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Quantum and Semiclassical Optics Journal of the European Optical Society Part B

Multiphoton antibunching in the photodetection of cavity radiation

Ching Tsung Lee

Published Dec 1, 1995• 1 citation
Publisher

Abstract

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.

DOI
10.1088/1355-5111/7/6/006

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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.
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.
Photon antibunching is a quantum phenomenon typically observed in strongly nonlinear systems where photon blockade suppresses the probability of detecting two photons at the same time. Antibunching has also been reported with Gaussian states, where optimized amplitude squeezing yields classically forbidden values of the intensity correlation, g(2)(0)<1{g}^{(2)}(0)<1g(2)(0)<1. As a consequence, observation of antibunching is not necessarily a signature of photon-photon interactions. To clarify the significance of the intensity correlations, we derive a sufficient condition for deducing whether a field is non-Gaussian based on a g(2)(0){g}^{(2)}(0)g(2)(0) measurement. We then show that the Gaussian antibunching obtained with a degenerate parametric amplifier is close to the ideal case reached using dissipative squeezing protocols. We finally shed light on the so-called unconventional photon blockade effect predicted in a driven two-cavity setup with surprisingly weak Kerr nonlinearities, stressing that it is a particular realization of optimized Gaussian amplitude squeezing.
Based on a classical inequality, which is a generalization by Muirhead [Proc. Edinburg Math. Soc. 21, 144 (1903)] of the arithmetic-geometric mean inequality, and the expression for factorial moments of photon numbers in the P representation, the concept of two-photon antibunching is extended to involve many photons from the same mode, or from two different modes, of the radiation field. A systematic study is carried out to examine the conditions for the existence of many-photon antibunching in pair coherent states introduced recently by Agarwal [J. Opt. Soc. Am. B 5, 1940 (1988)]. It is proved analytically that the intramode antibunching always exists and that intermode antibunching occurs whenever a certain condition is satisfied by the relevant parameters; otherwise, numerical study shows that it occurs only when the eigenvalue of the pair-annihilation operator is large enough. The pair coherent states are then generalized by using a more realistic initial condition for their generation through the competition of different nonlinear processes in a two-photon medium. It is again established analytically that intramode antibunching always exists in these generalized pair coherent states; and numerical study reveals the general features of the intermode antibunching.