Generating entangled polaritonic condensates by pumping with entangled pairs of photons

Abstract

We investigate the steady state of two single-mode uniform spatially separated polaritonic conden- sates exposed to resonant pumping with entangled pairs of photons. We demonstrate the principal possibility of driving the system to an entangled state despite its exposure to noises arising from the excitonic reservoir and photon leakage through the microcavity mirrors. Estimates are provided for the flux of entangled particles required to drive the system into a steady state that violates the partial-transpose criterion for entanglement. Furthermore, we trace the evolution of the system after a sudden disappearance of the entangled pumping. Our analysis provides estimates for the entanglement lifetime in a system of two exciton-polariton condensates

Figures (4)

• Figure 1: The schematic of a Gedankenexperiment where two exciton-polariton condensate modes ($c_1$ and $c_2$) are pumped by a source of entangled photons and coupled to independent incoherent exciton reservoirs ($R_1$ and $R_2$) that replenish polariton modes by stimulated scattering.
• Figure 2: Dispersion curves $\varepsilon(k)$ for the lower and upper polariton modes (orange lines). For the lower polariton branch, the energy offset $E$ between the condensate and the reservoir is indicated.
• Figure 3: Wigner quasiprobability distribution illustrated for the state of type \ref{['eq:Wigner_stationary']}. The marginal distributions for (a) $p_j(x_j)$; (b) $x_j(x_{3-j})$ (for $p_j(p_{3-j})$ it looks the same); (c) $x_j(p_{3-j})$ (for $p_j(x_{3-j})$ it looks the same); are demonstrated. The Hamiltonian \ref{['eq:Hamiltonian']} generates squeezing in quadratures $x_j-p_{3-j}$, which results in deformation of the distributions in panel (c). These illustrative pictures are generated by simulating stochastic evolution governed by \ref{['eq:quadrature evolution']} with the simplest quadratic model for $G[\rho]=2\rho-\rho^2$, $\eta=1$, $\chi=0.4$.
• Figure 4: Phase diagram for polariton entanglement. The region of entanglement $\zeta>\zeta^{\eta = 1}_{\rm crit}(\kappa)$ is shaded in green and limited by the lines $\zeta^{\eta}_{\rm crit}(\kappa)$ for $\eta>1$ (the higher is the reservoir effective temperature $T_R$, the higher is $\eta$). Red lines correspond to the dependence $\kappa(\zeta)$ within the model \ref{['eq:saturation_model']}, blue ones are the ones given by the model \ref{['eq:linear_saturation_model']}, $f$ is the normalized excess pump intensity as defined by \ref{['eq:excess']}.