the strength of the linear gradient, and be used to measure more complicated forces.
We demonstrate that the stochastic resonance phenomenon can occur in a pure quantum regime for a wider class of microscopic systems described by a dissipative anharmonic oscillator driven by two periodic forces. We apply a quantum-state diffusion method, and display the synchronization of quantum trajectories by the stochastic resonance process. The model proposed is accessible for experiments, and results in the formation of quantum states of the anharmonic oscillator, namely sub- and super-Poissonian statistics for time intervals exceeding the relaxation rate. We show that stochastic resonance phenomenon can be described in terms of the minimization of the quantum von Neuman entropy, and demonstrate the possibility of controlling both the dissipative dynamics and quantum statistics of anharmonic oscillator by two external periodic forces.