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Physical Review A

Squeezed vacuum states in optically bistable two-photon media

Christopher C. Gerry, Edward R. Vrscay

Published Jun 1, 1988• 20 citations
Publisher

Abstract

The time evolution of squeezed vacuum states, taken to be SU(1,1) coherent states, interacting with a two-photon medium is examined using numerical methods. The non-photon-conserving medium is modeled by a Hamiltonian which consists of the free-field term, a non-photon-conserving term in the form of a degenerate parametric amplifier, and an anharmonic term which gives rise to optical bistability. This system has previously been shown to produce enhanced squeezing when interacting with ordinary coherent light. In the present work we find that the squeezing property is generally revoked by the anharmonic term and increased by the nonconserving term. The combined effects are not additive, however, and a quantum interference effect is observed in the calculations.

DOI
10.1103/physreva.37.4265

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•Jan 1, 1984•0 citations
The time evolution of squeezed vacuum states, taken to be SU(1,1) coherent states, interacting with a two-photon medium is examined using numerical methods. The non-photon-conserving medium is modeled by a Hamiltonian which consists of the free-field term, a non-photon-conserving term in the form of a degenerate parametric amplifier, and an anharmonic term which gives rise to optical bistability. This system has previously been shown to produce enhanced squeezing when interacting with ordinary coherent light. In the present work we find that the squeezing property is generally revoked by the anharmonic term and increased by the nonconserving term. The combined effects are not additive, however, and a quantum interference effect is observed in the calculations.
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We study the time evolution of SU(1,1) coherent states in an exactly solvable model of a single-mode quantized electromagnetic field in a four-photon medium that has previously been shown to give squeezed states from ordinary coherent states. If the SU(1,1) coherent state initially exhibits squeezing in the X1{X}_{1}X1​ quadrature, the squeezing is revoked. We also show that for certain choices of phase in the initial state, enhanced squeezing may appear in the X2{X}_{2}X2​ quadrature. Numerical results are also presented for the case when the model is not exactly solvable.
In Chapter 1 we consider the question of squeezing in a two-photon laser. A two-photon laser is modelled as N two-level atoms interacting via a two-photon transition with a single resonant cavity field mode. A Fokker-Planck equation containing all leading noise terms is derived. A linearised fluctuation analysis reveals that there is no squeezing in a two-photon laser with injected signal. A small amount of squeezing is present in two-photon optical bistability. In Chapter 2 a microscopic model of degenerate four wave mixing including the quantisation of the medium is presented. Time-dependent solutions show ideal squeezing to be obtained in the limits of large detuning, low saturation and zero loss. The effect of nonideal atomic parameters is analysed. Equations describing the spatial propagation of the field through the medium are also derived. In Chapters 3 and 4 we are concerned with quantum effects, in particular violation of Bell's Inequalities, present in optical systems. An optical field produced by an intracavity four wave mixing is shown to exhibit the nonclassical features of photon antibunching, squeezing and violation of Cauchy-Schwarz and Bell's Inequalities. These intrinsic quantum mechanical effects are shown to be associated with the nonexistence of a positive normalizable Glauber-Sudarshan P-function.