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Physical Review A

Amplitude-squared squeezing inside and outside a cavity

Daoqi Yu

Published Feb 1, 1992• 12 citations
Publisher

Abstract

Fluctuations of the square of the field amplitude inside and outside a degenerate parametric oscillator are investigated. It is shown that a large reduction of the noise of the square of the field amplitude can be achieved outside the cavity while the maximum amplitude-squared squeezing inside the cavity is only by 50%. This situation is similar to that for normal squeezing.

DOI
10.1103/physreva.45.2121

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Fluctuations of the square of the field amplitude inside and outside a degenerate parametric oscillator are investigated. It is shown that a large reduction of the noise of the square of the field amplitude can be achieved outside the cavity while the maximum amplitude-squared squeezing inside the cavity is only by 50%. This situation is similar to that for normal squeezing.
It is shown that a four-wave-mixing oscillator [R. Ghosh and G. S. Agarwal, Phys. Rev. A 39, 1582 (1989)] operating above threshold exhibits nonclassical effects in the average phase and the amplitude difference of two radiation fields and shows two-mode squeezing. A maximum of 50% intracavity squeezing is found in the fluctuations of two Hermitian operators corresponding to the average phase and the relative amplitude, which becomes 75% squeezing outside the cavity. The variance in the intensity difference between the two fields is half the shot-noise limit inside the cavity but is perfectly suppressed outside the cavity, and both variances inside and outside the cavity are independent of how far above threshold the oscillator is.
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.
This paper clarifies the origins of the standard quantum limit for the amplitude noise of a laser-oscillator outgoing field. The amplitude noise within the cavity bandwidth, \ensuremath{\Omega}\ensuremath{\le}\ensuremath{\omega}/Q, is ultimately caused by the pump amplitude fluctuation, while that above the cavity bandwidth, \ensuremath{\Omega}\ensuremath{\ge}\ensuremath{\omega}/Q, is due to the field zero-point fluctuation. The uncertainty product of the amplitude- and phase-noise spectra at an extremely high pumping level is still larger than the Heisenberg minimum-uncertainty product because of the presence of nonstationary phase-diffusion noise. In this sense, an ordinary laser oscillator is not a quantum-limited device. This paper suggests that a laser oscillator can produce an amplitude-squeezed state in itself if the pump amplitude fluctuation is suppressed below the ordinary shot-noise level. The paper discusses possible schemes for suppressing pump fluctuation, commutator bracket preservation without pump fluctuation, and resulting amplitude and phase spectra. The similarity of and difference between a pump-noise-suppressed laser and a cavity degenerate parametric amplifier are delineated.
The fluctuations in the phase of the pump in a degenerate optical parametric oscillator are modeled by a classical phase-diffusion process, and their influence on squeezing is studied. To this end, appropriate quadrature variables, relative to the instantaneous phase of the pump, are introduced. The squeezing is calculated both inside and outside the cavity. In both cases it is found to be degraded by the phase fluctuations, which may be understood in terms of the time lag in the response of the system to an instantaneous change in the pump phase. This effect might account for a small part of the residual noise present in current experiments. Correlation functions for the field of the oscillator for finite pump linewidth are derived and discussed.
Quantum fluctuations and squeezing of the signal field generated by a degenerate optical parametric oscillator are sensitive to the phase and amplitude fluctuations of the second-harmonic pump. The analysis reported here extends our previous calculations for a perfectly monochromatic noise-free pump to allow for finite pump amplitude and phase fluctuations. We treat the typically intense pump field with its fluctuations as a classical Gaussian stochastic process in two limits: first, when the pump has amplitude fluctuations but its phase is fixed and second, when its phase diffuses but its amplitude is fixed. Since pump amplitude noise affects the evolution of the signal field multiplicatively, it has a lesser impact on the quantum fluctuations of the signal than pump phase diffusion which compromises such fluctuations via the extreme phase sensitivity of the parametric amplification process. For the latter limit, our calculations extend the work of Gea-Banacloche and Zubairy [Phys. Rev. A 42, 1742 (1990)] to cavities with arbitrary transmission coefficients for the bounding mirrors.
Although an ideal degenerate optical parametric oscillator (DOPO) can generate perfect squeezing at the output of a one-sided optical cavity when operating just below threshold, its intracavity squeezing is limited to less than one-half (50%) of its perfect value. However, when two-level atoms are introduced into the DOPO cavity, the amount of intracavity squeezing can be enhanced, from its maximum value of 50%, to a maximum value of 75% in the good-cavity limit due to the strong interaction between the two-level atoms and the subharmonic field mode. This extra intracavity squeezing is significant in studying spectroscopy of atoms interacting with a squeezed field mode inside an optical cavity.