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Journal of the Optical Society of America B

Statistical properties of multiphoton time-dependent three-boson coupled oscillators

M. Sebawe Abdalla, Jan Peřina, J. Křepelka

Published Jun 1, 2006• 10 citations
Publisher

Abstract

We investigate the quantum statistics of three time-dependent coupled oscillators in the presence of multiphoton processes. The system is connected with the two-atom multiphoton Tavis-Cummings model. The solution of the Heisenberg equations of the motion is obtained in a compact form. We assume that the modes are initially prepared in coherent states, and we discuss nonclassical phenomena (squeezing and sub-Poissonian behavior). Further, we examine the joint quasi-distribution functions as well as photon-number distribution and its factorial moments. The system has shown that the nonclassical effect is apparent in compound modes (1,3) and (2,3). Moreover, the superstructure phenomenon is observed when the photon transition is increased.

DOI
10.1364/josab.23.001146

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We investigate the quantum statistics of three time-dependent coupled oscillators in the presence of multiphoton processes. The system is connected with the two-atom multiphoton Tavis-Cummings model. The solution of the Heisenberg equations of the motion is obtained in a compact form. We assume that the modes are initially prepared in coherent states, and we discuss nonclassical phenomena (squeezing and sub-Poissonian behavior). Further, we examine the joint quasi-distribution functions as well as photon-number distribution and its factorial moments. The system has shown that the nonclassical effect is apparent in compound modes (1,3) and (2,3). Moreover, the superstructure phenomenon is observed when the photon transition is increased.
In this paper, we treat the problem of the multi-photon Tavis–Cummings classically, where the effect of time-dependence takes place. Under certain integrability conditions the time-dependent wave function in the Schrodinger picture is obtained. Some statistical properties of the system are discussed based on the solution for the equations of motion in the Heisenberg picture. Using the atomic coherent state as a basis, the phenomenon of squeezing is observed in the quadrature variances Fx and Fy; however, it was pronounced in the quadrature Fy. The phenomenon of squeezing is also reported for the usual atomic state case where squeezing is only observed in the first quadrature Fx. An examination of the correlation function using the atomic state showed us that the system is sensitive to variation in the integrability parameter β. The nonclassical effect is also found to be pronounced for small values of the parameter β.
Quantum-statistical properties such as the photon-number probability distribution and sub-Poissonian distribution are studied by considering the resonant interaction of two radiation fields, one of which is in a squeezed state with a cascade-structure three-level atom. It is noteworthy to emphasize that the direction of squeezing, i.e., the angle \ensuremath{\theta}, and the squeezing parameter r as well as the initial atomic state play important roles in the determination of the nonclassical behavior of the radiation field. At the same time we give a possible explanation for the effect of the ratio of the intensity of the two fields on the quantum-statistical properties.
Multiphoton interaction of single-mode squeezed-state light and a two-level atom is considered based on the K-photon Jaynes–Cummings model. Time evolution of quantum fluctuation and photon statistical properties of the initial squeezing light are discussed. It is found that through interaction with a two-level atom, larger squeezing levels cannot be achieved in one-photon or multiphoton processes. For photon antibunching behavior of the light field, it is shown that a smaller initial squeezing level and an appropriately larger coherent part of the initial average photon number of the radiation field favor the generation of this nonclassical behavior, especially in the lower-order interaction processes.
We investigate the quantum statistics of three harmonic oscillators mutually interacting with each other determining quadratures squeezing, second-order correlation function and phase space distributions. We assume that the modes are initially prepared in coherent states. We show that the initial coherent states can evolve into squeezed states which are not minimum uncertainty states governed by the interaction parameters. Moreover, we demonstrate that the interaction is able to produce squeezing of different types, i.e. single-mode, two-mode and three-mode squeezing. Further, we show for specific modes and under certain conditions the oscillatory behaviour in the photon-number distribution and the bifurcation phenomenon in the phase distribution for squeezed light.
The quantum properties of atoms in Gaussian coupling Tavis-Cummings model in the multi-photon transition process are studied.The influence on atomic population inversion and double-atom dipole squeezing from atomic motion,the mean photon number in initial states of the light field,number of transition photons in the multi-photon transition process are discussed with the numerical calculation method.The results show that the variation of atomic motion changes the time for effective action between atomic population inversion,double-atom dipole squeezing and fight field.The variation of number of transition photons changes oscillation amplitude and frequency of time evolution of atomic population inversion and double-atom dipole squeezing.