Many-photon antibunching in generalized pair coherent states

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Abstract
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.

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