Abstract
We investigate quantum features of three coupled dissipative nano-optomechanical oscillators. The Hamiltonian of the system is somewhat complicated due not only to the coupling of the optomechanical oscillators but to the dissipation in the system as well. In order to simplify the problem, a spatial unitary transformation approach and a matrix-diagonalization method are used. From such procedures, the Hamiltonian is eventually diagonalized. In other words, the complicated original Hamiltonian is transformed to a simple one which is associated to three independent simple harmonic oscillators. By utilizing such a simplification of the Hamiltonian, complete solutions (wave functions) of the Schrödinger equation for the optomechanical system are obtained. We confirm that the probability density converges to the origin of the coordinate in a symmetric manner as the optomechanical energy dissipates. The wave functions that we have derived can be used as a basic tool for evaluating diverse quantum consequences of the system, such as quadrature fluctuations, entanglement entropy, energy evolution, transition probability, and the Wigner function.
Highlights
Physical systems in nature do not behave independently in most cases because they are not isolated in usual. e coupling of a system to another one often results in various mutual phenomena, such as energy exchange, dissipation, entanglement, amplitude fluctuations, and decoherence [1, 2]. e model of a chain of oscillatory motions can be utilized in analyzing the dynamical characteristics of coupled optomechanical [3,4,5,6], nanoelectromechanical [7, 8], chemical [9, 10], and biological systems [11]. e mechanical analyses of coupled oscillators have been extensively explored so far through different approaches
We have investigated quantum mechanical features of dissipative three coupled nano-optomechanical oscillators
In order to remove the coupling terms xixj, we used a diagonalization method. rough these procedures, the Hamiltonian eventually diagonalized. e transformed Hamiltonian was given in the form associated to three independent harmonic oscillators
Summary
Physical systems in nature do not behave independently in most cases because they are not isolated in usual. e coupling of a system to another one often results in various mutual phenomena, such as energy exchange, dissipation, entanglement, amplitude fluctuations, and decoherence [1, 2]. e model of a chain of oscillatory motions can be utilized in analyzing the dynamical characteristics of coupled optomechanical [3,4,5,6], nanoelectromechanical [7, 8], chemical [9, 10], and biological systems [11]. e mechanical analyses of coupled oscillators have been extensively explored so far through different approaches. E mechanical analyses of coupled oscillators have been extensively explored so far through different approaches Such systems can be usually investigated using invariant operator methods [12, 13], Bogoliubov transformation methods [14, 15], Jaynes–Cummings approaches [16], path integral methods [17], and adiabatic approaches [2]. We will show that we can unfold the quantum dynamics of optomechanical physical systems described by a Hamiltonian of dissipative three coupled oscillators through neither introducing a dynamical invariant nor imposing an adiabatic condition in the dissipation. By taking advantage of such a diagonalization, the quantum solutions of the system will be investigated. e concluding remarks are given in the last section
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