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Journal of the Optical Society of America B

Rigged-reservoir response II Effects of a squeezed vacuum

M.‐A. Dupertuis, Stephen Mark Barnett, Stig Stenholm

Published Jul 1, 1987• 43 citations
Publisher

Abstract

As a specific example of the linear response induced by a rigged reservoir, we construct one from an assembly of harmonic oscillators in a multimode squeezed state. In the rotating frame of the boson mode the squeezed reservoir offers noise properties corresponding to those characterizing a stationary random process. With a squeezed reservoir an attenuator can produce a squeezed output, irrespective of its input. For an arbitrarily squeezed reservoir the amplifier can provide a squeezed output for a gain even larger than 2, thus beating the cloning limit.

DOI
10.1364/josab.4.001102

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As a specific example of the linear response induced by a rigged reservoir, we construct one from an assembly of harmonic oscillators in a multimode squeezed state. In the rotating frame of the boson mode the squeezed reservoir offers noise properties corresponding to those characterizing a stationary random process. With a squeezed reservoir an attenuator can produce a squeezed output, irrespective of its input. For an arbitrarily squeezed reservoir the amplifier can provide a squeezed output for a gain even larger than 2, thus beating the cloning limit.
In this paper we utilize the idea of multiatom squeezed states to build a rigged reservoir for linear amplification or attenuation. The reservoir state is constructed such that the processed boson mode is driven by a collective reservoir operator that offers squeezed stationary noise. Then the amplifier can retain squeezing for arbitrary gain, and the amplifier added noise can be made widely different in the two quadrature components. The attenuator drives the signal toward a squeezed noise state. In contrast to the case of a multimode squeezed reservoir, we can in this case make the noise exactly zero for one component, but only at the expense of a vanishing linear gain (or loss) coefficient. The noise-over-gain ratio can, however, become arbitrarily small. The results are discussed and related to earlier work.
We present the general theory of the linear response of a single boson mode embedded in an arbitrary background treated as a reservoir. This gives the master equation for linear amplifiers and attenuators. A conservation law similar to the Manley–Rowe relation aids the derivations. For a rigged reservoir the master equation is found to contain anomalous terms. We divide the reservoir correlation functions into linear-response and fluctuation contributions. The former give gain or loss; the latter determine the noise. The equation is written for the Wigner function, because this is suitable to describe squeezed states. The anomalous terms make the noise properties anisotropic, and the output may be squeezed, in contrast to that emerging from a device interacting with a thermal bath. For both components the output satisfies the added-noise inequality of Caves. We derive expressions for the excess noise in terms of reservoir correlation functions. In a thermal bath a fluctuation-dissipation theorem guarantees that the amplifier output cannot be squeezed when the gain exceeds the cloning value 2.
Conventional amplifiers add quantum noise to a signal. Both amplifiers and attenuators lead to a reduction of the signal-to-noise ratio. We find, however, that devices exhibiting squeezed fluctuations in the gain or loss medium lead to an improved signal-to-noise ratio, in one quadrature of the output, compared to the limits associated with conventional devices. We investigate amplifier and attenuator noise properties using a simple model in which the gain or loss medium is a broad-band reservoir in a specially prepared, or ‘rigged’, state.
In this thesis we examine linear amplification of squeezed light, the phase properties of squeezed light and the effect on the phase of light from linear amplification. Previous studies of linear amplifiers of light have shown that (i) when amplifying squeezed light the power gain must be less than 2 to preserve some squeezing in the output light; and (ii) a squeezed output cannot be generated from a non-squeezed input. However, these studies were restricted to a class of linear amplifier that can now be identified as not being squeezed. In this thesis we show how to breach the gain limit with a squeezed linear amplifier, and how to generate squeezed light using a squeezed linear attenuator.
Recently optical parametric amplifiers (OPAs) with vacuum inputs have been extensively studied and shown to generate a significant amount of squeezing, but little is known about the quantum noise behavior of an OPA with an injected signal field. We have performed a linearized quantum analysis of a nondegenerate OPA operated in the saturated gain regime showing that the amplified output intensity of a coherent-state input signal becomes squeezed when the classical small-signal gain falls below unity. In uses such as master-oscillator power amplifiers, for which the signal of interest is the mean output intensity, the output signal-to-noise ratio (SNR) can be higher than the input SNR over a broad operating range. For an OPA pumped at 90% of threshold, the SNR improvement is about a factor of 3, and with a 10-Db amplitude squeezed pump, the improvement increases to about a factor of 7. Such a tunable gain-saturated OPA with large-signal gain and improved SNR can be potentially useful in digital communication.
The squeezing, entanglement, and statistical properties of cavity modes produced by V-type three-level laser coupled to squeezed vacuum reservoir were studied employing the steady state solutions of the expectation values of the cavity mode operators. The study showed that a light in squeezing state can be produced by the system under consideration under the condition that the cavity decay constant is larger than linear gain coefficient and the squeezing occurs in the plus-quadrature. The cavity modes do not exhibit entanglement properties. It is also observed that the degree of squeezing increases with the linear gain coefficient and squeezing parameter. We also determined the mean and variance of the photon number, intensity difference fluctuations, and the second order correlation function of the two modes. The mean and variance of the photon number as well as the correlation function of two modes decrease as the difference of the probability of the two states at initial time increases. The photons have super-poissionian statistics. The point, η, at which the maximum intensity difference fluctuation occurred depends on linear gain coefficient but not squeezing parameter. The result shows that the correlation of the two modes decreases as η the linear gain coefficient and squeezing parameter.