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Acta Physica Sinica

The time-revolution of the quantum fluctuation and the nonclassical statistical behavior for the polariton system

YU Xiao-min, Liang Guo-Dong, Yanhua Zhong, (1)暨南大学物理系，广州 510632; (2)江门职业技术学院计算机系，江门 529020

Published Jan 1, 2006• 2 citations
Publisher

Abstract

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.

DOI
10.7498/aps.55.2128

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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.
Quantum statistical properties are derived for stimulated Raman scattering by squeezed phonons including squeezing of vacuum fluctuations in radiation modes and sub-Poisson photon behaviour.Initial radiation can be in squeezed thermalized and/or sub-Poisson states, phonon system can also be squeezed.In particular, effects of initial phase conditions, losses, initial nonclassical behaviour and phonon squeezing are demonstrated in terms of reduced factorial moments up to the fifth order in combined photon-photon and photon-phonon modes.Also photon number distribution, quadrature variances and principał squeeze parameters are shown.
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.
Microcavity polaritons are a hybrid photonic system that arises from the strong coupling of confined photons to quantum-well excitons. Due to their light-matter nature, polaritons possess a Kerr-like nonlinearity while being easily accessible by standard optical means. The ability to engineer confinement potentials in microcavities makes polaritons a very convenient system to study spatially localized bosonic populations, which might have great potential for the creation of novel photonic devices. Careful engineering of this system is predicted to induce Gaussian squeezing, a phenomenon that lies at a heart of the so-called unconventional photon blockade associated with single photon emission. This paper reveals a manifestation of the predicted squeezing by measuring the ultrafast time-dependent second-order correlation function g(2)(0) by means of a streak-camera acting as a single photon detector. The light emitted by the microcavity oscillates between Poissonian and super-Poissonian in phase with the Josephson dynamics. This behavior is remarkably well explained by quantum simulations, which predict such dynamical evolution of the squeezing parameters. The paper shows that a crucial prerequisite for squeezing is presence of a weak, but non-zero nonlinearity. Results open the way towards generation of nonclassical light in solid-state systems possessing a single particle nonlinearity like microwave Josephson junctions or silicon-on-chip resonators.