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Physical Review A

Nonclassical effects and antibunching in the external photodetection of cavity radiation

Ching Tsung Lee

Published Apr 1, 1995• 2 citations
Publisher

Abstract

The nonclassical effects of radiation are defined to be when its P function [R. J. Glauber, Phys. Rev. Lett. 10, 84 (1963)] is not positive definite, and antibunching is defined to be when the conditional waiting time in the photodetection is longer than the unconditional one. Based on these two definitions, it is proven rigorously that antibunching implies nonclassical effects of cavity radiation detected externally by an imperfect detector.

DOI
10.1103/physreva.51.3386

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The nonclassical effects of radiation are defined to be when its P function [R. J. Glauber, Phys. Rev. Lett. 10, 84 (1963)] is not positive definite, and antibunching is defined to be when the conditional waiting time in the photodetection is longer than the unconditional one. Based on these two definitions, it is proven rigorously that antibunching implies nonclassical effects of cavity radiation detected externally by an imperfect detector.
A simple model is introduced to simulate the detection of cavity radiation with the detector placed outside the cavity. Explicit expressions, in terms of initial photon-number distribution, for the time-dependent distributions of photoelectron number and conditional as well as unconditional waiting times are derived. The effect of photodetection on the quantum state of the radiation in the present arrangement is found to be unchanged from that with the detector placed inside the cavity. The well-known Q parameter introduced by Mondel [Opt. Lett. 4, 205 (1979)] is found to be exactly equal to the change in the expectation value of photon number due to the detection of a photon. Photon bunching or antibunching, reflecting classical or nonclassical radiation, is determined by whether conditional waiting time is less or greater than unconditional waiting time. When this criterion is applied to three specific examples, namely, coherent, thermal, and number states, the results are as expected.
Antibunching is defined to be when the conditional waiting time in the photodetection is longer than the unconditional one. However, when this criterion is used on the waiting times for the closed-system detection of one photon from the so-called odd-shadowed thermal state, it shows no antibunching, although the state is proven to be non-classical. It does show antibunching in the waiting times for two-photon detection. This provides the motivation for extending the concept of photon antibunching to the detection of more than one photon. The general expressions for the expectation values of unconditional and conditional waiting times for multiphoton detection are derived. Then it is rigorously proven that multiphoton antibunching implies non-classicality which is defined to be when the P function is not positive definite.
A simple difference-differential equation derived by Scully and Lamb [Phys. Rev. 179, 368 (1969)] is used to describe the photoelectric detection of the radiation in a cavity totally isolated except for its interaction with the detector. As results of the solution, the expressions for the distributions of unconditional and conditional waiting times are obtained. Based on the definition that we have antibunching whenever the conditional waiting time is greater than the unconditional waiting time, the criterion for the occurrence of antibunching is established.
Experiments on nonclassical optical fields have recently been performed. One of the main properties reported is the antibunching effect of photoelectrons, a property that cannot be explained in the framework of the classical theory of optical fields. By carefully studying the random point process of the detection of the optical field, we show that bunching and antibunching effects can be fully explained by a concidence function. In the classical theory, this function is a correlation function which introduces necessarily a bunching effect. But this coincidence function has no reason to be in any case a correlation function. Therefore antibunching effects can simply be derived from the properties of the coincidence function. After having given a precise definition of this coincidence function, some of its properties are discussed and especially its relationship with bunching and antibunching effects. Similarly, its relationship with statistical properties of lifetimes and intervals between points of the process is established. Various examples are presented and analyzed. Several calculations and computer simulations highlight the theoretical results.
In 1963 Glauber /Phys. Rev. 130, 2529 and 131, 2766/ published a basic theoretical study that revealed the broad variety of possible photon states. Later on a quantum-statistical analysis showed that states with classical analog (this light Is termed classical light) as well as states without classical analog (so-called nonclassical light) can occur. Following the definition given by Teich, Saleh, and Perina /JOSAB2 (1985) 275) nonclassical light exhibits one or more of the attributes squeezed, antibunched, sub-Poissonian, what is connected with a negative value of the field-fluctuation excess, the bunching excess, or the Poisson excess. These negative values mean quantum fluctuations below the classical standard quantum limits of ideal laser light; thus, nonclassical light may yield an essential improvement of the optical measurement accuracy, in particular of the signal-to-noise ratio. There exists a common property of the three attributes concerning the Glauber-Sudarshan representation P(c ), which is the real weight function belonging to the incoherent mixture (density operators) of Glauber states with different complex amplitudes. In the case of classical light P(oç ) is a positive definite function, whereas nonclassical light requires a nonpositive definite function P(o.), which cannot be interpreted as a proper probability distribution - as it is possible in the case of light with a classical analog /M. Schubert, Ann. d. Phys. 4k (1987) 53/. In addition to its possible important applications nonclassical light yields a deep insight into the quantum nature of the radiation field.
A model for photodetection is presented which permits evolution of the detected field during the detection process. The integrated univariate and bivariate statistics of the photocount are obtained exactly for detection of single-mode thermal, coherent and free-field cavity radiation. The scheme encompasses the results of three hitherto disparate photocounting models, and demonstrates explicitly the relation between the univariate photon counting statistics and the photon statistics of the field. First-order photocount correlation functions are derived and compared with the corresponding cavity photon population correlations. Photocount antibunching is examined and found to be possible in this model.