IOP PUBLISHING JOURNAL OF PHYSICS B: ATOMIC, MOLECULAR AND OPTICAL PHYSICS J. Phys. B: At. Mol. Opt. Phys. 40 (2007) 2901–2916 doi:10.1088/0953-4075/40/14/009 Squeezing, photon bunching, photon antibunching and nonclassical photon statistics in degenerate hyper Raman processes Biswajit Sen and Swapan Mandal Department of Physics, Visva-Bharati, Santiniketan-731235, West Bengal, India Received 27 April 2007, in final form 11 June 2007 Published 5 July 2007 Online at stacks.iop.org/JPhysB/40/2901 Abstract 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. 1. Introduction With the help of nonlinear matter–field interactions, we have invented a large variety of new laser sources in last fifty years. The advent of these new laser sources has enriched the subject of nonlinear optics, laser spectroscopy and quantum optics. In particular, the nonclassical properties of the radiation field coupled to a nonlinear medium are extremely interesting from the fundamental and the practical points of view. For example, the squeezed states [1–9] which are regarded as the nonclassical states of the radiation field could be used in gravitational wave detection [1, 2], noise-free transmission of signals and of course in the field of emerging area of quantum information theory. The photon antibunching [10–22] is an important nonclassical property of the radiation field which can be used to devise single-photon sources. The single- photon source is perhaps the key requirement for quantum information theory. Therefore, in 0953-4075/07/142901+16$30.00 © 2007 IOP Publishing Ltd Printed in the UK 2901