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Journal of the Optical Society of America B

Rigged-reservoir response III Multiatom squeezed states

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

Published Jul 1, 1987• 45 citations
Publisher

Abstract

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.

DOI
10.1364/josab.4.001124

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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.
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.
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.
In our work, we show how, for a network of bosonic modes, canonical commutation relations constrain the coefficients relating input and internal modes. Based on these constraints, we derive a lower bound on the total steady-state squeezing achievable in reservoir-engineered (dissipative) squeezing schemes, quantified by the sum of mode-optimal quadrature variances normalized to its corresponding input variance. The bound follows solely from canonical commutation relations and stability, and is saturated in the strong-coupling limit at 1. Furthermore, we show that adding independent parametric driving terms for each mode changes the quantum noise-gain balance and yields a distinct optimum bound, approaching 1/2. In addition, we show how these constraints allow us to reformulate the Duan inseparability criterion for a three-mode bosonic system in terms of a single parameter-dependent figure of merit. Our results apply directly to current electromechanical and nanomechanical experiments and indicate that the two-mode bounds can be experimentally approached even at room temperature.
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.
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.