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Annual Meeting Optical Society of America

Exception to the cloning limit—amplification of amplitude-squared squeezed states

Mark S. Hillery, D. Yu

Published Jan 1, 1991• 0 citations
Publisher

Abstract

An amplifier consists of a collection of inverted two-level atoms. It can be used to amplify a light signal but in the process the fluctuation behavior of the lights will be modified. In particular, for sufficiently large gains, nonclassical input states will become classical at the output. Hong, Friberg, and Mandel examined the effect of amplification on sub-Poissonian photon statistics and normal squeezing. They found that both of these effects disappear at the output if the intensity gain |G|2 > 2. The gain |G|2 = 2 is known as the photon cloning limit because one gets two photons out for every one that goes in. This gain has stood as an upper limit for the amplification of nonclassical behavior.

DOI
10.1364/oam.1991.moo3

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Annual Meeting Optical Society of America•Jan 1, 1991•0 citations
An amplifier consists of a collection of inverted two-level atoms. It can be used to amplify a light signal but in the process the fluctuation behavior of the lights will be modified. In particular, for sufficiently large gains, nonclassical input states will become classical at the output. Hong, Friberg, and Mandel examined the effect of amplification on sub-Poissonian photon statistics and normal squeezing. They found that both of these effects disappear at the output if the intensity gain |G|2 > 2. The gain |G|2 = 2 is known as the photon cloning limit because one gets two photons out for every one that goes in. This gain has stood as an upper limit for the amplification of nonclassical behavior.
We examine the phase-insensitive amplification of three different kinds of higher-order squeezing. In particular, we consider fourth-order squeezing, intrinsic fourth-order squeezing, and amplitude-squared squeezing. It is found that for any input state both fourth-order squeezing and intrinsic fourth-order squeezing disappear at the output if the intensity gain is greater than 2. Amplitude-squared squeezing, on the other hand, can survive amplification at gains slightly greater than 2. Therefore the photon-cloning limit (intensity gain equals 2) is not a fundamental limit to nonclassical behavior.
The necessary and sufficient conditions on the gain of the linear amplifier are determined under which the light output exhibits sub-Poissonian photon statistics or squeezing. It is found that for these effects the intensity gain must not exceed 2 under any circumstances. It is also shown that there exists a weaker sufficiency condition on the gain above which all nonclassical features of the field disappear. This suggests the possibility that other quantum effects may persist in the intermediate, still unexplored, domain of operation of the amplifier.
Various authors have shown that for a particular type of atomic light amplifier, which can be identified as an unsqueezed amplifier, squeezing in the output is destroyed for gains greater than 2, and if the input is classical light then there are no non-classical effects (squeezing or sub-Poisson photon statistics) in the output for any value of the gain; however, these results are not necessarily true for a squeezed amplifier. Here we investigate single-stage and multi-stage squeezed atomic light amplifiers and show that the above non-classical effects can occur even with a coherent-state input. We find that the output of a multistage squeezed amplifier can be squeezed in principle for any desired gain, and that when this amplifier is used as an attenuator, output light can in principle be produced with any desired amount of squeezing for any input.
We study statistical properties of quantum superposition states (Schr\"odinger-cat states) amplified by phase-sensitive (squeezed) amplifiers. We show that the phase-sensitive amplifier with a properly chosen phase can preserve quantum coherences and nonclassical behavior of the Schr\"odinger-cat-state input even for a gain factor G larger than 2. In particular, we show that for an even coherent state (CS) phase-sensitive amplifiers can preserve squeezing for G>2 but simultaneously in the process of amplification the noise added by the amplifier leads to a rapid increase of fluctuations in the photon number. Because of the finite maximum degree of squeezing obtainable for the even CS the maximum gain factor Gm{\mathit{G}}_{\mathit{m}}Gm​ for which squeezing can still be observed in the output state is finite. The phase-sensitive amplifier with a properly chosen phase can also reduce fluctuations in the photon number of the initial even CS. Nevertheless, one cannot amplify the initial even CS with super-Poissonian photon statistics into the state with sub-Poissonian photon statistics.
It has long been known that amplification will degrade an optical signal and will rapidly destroy any intrinsically quantum features that may have been associated with the input. However, devices that exhibit squeezed fluctuations in the gain or loss medium can reduce the detrimental effects of the inevitable amplifier noise. This makes it possible to retain nonclassical features (in particular squeezing) at higher levels of gain than is possible in conventional devices. In this paper we study the effect of these amplifiers on the photon-number fluctuations. We find that, for suitable inputs, phase-sensitive amplifiers can reduce the tendency for the photon-number distribution to spread and allow us to retain sub-Poissonian statistics at a higher level of gain than is possible in conventional devices.
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.