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Acta Physica Sinica

Pancharatnam phase in interaction model of light and phonon

Liming Zheng, Faqiang Wang, Songhao Liu, (1)华南师范大学信息光电子科技学院，广州 510006; (2)暨南大学信息科学技术学院电子工程系，广州 510632

Published Jan 1, 2009• 0 citations
Publisher

Abstract

The Pancharatnam phase in simple polariton model is investigated, and the influences of temperature, coupling strength, frequency difference of photon and phonon and average photon number on the evolution dynamics of Pancharatnam phase are also discussed. The results show that the Pancharatnam phase oscillates with time, the oscillating frequency and wave-form vary with time, and the variation increases with the enhancement of temperature, coupling strength and frequency difference of photon and phonon. The system Pancharatnam phase evolutes regularly when the average photon number of coherent light is small, while it becomes more chaotic as the average photon number increases.

DOI
10.7498/aps.58.2884

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The Pancharatnam phase in simple polariton model is investigated, and the influences of temperature, coupling strength, frequency difference of photon and phonon and average photon number on the evolution dynamics of Pancharatnam phase are also discussed. The results show that the Pancharatnam phase oscillates with time, the oscillating frequency and wave-form vary with time, and the variation increases with the enhancement of temperature, coupling strength and frequency difference of photon and phonon. The system Pancharatnam phase evolutes regularly when the average photon number of coherent light is small, while it becomes more chaotic as the average photon number increases.
The Pancharatnam phase properties of two coupling-atoms and a single-mode squeezed state light field in nonlinear Kerr medium were studied.Selecting proper initial conditions to solve the Schrodinger equation by the rotating wave approximation,and the Pancharatnam phase specific form was obtained.The results show that the two coupling-atoms' initial states are in any form,the Pancharatnam phase frequency increases when the interaction strength between atoms and light field,and the dipole-dipole coupling strength between two atoms or the Kerr medium's nonlinearity increases.The Pancharatnam phase evolution shows obvious trend of oscillating and rising(or fall) when the initial state is that two atoms are both in the excited states.As the growth of the Kerr medium'nonlinearity,the Pancharatnam phase evolution becomes disordered when the initial state is that just one atom is in excited state.
The Pancharatnam phase of deformed Jaynes-Cummings(J-C) model was obtained analytically.The evolution of Pancharatnam phase for deformed Jaynes-Cummings model,was also discussed.The difference between the Pancharatnam phase evolution for deformed J-C model and that of conventional J-C model has been investigated.The results show that the Pancharatnam phase reveals some information of population reversion of an atom and the quantum nature of the cavity field.And the larger is the average photon number,the larger is the difference of Pancharatnam phase evolution between deformed J-C model and conventional J-C model.This exhibits that the evolution of Pancharatnam phase is closely relative to the quantum algebra structure of the system.
We study the phase evolution behaviour of coherent light interacting with phonons initially in thermal equilibrium at temperature T in terms of phase distribution probability. It is shown that the phase not only shifts but also diffuses. The phase distribution broadens and narrows periodically with time. There is a threshold in the variation of the width of phase distribution as a function of coupling coefficient in the detuning case for fixed temperature. The phase diffusion changes rapidly with temperature for coupling coefficient above the threshold while it changes little with temperature for coupling coefficient below the threshold.
The Pancharatnam phase of a Tavis-Cummings model with the coherent state in Kerr medium is investigated theoretically and numerically. An exact expression of the Pancharatnam phase under this general system is obtained. The numerical results show that the dipole-dipole coupling strength between two atoms can change the quasi-period of the Pancharatnam phase evolution,and it is also proved that the Pancharatnam phase contains the information of atoms and the field. In the nonlinear interaction regime, the nonlinearity can cause the chaotic behavior of the Pancharatnam phase.
In this paper, we have considered the polariton system described by the model effective Hamiltonian involving a single-mode photon field interacting with a transverse optical phonon in a more realistic form. On this basis, the dynamical evolution of the polariton system, and the quantum fluctuation and the non-classical properties for this system have been investigated in an analytic form. By the nonlinear interactions of the system, when the radiation field was initially in the coherent state and the polarization wave field in the vacuum state, the radiation field and the phonon field can be developed to the squeezed state with time evolution and their second-order squeezing oscillates with time evolution in a complex periodical form. When k1=0 or k2=0, the squeezed effects do not occur. The non-classical properties are determined by the nonlinear coupling of the system and depend on the existence of the k1 and k2 terms simultaneously. At the same time, it is shown that the new results indicate that the statistical distribution of the photon and phonon can oscillate between super-Poisson and sub-Poisson distribution with time evolution, the nonlinear terms k1(a++) and k2(a+b++ab) have contributions to the non-classical statistical feature.
We have set up a new reduced model Hamiltonian for the polariton system, in which the nonlinear interaction contains the rotating term k 1 (a + b + ab + ) and the attractive two-mode squeezed coupling −k 2 (a + b + +ab). The dynamical evolution of this system has been solved and the nonclassical features relevant to the second-order and high-order squeezing have been obtained in an analytical form. For the first time, in contrast to the existing result, we have confirmed for the phonon field that the attractive two-mode squeezed interaction will not only result in the second-order and high-order squeezing in X-component with the time evolution, but also in time average. Furthermore, the phenomena of collapse and revival of inversion will occur as well in the time evolution of the average number of photon and phonon, as also in the second-order and high-order squeezing of photon field, particularly, in the high-order squeezing of phonon field.