Photon Correlations in Multi-photon Raman Processes

Lower- and higher-order nonclassical features in non-degenerate hyper-Raman processes

“…In fact, hyper-Raman scattering represents a very interesting nonlinear optical process as it allows self-interaction of the pump modes and thus leads to the generation of different types of nonclassicality. Specifically, the presence of antibunched, sub-Poissonian and squeezed light in the degenerate hyper-Raman processes has already been reported in the past [12,[19][20][21]. However, only antibunching in the photon and phonon modes of its nondegenerate counterpart have been reported until now [23].…”

“…Among these Raman processes non-degenerate hyper-Raman process is most general in nature as the Hamiltonians of spontaneous and stimulated Raman scattering and nondegenerate hyper-Raman process (in the simplest case which can be viewed as a 3 photon analogue of stimulated Raman scattering [12]) can be obtained as limiting cases of it. Nonclassicality in spontaneous and stimulated Raman scattering (see [13][14][15][16] and references therein, Section 10.4 of [17] and [18] for reviews) and non-degenerate hyper-Raman processes [12,[19][20][21] has already been studied in detail. However, nondegenerate hyper-Raman process has not yet been investigated rigorously because of its inherent mathematical complexity and the potential difficulties associated with the experimental realization of this process.…”

“…Motivated by the above, to investigate the possibilities of observing nonclassical features in non-degenerate hyper-Raman process (illustrated in Figure 1), a completely quantum mechanical description of the system is used here to construct a Hamiltonian of the system. To obtain a closed analytic expression for the time evolution of each mode involved here, we have used Sen-Mandal perturbative technique ( [15,[39][40][41] and references therein), which is known to be a superior method compared to the corresponding short-time technique [17,20,42]. Further, we have established the general nature of the obtained solution by obtaining the existing Sen-Mandal solutions of Raman and degenerate hyper-Raman processes [12][13][14][15][16], (as limiting cases of the solution obtained here) which were already reduced to corresponding short-time solutions in the past [17,20,42].…”

“…To obtain a closed analytic expression for the time evolution of each mode involved here, we have used Sen-Mandal perturbative technique ( [15,[39][40][41] and references therein), which is known to be a superior method compared to the corresponding short-time technique [17,20,42]. Further, we have established the general nature of the obtained solution by obtaining the existing Sen-Mandal solutions of Raman and degenerate hyper-Raman processes [12][13][14][15][16], (as limiting cases of the solution obtained here) which were already reduced to corresponding short-time solutions in the past [17,20,42]. Subsequently, the obtained time evolution of all the photon and phonon modes has allowed us to use a finite set of moments-based criteria [43] to establish the highly nonclassical behavior of the hyper-Raman processes.…”

Quantum-statistical properties of a Raman-type model

“…The model systems associated with the Hamiltonian of Eq. (1) have been examined using various techniques, such as numerical solution [17,18], operator linearization method [19], and the short-time approximation [20]. The Heisenberg dynamical equations have been solved exactly [21] by applying some iterative procedure.…”