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Journal of Physics B Atomic Molecular and Optical Physics

Squeezing, photon bunching, photon antibunching and nonclassical photon statistics in degenerate hyper Raman processes

Biswajit Sen, Swapan Mandal

Published Jul 5, 2007• 10 citations
Publisher

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.

DOI
10.1088/0953-4075/40/14/009

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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 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.
A perturbative analytic operator solution of a completely quantum mechanical Hamiltonian of multi-photon pump non-degenerate hyper-Raman process is obtained. It is shown that the obtained solution is general in nature as the solutions of non-degenerate hyper-Raman and stimulated Raman processes can be obtained as special cases of the present solution. The analytic solutions obtained here are used to investigate the nonclassical properties of the different modes in the stimulated, spontaneous and partially spontaneous multi-photon pump non-degenerate hyper-Raman processes. The nonclassical nature of these processes is witnessed by means of single mode and intermodal quadrature squeezing, intermodal entanglement of different orders, lower order and higher order photon antibunching. Interestingly, manifesting the multiphoton nature of the pump modes, a bunch of nonclassicality involving them are observed due to self-interaction of various pump modes.
The Hamiltonian and the equations of motion for various modes involving spontaneous and stimulated Raman processes are derived. The coupled differential equations involving these modes are solved analytically by using an intuitive approach (IA). The solution of the present paper does not require any short time approximation. As a matter of fact, the present solution for field operators and hence the squeezing for various modes are valid for all interaction time t. In this way, the present paper is more general compared to the earlier investigations where short-time approximations were found a must. By exploiting the solutions for the field operators, we obtain the squeezing effects of input coherent light for pure and for mixed field modes. The IA employs the perturbation theory and hence we came across the secular terms in the solution. Of course, for small coupling constants these secular terms could be summed for all orders. To establish our claim, we remove the secular terms at least for one occasion.
The nonclassical effect of squeezing of light in hyper-Raman processes is investigated under the short-time approximation based on a fully quantum mechanical approach. Effects of squeezing in spontaneous and stimulated processes are studied. A hyper-Raman process is looked upon as a three-photon and one-phonon interaction process. Squeezing in amplitude, squared amplitude and cubed amplitude have been investigated. Squeezing occurs invariably in the fundamental mode in both spontaneous and stimulated processes, whereas the squeezing in the Stokes mode is found to be dependent on amplitude-squared squeezing of the initial pump field.
Coherent light coupled to a third-order nonlinear medium is responsible for spontaneous and for stimulated Raman processes. The analytical solutions up to second order in coupling constants of various field modes for spontaneous Raman and for stimulated Raman processes are utilized to obtain the amplitude-squared and amplitude-cubed squeezing of the input coherent light. The amplitude-squared and amplitude-cubed squeezing are completely ruled out for all modes for spontaneous Raman processes. For stimulated Raman processes, we observe that the squeezing for amplitude-squared and amplitude-cubed are possible for pump and for vibrational phonon modes. It is found that the percentage of higher ordered amplitude squeezing decreases with the increase of the orders. The squeezing in Stokes and in anti-Stokes modes are ruled out even for stimulated Raman processes.
The light initially prepared in a coherent state runs the stimulated and spontaneous Raman processes in a second-order nonlinear medium. Using analytical expressions of field operators for the light modes, we determine the quantum statistical properties of the modes in the stimulated and spontaneous Raman processes. By a choice of phase, we obtain a boson-pair property correlating the pump and vibration modes and such a property correlating the pump and anti-Stokes modes. The Stokes and vibration modes exhibit the boson-pair property for all initial phase differences between the pump mode and the other ones. In the spontaneous Raman process only the Stokes and vibration modes show such a property.