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Optics and Spectroscopy

Evolution dynamics of initial coherent states of a field in an unstable region of the behavior in the process of intracavity third harmonic generation

S. T. Gevorgyan, M. S. Gevorgyan

Published Nov 1, 2012• 1 citation
Publisher

Abstract

The quantum dynamics of the state of a field is studied for the process of intracavity third harmonic generation in the region of unstable behavior of the system in the case in which the interacting modes are developed from initial coherent states. It is shown that the Wigner functions of the states of the modes and mean values of the quadrature amplitudes of the fields can have oscillations disappearing with the transition of the system to a stable region.

DOI
10.1134/s0030400x1208005x

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The quantum dynamics of the state of a field is studied for the process of intracavity third harmonic generation in the region of unstable behavior of the system in the case in which the interacting modes are developed from initial coherent states. It is shown that the Wigner functions of the states of the modes and mean values of the quadrature amplitudes of the fields can have oscillations disappearing with the transition of the system to a stable region.
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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).
We show how quantum instability is displayed in the von Neumann entropy and in the Wigner function. For this purpose, an intracavity second-harmonic generation close to the Hopf bifurcation range is studied. We examine the role of dissipation in unstable dynamics and the formation of the quantum states of the cavity modes, and discuss contrast ensemble behavior with that of individual realization on the basis of a quantum-jump simulation method. Namely, it is found that the Wigner functions for fundamental and second-harmonic modes prepared initially in a vacuum state acquire the three-hump structure due to phase symmetry breaking in the bifurcation range. The time evolution of coherent states leads to long-lived swing of the system between two side humps in a phase space.