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ISRN Optics

Quantum Dynamics of Interacting Modes in Intracavity Third Harmonic Generation Process

M. S. Gevorgyan, S. T. Gevorgyan

Published Nov 14, 2012• 0 citations
Publisher

Abstract

We study the quantum dynamics of the number of photons of the interacting modes, the dynamics of the quantum entropy, and the Wigner function of the states of the fundamental and the third harmonic modes for the process of intracavity third harmonic generation. It is shown that the quantum dynamics of the system strongly depends on the external resonant perturbation of the fundamental mode and on the coupling coefficient of the interacting modes. In the region of long interaction times, the modes of the field can be both in stable and in unstable states—depending on the above-mentioned quantities. In the paper, we also investigate the dynamics of transition of the system from stable to unstable states.

DOI
10.5402/2012/476817

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The quantum dynamics of the mean number of photons and quantum entropy of interacting modes, as well as the Wigner function of the stationary state of the fundamental mode and the third subharmonic mode has been investigated for the intracavity third-subharmonic generation. It is shown that the quantum dynamics of the system depends strongly on the nonlinear coupling coefficient between the modes. It is also demonstrated that, in the steady-state limit, depending on the intermodal coupling coefficient, the fundamental mode can be either in a pure coherent state, or in a squeezed state, or in a pure vacuum state. The third subharmonic mode in the subthreshold regime of generation of this mode is in the vacuum state. The Wigner function is squeezed over three sides of an equilateral triangle (squeezed vacuum). The quantum entropy of this state is nonzero. It is also shown that the third subharmonic mode, depending on the nonlinear coupling coefficient in the steady-state limit, can be localized in the three-component state with the same probability of detecting a field in each coherent component of the state and with the presence of quantummechanical interference between the state components. The mean number of photons in this state is smaller than unity. Depending on the nonlinear coupling coefficient, the third subharmonic mode can also be localized in the three-component state, which is a statistical mixture of three squeezed states.
The dynamics of correlation function of quantum fluctuations of quadrature amplitudes, as well as the dynamics of correlation function of quantum fluctuations of photon-numbers of fundamental and the third-harmonics mode are investigated for the process of intracavity generation of the third-harmonic. In the case of the evolution of system from initial vacuum state of both modes into the region of great times of interaction, both correlation functions tend to the stationary value. It is shown that these correlations depend strongly on the non-linear coupling coefficient between these modes. In the case of small coupling coefficients the correlation of fluctuations of the quadrature amplitudes as well as the correlation of fluctuations of photon-number are weak. As the coupling coefficient is rising both correlations are also rising (the state of the sub-systems becomes more entangled by the corresponding variables). By further rise of the coupling coefficient the correlation of quadrature amplitudes of fluctuations vanishes (the entanglement of subsystem states over the quadrature amplitudes is also vanishing) but the correlation of fluctuations of the photon-numbers is not vanishing (the subsystems remain entangled over the photon-number variables).
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