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Journal of the Optical Society of America B

Conditions for nonclassical behavior in the light amplifier

C. K. Hong, Stephen R. Friberg, L. Mandeļ

Published Mar 1, 1985• 56 citations
Publisher

Abstract

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.

DOI
10.1364/josab.2.000494

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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.
We make a comparison between the necessary and sufficient conditions on the gain of the linear amplifier under which the light output exhibits sub-Poissonian photon statistics or squeezing and exact numerical results, obtained by solving the master equation by means of matrix procedures, and find good agreement. We find numerically that higher-order squeezing persists in a region in which sub-Poissonian statistics and second-order squeezing have already disappeared, for certain parameter ranges of input binomial states.
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.
A parameteric study was performed of the sub-Poissonian photon statistics and higher-order squeezing characteristics of Bernouilli states undergoing a linear amplification process. The necessary and sufficient conditions on the amplifier gain under which the output light exhibits sub-Poissonian photon statistics or squeezing were compared with exact numerical results, and good agreement was obtained. On the other hand, it was shown that Bernouilli states exhibit higher-order squeezing for some parameter ranges. The degree of higher-order squeezing decreases, and its duration becomes shorter, as the phase of the Bernouilli state increases.
We consider nonclassical properties of the field at the output of an amplifier under the operational condition that the output exhibits neither squeezing nor sub-Poissonian statistics but has the nonclassical P function. We also present explicit results for the output P function when the input is strictly a quantum-mechanical state similar to a Fock state. The nonclassical properties of the marginal distribution associated with the output are derived. The domain where the marginal distribution remains nonclassical is different from the domain over which the output P function is nonclassical. The amplifier is shown to be a useful device for direct measurements of the quasiprobabilities.
The statistical fluctuations of light can, under certain circumstances, exhibit a number of interesting nonclassical features. These include photon antibunching, sub-Poissonian statistics, and squeezing, all of which exist only in a quantum field. The three effects are distinct, and do not necessarily go together, although the first two are sometimes mistakenly treated as interchangeable. Both photon antibunching and sub-Poissonian statistics have been observed in experiments on resonance fluorescence from single atoms, which is described. Squeezing has not yet been seen experimentally, although many nonlinear processes are expected to give rise to it. The squeezed state can be recognized in heterodyne or homodyne experiments, where the squeezing becomes manifest as sub-Poissonian photon fluctuations.
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.