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AIP conference proceedings

Generation and decay of entanglement in exciton∕polariton trapped systems

Luis Quiroga, C. Tejedor, Jisoon Ihm, Hyeonsik Cheong

Published Jan 1, 2011• 0 citations
Publisher

Abstract

The entanglement evolution of interacting trapped solid‐state bosons, i.e. excitons or polaritons, is theoretically studied. From an initially separable state the quasi‐particle interactions generate boson entanglement which is degraded as dissipation takes place. Based on exact solutions of a Markovian Master equation at T = 0 K, we discuss how dissipation affects the quantum entanglement dynamics of coupled solid‐state boson systems. The single trap Wigner function is also calculated and its relationship to the trapped boson entanglement is discussed.

DOI
10.1063/1.3666733

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The entanglement evolution of interacting trapped solid‐state bosons, i.e. excitons or polaritons, is theoretically studied. From an initially separable state the quasi‐particle interactions generate boson entanglement which is degraded as dissipation takes place. Based on exact solutions of a Markovian Master equation at T = 0 K, we discuss how dissipation affects the quantum entanglement dynamics of coupled solid‐state boson systems. The single trap Wigner function is also calculated and its relationship to the trapped boson entanglement is discussed.
We study in detail the generation and relaxation of quantum coherences (entanglement) in a system of coupled polariton traps. By exploiting a Lie algebraic based super-operator technique we provide an analytical exact solution for the Markovian dissipative dynamics (Master equation) of such system which is valid for arbitrary cluster size, polariton-polariton interaction strength, temperature and initial state. Based on the exact solution of the Master equation at T = OK, we discuss how dissipation affects the quantum entanglement dynamics of coupled polariton systems.
We study the dynamics of two‐bosonic condensates of exciton–polaritons confined in coupled elliptical traps. Within the mean field approximation the system is described by a generalized two‐body Schrödinger equation that accounts for the pumping of polaritons to the coupled condensates from two independent exciton reservoirs. The system is conveniently described by a truncated 4 x 4 density matrix. Applying a pair of control optical pulses, we demonstrate how coherent interactions between the condensates transform the system from an initial separable pure state with zero entanglement (negativity = 0) to an entangled state characterized by negativity close to 0.5. This study underscores the high potentiality of exciton–polariton systems for analog and quantum simulations and paves the way for the realization of ultrafast, many‐body quantum computation platforms.
We describe the evolution of the quantum entanglement in a system composed of two interacting bosonic modes immersed in a thermal reservoir, in the framework of the theory of open systems based on completely positive quantum dynamical semigroups. The evolution of entanglement is described in terms of the covariance matrix for Gaussian initial states. We calculate the logarithmic negativity and show that for separable initial squeezed thermal states entanglement generation may take place, for definite values of squeezing parameter, average photon numbers, temperature of the thermal bath, dissipation constant and the strength of interaction between the two modes. After its generation one can observe temporary suppressions and revivals of the entanglement. For entangled initial squeezed thermal states, entanglement suppression takes place, for all temperatures of the reservoir, and temporary revivals and suppressions of entanglement can be observed too. In the limit of infinite time the system evolves asymptotically to an equilibrium state which may be entangled or separable.
Exciton polaritons are coupled states of matter and light, originated by the strong interaction between an optical mode and semiconductor excitons. This interaction can be obtained also at a single-particle level, in which case it has been shown that a quantum treatment is mandatory. In this work we study the light-matter entanglement of polaritons from a fully quantum formalism including pumping and dissipation. We find that the entanglement is completely destroyed if the exciton and photon are tuned at the resonance condition, even under very low pumping rates. Instead, the best condition for maximizing entanglement and purity of the steady state is when the exciton and photon are out of resonance and when incoherent pumping exactly compensates the dissipation rate. In the presence of multiple quantum dots coupled to the light mode, matter-light entanglement survives only at larger detuning for a higher number of quantum dots considered.
In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we study the continuous variable entanglement for a system consisting of two independent harmonic oscillators interacting with a general environment. We solve the Kossakowski-Lindblad master equation for the time evolution of the considered system and describe the entanglement in terms of the covariance matrix for an arbitrary Gaussian input state. Using Peres–Simon necessary and sufficient criterion for separability of two-mode Gaussian states, we show that for certain values of diffusion and dissipation coefficients describing the environment, the state keeps for all times its initial type: separable or entangled. In other cases, entanglement generation, entanglement sudden death or a periodic collapse and revival of entanglement take place. We analyze also the time evolution of the logarithmic negativity, which characterizes the degree of entanglement of the quantum state.
We describe the evolution of the quantum entanglement of an open system consisting of two bosonic modes interacting with a common thermal environment, described by two different models. The initial state of the system is taken of Gaussian form. In the case of a thermal bath, characterized by temperature and dissipation constant which correspond to an asymptotic Gibbs state of the system, we show that for a zero temperature of the thermal bath an initial entangled Gaussian state remains entangled for all finite times. For an entangled initial squeezed thermal state, the phenomenon of entanglement sudden death takes place and we calculate the survival time of entanglement. For the second model of the environment, corresponding to a non-Gibbs asymptotic state, we study the possibility of generating entanglement. We show that the generation of the entanglement between two uncoupled bosonic modes is possible only for definite values of the temperature and dissipation constant, which characterize the thermal environment.