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Physical Review A

Effect of squeezing on the degenerate parametric oscillator

Javed Anwar, Muhammad Suhail Zubairy

Published Feb 1, 1992• 40 citations
Publisher

Abstract

The effect of squeezing on the degenerate parametric oscillator is studied. It is shown that when the ordinary-vacuum reservoir is replaced by a squeezed-vacuum reservoir, the maximum 50% limit of the second-order squeezing inside the cavity can be crossed. It is also shown that the mean number of photons increases considerably. An exact steady-state solution for the Fokker-Planck equation for the field mode is also presented. The photon distribution for the intracavity field and the higher-order variances have been obtained by using the solution of this equation.

DOI
10.1103/physreva.45.1804

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The effect of squeezing on the degenerate parametric oscillator is studied. It is shown that when the ordinary-vacuum reservoir is replaced by a squeezed-vacuum reservoir, the maximum 50% limit of the second-order squeezing inside the cavity can be crossed. It is also shown that the mean number of photons increases considerably. An exact steady-state solution for the Fokker-Planck equation for the field mode is also presented. The photon distribution for the intracavity field and the higher-order variances have been obtained by using the solution of this equation.
A degenerate optical parametric oscillator (DOPO) in the above threshold regime is a prominent source of squeezed field. In this study, a driven DOPO whose pump mode is coupled to a thermal bath while the signal mode is coupled to a squeezed vacuum reservoir is explored to understand the effect of the external squeezed light and the thermal fluctuations on the squeezing properties of both the intracavity and output pump and signal modes. Our findings showed that the injected squeezed vacuum reservoir enables the intracavity squeezing to surpass the maximum squeezing limit of 50% attainable in a DOPO coupled to an ordinary vacuum reservoir. We also found that the maximum squeezing of the output signal mode shifts from resonance to off-resonance in the presence of the injected squeezed vacuum field. Furthermore, the output pump mode exhibits nearly perfect squeezing for a squeezing parameter of r=2. Unlike the output signal mode, the maximum squeezing of the output pump mode occurs at resonance in the presence of the injected squeezed vacuum reservoir. Moreover, a considerable amount of squeezing is observed even in the presence of thermal fluctuations, as they are counterbalanced by the external squeezed light. Notably, relative damping rate between the pump and signal modes is observed to be a parameter that significantly influences squeezing, indicating the importance of optimizing the amount of damping depending on the intended purpose of the DOPO.
We study the squeezing as well as the statistical properties of the output radiation from a degenerate parametric oscillator coupled to a squeezed vacuum reservoir employing the stochastic differential equations associated with the normal ordering. It is found that the degree of squeezing of the output radiation is less than the corresponding cavity radiation. However, for output radiation the correlation of the quadrature operators evaluated at different times also exhibits squeezing, which is the reason for quenching of the overall noise in one of the quadrature components of the squeezing spectrum even when the oscillator is coupled to a vacuum reservoir. Moreover, coupling the oscillator to the squeezed vacuum reservoir enhances the squeezing exponentially and it also increases the mean photon number.
We consider a two-mode light generated by nondegenerate three-level laser with parametric oscillator in optomechanical cavity coupled to two-mode squeezed vacuum reservoir. Effects of pump mode, optomechanical coupling strength and squeezed vacuum reservoir on squeezing and entanglement properties of the cavity modes have been analyzed using the expectation values of cavity mode variables at steady state. The results show that the two-mode light produced by the system under consideration exhibits quadrature squeezing and entanglement. The presence of parametric oscillator in the cavity and squeezed vacuum reservoir enhance the degree of squeezing, entanglement and mean photon number of the cavity mode lights. The optomechanical cavity has no effect on the mean photon number and entanglement of the cavity mode but increases the degree of quadrature squeezing.
Employing the quantum Hamiltonian describing the interaction of a two-mode light (signal–idler modes) generated by a non-degenerate parametric oscillator (NDPO) with two uncorrelated squeezed vacuum reservoirs (USVR), we derive the master and the Fokker–Planck equations. The corresponding Fokker–Planck equation for the Q-function is then solved employing a propagator method developed by K. Fesseha [J. Math. Phys. 33 2179 (1992)]. Making use of this Q-function, we calculate the quadrature fluctuations of the optical system. From these results we infer that the signal–idler modes are in squeezed states. When the NDPO operates below threshold we show that, for a large squeezing parameter, a squeezing amounting to a noise suppression approaching 100% below the vacuum level in one of the quadratures can be achieved.
Applying stochastic differential equations, we study the squeezing and statistical properties of the cavity and output modes of a degenerate three-level laser whose cavity contains a parametric amplifier and coupled to a squeezed vacuum reservoir. We consider the case in which the top and bottom levels of the three-level cascade atoms injected into the cavity are coupled by the pump mode emerging from the parametric amplifier. It turns out that the presence of the squeezed vacuum reservoir and the parametric amplifier contribute considerably to the mean photon number and the degree of squeezing of the cavity and output modes. It appears that almost perfect squeezing can be achieved at steady state and at threshold for a suitable choice of parameters.
We investigate the statistical and quadrature squeezings, as well as the entanglement properties, of a two-mode light generated by non-degenerate parametric oscillations coupled to a two-mode squeezed vacuum reservoir, by employing the solutions of the quantum Langevin equations. It is found that the two-mode light shows the two-mode squeezing and entanglement for all values of the time. Moreover, it is observed that the squeezed vacuum reservoir and the growing amplitude of the pump mode enhance the degrees of two-mode squeezing and entanglement. We have also shown that the amounts of squeezing and entanglement are significant in a region, where the mean photon number is higher, and the photon number correlation is lower.