Maximum photon antibunching in generalized coherent states

Hari Prakash, Pankaj Kumar

Ching Tsung Lee

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.

S. Sivakumar

Rupesh Singh, Dilip Kumar Giri

We studied photon antibunching in the pump and the harmonic modes of the sixth harmonic generation process. The generalized interaction Hamiltonian is solved for several particular cases in the Heisenberg picture, and the possibility of observing photon antibunching is investigated using the short-time approximation technique. It is shown that the photon antibunching in the pump field depends on the number of pump photons, the interaction time, and the coupling of the field between the modes. With the same amount of pump photons, we deduced that third-order photon antibunching is more nonclassical than second- and first-order photon antibunching. In this process, the effect of photon antibunching is not seen in the harmonic mode over pump mode. It is shown that photon antibunching is more noticeable with shorter interaction times as the depth of nonclassicality increases and the second-order correlation function decreases. The first-order Hamiltonian interaction, which stimulates both pump and harmonic fields, is demonstrated to be more nonclassical than the second-order Hamiltonian interaction. It is clear that the coherent state, or vacuum state, of a pump field with a nonzero harmonic field creates photon clusters because the pump field causes interaction, which leads to bunching effects. It is interpreted that the degree of photon antibunching is maximum in the regions where the second correlation function is minimum. Photon antibunching has been shown to be one of the quantum properties of light.

Ching Tsung Lee

Based on inequalities derived from the partial ordering by majorization, some higher-order criteria for the existence of nonclassical effects in photon statistics are introduced. These generalize the well-known concept of two-photon antibunching to many-photon antibunching. The photon-number distribution of the famous two-photon coherent state is used to illustrate these new criteria.

雅斗 小芦