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16th Congress of the International Commission for Optics: Optics as a Key to High Technology

The dissipative third-order nonlinear oscillator with initial squeezed and displaced number states

Vlasta Peřinová

Published Jul 26, 1993• 0 citations
Publisher

Abstract

The evolution of squeezed and displaced number states in the dissipative third-order nonlinear oscillator is investiga- ted from the point of view of the principal squeezing of vacuum fluctuations, crescent states in both the strong and the weak sense, and of the generation of superposition states. A destructive effect of losses on quantum coherence is demonstrated.

DOI
10.1117/12.2308451

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Physical Review A•Feb 1, 1996•16 citations
The evolution of squeezed and displaced number states in the dissipative third-order nonlinear oscillator is investiga- ted from the point of view of the principal squeezing of vacuum fluctuations, crescent states in both the strong and the weak sense, and of the generation of superposition states. A destructive effect of losses on quantum coherence is demonstrated.
The statistical properties of radiation passing through a nonlinear medium modelled as a third-order nonlinear dissipative oscillator interacting with squeezed light have been investigated. Whereas the photon statistics, being insensitive to the nonlinearity, are determined exactly, an approximative approach has been adopted in the description of squeezing in order to involve fluctuations. As a consequence of the general treatment, new results for a damped linear oscillator with initial squeezed light are provided.
The statistical properties of nonlinear oscillators modeling dissipative forward four-wave mixing are investigated, adopting the Fokker-Planck equation approach. The photon statistics are shown to be insensitive to the nonlinearities and are formulated in terms of the superposition of coherent and chaotic fields. The only approximation in describing the squeezing properties consists in the way of including thermal noise. The effect of the initial coherent amplitudes, that of the interplay of the coupling constants, and that of the reservoir on the squeezing properties are studied. An interesting connection between the revivals of coherent amplitudes and squeezing is pointed out.
The evolution of a quadrature-squeezed state through a Kerr medium is studied from the point of view of amplitude squeezing. We propose a Mach-Zehnder interferometer configuration, which incorporates a squeeze- state generator and a nonlinear Kerr medium, to generate and subsequently displace these states. The displaced states show amplitude squeezing for a proper choice of the initial quadrature squeezed state, and we study two such cases here in detail. In the limit where the evolution through a Kerr medium results in a macroscopic superposition, an initial phase-squeezed coherent state shows significant amplitude squeezing, and we have shown that the photon-number uncertainty 〈(\ensuremath{\Delta}n^)2{)}^{2})2〉 can be minimized to a value smaller than 〈n^〉2/3{\mathrm{〉}}^{2/3}〉2/3. On the other hand, an initial quadrature-squeezed state, whose direction of squeezing is along the direction of excitation, upon evolving through a Kerr medium for a suitable small duration of time shows substantial amplitude squeezing for an appropriate displacement, and we show that the photon-number uncertainty in this case can be minimized to 〈n^〉1/5{\mathrm{〉}}^{1/5}〉1/5, which is far below the previously achieved limits. \textcopyright{} 1996 The American Physical Society.