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Modern Physics Letters B

PHOTON-BUNCHING, PHOTON-ANTIBUNCHING AND NONCLASSICAL PHOTON STATISTICS OF COHERENT LIGHT COUPLED TO A CUBIC NONLINEAR MEDIUM

Anirban Pathak, Swapan Mandal

Published Mar 10, 2003• 13 citations
Publisher

Abstract

The quantum statistical properties of a single mode of the radiation field, prepared in the coherent state, interacting with a nonlinear medium of inversion symmetry are studied with the help of the usual two photon correlation function for zero time delay. We report the photon antibunching and sub-Poissonian photon statistics in addition to the usual photon bunching and the super-Poissonian photon statistics for an input vacuum field. The manipulation of the phase of input coherent light gives rise to the well known self induced transparency. The possible physical explanations for these events are presented.

DOI
10.1142/s0217984903005123

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The quantum statistical properties of a single mode of the radiation field, prepared in the coherent state, interacting with a nonlinear medium of inversion symmetry are studied with the help of the usual two photon correlation function for zero time delay. We report the photon antibunching and sub-Poissonian photon statistics in addition to the usual photon bunching and the super-Poissonian photon statistics for an input vacuum field. The manipulation of the phase of input coherent light gives rise to the well known self induced transparency. The possible physical explanations for these events are presented.
The initially prepared coherent state coupled to a third-order nonlinear medium is responsible for stimulated Raman and spontaneous Raman processes. By exploiting the analytical solutions of field operators for various modes, we investigate the quantum statistical properties for pure and two modes of the input coherent light responsible for stimulated Raman and spontaneous Raman processes. For spontaneous Raman processes the photons are unbunched for the pure and two-mode cases. By a suitable choice of phase, we obtain the bunching and antibunching of photons for stimulated Raman processes.
Under the assumption of strong (classical) pump condition, the coherent light interacting with a medium of second-order nonlinearity gives rise to a model represented by a quadratic Hamiltonian. By exploiting this model, we obtain the squeezing and the higher-order squeezing of the input coherent light. These phenomena are found to depend on the classical intensity but do not depend on the number of photons present in the input coherent radiation field. For the same physical model, it is found that the photons are bunched in the input vacuum field provided that two-photon processes dominate over one-photon processes. Depending on the suitable choice of phases and interaction time, we show both photon bunching and photon antibunching phenomena for the vacuum field and for the field with a large number of photons as well. The results obtained in this paper are completely analytical in nature and provide a feeling for the physical situation in an explicit manner.
A review is given of recent theoretical studies devoted to the problem of generating radiation fields that exhibit the opposite of the well-known bunching of photons observed in light from thermal sources, the so-called antibunching effect. It is made clear that this phenomenon reflects the corpuscular nature of light and, hence, cannot be interpreted in terms of classical electrodynamics, needing, instead, the quantum-mechanical formalism for its description. It is shown in some detail that nonlinear interaction mechanisms like multiphoton absorption and parametric three-wave interaction are suited to change the photon statistical properties of incident (in most cases coherent) light such that the output field will be endowed with antibunching properties. Special emphasis is given to the problem of correctly specifying the dimensions of the mode volume occurring in the usual single-mode treatment of the field, which is, in fact, of great practical interest, since the magnitude of the antibunching effect is determined by the inverse average number of photons contained in that volume. In a later section it is pointed out that destructive interference with a coherent reference beam provides a means of (a) effectively enhancing photon antibunching that is already present in a high-intensity field, through reduction of the intensity, and (b) transforming phase fluctuations produced in a Kerr medium into antibunching-type intensity fluctuations. On the other hand, there exists a way of directly generating light with antibunching properties, the physical mechanism being resonance fluorescence from a single atom. The main features of this technique, both theoretical and experimental, are outlined, including a discussion of the first experimental results obtained a few years ago.
An initially prepared coherent state coupled to a second-order nonlinear medium is responsible for stimulated and spontaneous hyper Raman processes. By using an intuitive approach based on perturbation theory, the Hamiltonian corresponding to the hyper Raman processes is analytically solved to obtain the temporal development of the field operators. It is true that these analytical solutions are valid for small coupling constants. However, the interesting part is that these solutions are valid for reasonably large time. Hence, the present analytical solutions are quite general and are fresh compared to those solutions under short-time approximations. By exploiting the analytical solutions of field operators for various modes, we investigate the squeezing, photon antibunching and nonclassical photon statistics for pure modes of the input coherent light responsible for hyper Raman processes. At least in one instance (stimulated hyper Raman processes for vibration phonon mode), we report the simultaneous appearance of classical (photon bunching) and nonclassical (squeezing) effects of the radiation field responsible for hyper Raman processes.
The study investigates antibunching, sub-Poissonian statistics, and photon correlation functions in the pump and harmonic modes of the seventh harmonic generation process.We investigated various approaches to photon antibunching by solving the generalised interaction Hamiltonian in the Heisenberg picture using short-time approximation.It is inferred that the number of pump photons, coupling of the field strength, and interaction times significantly influence photon antibunching.It is observed that third-order antibunching in the pump mode has greater nonclassicality than second-and first-order antibunching.In the harmonic mode, the nonclassical effect is found to be less pronounced and becomes more evident as the interaction time decreases.The first-order Hamiltonian interaction induces a stronger nonclassical effect than the second-order interaction.The interaction of a coherent pump field with a nonzero harmonic field leads to photon clustering and bunching effects.Finally, photon antibunching appears most pronounced, indicating nonclassicality, as the second-order correlation function decreases.This confirms that antibunching is a fundamental quantum property of light.
We study the statistical properties of squeezed Kerr states generated by squeezing, with a two-photon parametric process, the output of a Kerr medium whose input is coherent light. The squeezing has the effect of allowing the photon statistics to depend on the Kerr nonlinearity. Without the squeezing the statistics are Poissonian, but after squeezing they may be either sub-Poissonian or super-Poissonian. We also study the Q-function quasiprobability distribution for these states and related distributions associated with the quantum-mechanical phase. Finally, we show that quadrature squeezing can be enhanced and that squeezing and sub-Poissonian statistics can coexist.