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Register a new userStationary density matrix of a pumped polariton system
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The density matrix, rho, of a model polariton system is obtained numerically from a master equation which takes account of pumping and losses. In the stationary limit, the coherences between eigenstates of the Hamiltonian are three orders of magnitude smaller than the occupations, meaning that the stationary density matrix is approximately diagonal in the energy representation. A weakly distorted grand canonical Gibbs distribution fits well the occupations.
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We observe for the first time two-photon excited condensation of exciton-polaritons. The angle-resolved photoluminescence (PL) from the Lower Polariton (LP) ground state in our planar GaAs-based microcavity structure exhibits a clear intensity threshold as a function of increased two-photon excitation power, coinciding with an interaction-induced blueshift and a narrowing of spectral linewidth, characteristic of the transition from a thermal distribution of lower polaritons to polariton condensation. Two-Photon Absorption (TPA) is evidenced in the quadratic dependence of the input-output curves below and above the threshold region. Second Harmonic Generation (SHG) is ruled out by both this threshold behavior and by scanning the pump photon energy and observing a lack of dependence of the LP emission peak energy. Our results pave the way towards realization of a polariton-based stimulated THz radiation source, stemming from the dipole-allowed transition from the Quantum Well (QW) 2p dark exciton state to the 1s-exciton-based LP ground state, as theoretically predicted in [A. V. Kavokin et al., Phys. Rev. Lett. 108, 197401 (2012)].
The dynamics of small perturbations against the stationary density matrix of a pumped polariton system with only one photon polarization is studied. Depending on the way the system is pumped and probed, decay times ranging from 30 to 5000 ps are found. The large decay times under resonant pumping are related to a bottleneck effect in the decay of the excess (probe) populations of dark polariton states. No singular behaviour at the threshold for polariton lasing is observed.
We develop a quantum field theory for parametrically pumped polaritons using Keldysh Greens function techniques. By considering the mean-field and Gaussian fluctuations, we find that the low energy physics of the highly non-equilibrium phase transition to the optical parametric oscillator regime is in many ways similar to equilibrium condensation. In particular, we show that this phase transition can be associated with an effective chemical potential, at which the systems bosonic distribution function diverges, and an effective temperature. As in equilibrium systems, the transition is achieved by tuning this effective chemical potential to the energy of the lowest normal mode. Since the occupations of the modes are available, we determine experimentally observable properties, such as the luminescence and absorption spectra.
The generalized Gross-Pitaevskii equation (gGPE) is an effective phenomenological description for the dynamics of incoherently pumped exciton-polariton condensates. However, a brute force numerical simulation of the gGPE provides little physical insight into condensate formation under arbitrary pumping configurations, and is demanding in terms of computational resources. We introduce in this paper a modal description of polariton condensation under incoherent pumping of arbitrary spatial profile, based on eigenmodes of the non-Hermitian generator of the linearized dynamics. A pump-dependent basis is then introduced to formulate a temporal coupled-mode theory that captures condensate dynamics in the presence of all nonlinear interactions. Simulations using a single set of modes for a given pumping and trapping configuration agree very well with a full integration of the gGPE in diverse dynamical regimes, supporting the validity of this modal description, while also providing a speedup in simulation times.
We report experimental evidence of longitudinal optical (LO) phonon-intersubband polariton scattering processes under resonant injection of light. The scattering process is resonant with both the initial (upper polariton) and final (lower polariton) states and is induced by the interaction of confined electrons with longitudinal optical phonons. The system is optically pumped with a mid-IR laser tuned between 1094 cm-1 and 1134 cm-1 (lambda=9.14 um and lambda=8.82 um). The demonstration is provided for both GaAs/AlGaAs and InGaAs/AlInAs doped quantum well systems whose intersubband plasmon lies at lambda=10 um wavelength. In addition to elucidating the microscopic mechanism of the polariton-phonon scattering, that is found to differ substantially from the standard single particle electron-LO phonon scattering mechanism, this work constitutes the first step towards the hopefully forthcoming demonstration of an intersubband polariton laser.
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