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Photonics 2017, 4(4), 48; doi:10.3390/photonics4040048

Higher-Order Interactions in Quantum Optomechanics: Analytical Solution of Nonlinearity

1
School of Electrical Engineering, Sharif University of Technology, P. O. Box 11365-9363, Tehran, Iran
2
École Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
Received: 15 May 2017 / Revised: 15 November 2017 / Accepted: 27 November 2017 / Published: 5 December 2017
View Full-Text   |   Download PDF [315 KB, uploaded 5 December 2017]

Abstract

A method is described to solve the nonlinear Langevin equations arising from quadratic interactions in quantum mechanics. While the zeroth order linearization approximation to the operators is normally used, here, first and second order truncation perturbation schemes are proposed. These schemes employ higher-order system operators, and then approximate number operators with their corresponding mean boson numbers only where needed. Spectral densities of higher-order operators are derived, and an expression for the second-order correlation function at zero time-delay has been found, which reveals that the cavity photon occupation of an ideal laser at threshold reaches 6 2 , in good agreement with extensive numerical calculations. As further applications, analysis of the quantum anharmonic oscillator, calculation of Q-functions, analysis of quantum limited amplifiers, and nondemoliton measurements are provided. View Full-Text
Keywords: quantum optics; optomechanics; nonlinear interactions; langevin equations quantum optics; optomechanics; nonlinear interactions; langevin equations
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Khorasani, S. Higher-Order Interactions in Quantum Optomechanics: Analytical Solution of Nonlinearity. Photonics 2017, 4, 48.

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