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Optics and Spectroscopy

Fluctuations in number of photons in region of unstable behavior in process of intracavity generation of second harmonic

S. T. Gevorkyan, M. S. Gevorkyan

Published Jan 1, 2011• 2 citations
Publisher

Abstract

Quantum fluctuations of the number of photons of the fundamental mode and of the second harmonic in the process of intracavity generation of the second harmonic in the unstable region of the system are studied. The distribution functions of the number of photons of interacting modes are calculated in the positive P -representation. The functions of the joint distribution of the number of photons of the fundamental mode and the number of photons in the second harmonic are also studied.

DOI
10.1134/s0030400x1101005x

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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.
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).