Following the experimental realization of Dicke superradiance in Bose gases coupled to cavity light fields, we investigate the behavior of ultra cold fermions in a transversely pumped cavity. We focus on the equilibrium phase diagram of spinless ferm
ions coupled to a single cavity mode and establish a zero temperature transition to a superradiant state. In contrast to the bosonic case, Pauli blocking leads to lattice commensuration effects that influence self-organization in the cavity light field. This includes a sequence of discontinuous transitions with increasing atomic density and tricritical superradiance. We discuss the implications for experiment.
We consider the possible phases of microcavity polaritons tuned near a bipolariton Feshbach resonance. We show that, as well as the regular polariton superfluid phase, a molecular superfluid exists, with (quasi-)long-range order only for pairs of pol
aritons. We describe the experimental signatures of this state. Using variational approaches we find the phase diagram (critical temperature, density and exciton-photon detuning). Unlike ultracold atoms, the molecular superfluid is not inherently unstable, and our phase diagram suggests it is attainable in current experiments.
We use the Bloch-Redfield-Wangsness theory to calculate the effects of acoustic phonons in coherent control experiments, where quantum-dot excitons are driven by shaped laser pulses. This theory yields a generalized Lindblad equation for the density
operator of the dot, with time-dependent damping and decoherence due to phonon transitions between the instantaneous dressed states. It captures similar physics to the form recently applied to Rabi oscillation experiments [A. J. Ramsay et al., Phys. Rev. Lett. 104, 017402 (2010)], but guarantees positivity of the density operator. At sufficiently low temperatures, it gives results equivalent to those of fully non-Markovian approaches [S. Luker et al., Phys. Rev. B 85, 121302 (2012)], but is significantly simpler to simulate. Several applications of this theory are discussed. We apply it to adiabatic rapid passage experiments, and show how the pulses can be shaped to maximize the probability of creating a single exciton using a frequency-swept laser pulse. We also use this theory to propose and analyze methods to determine the phonon density of states experimentally, i.e. phonon spectroscopy, by exploring the dependence of the effective damping rates on the driving field.
Solid state quantum condensates can differ from other condensates, such as Helium, ultracold atomic gases, and superconductors, in that the condensing quasiparticles have relatively short lifetimes, and so, as for lasers, external pumping is required
to maintain a steady state. In this chapter we present a non-equilibrium path integral approach to condensation in a dissipative environment and apply it to microcavity polaritons, driven out of equilibrium by coupling to multiple baths, describing pumping and decay. Using this, we discuss the relation between non-equilibrium polariton condensation, lasing, and equilibrium condensation.
We calculate the photoluminescence spectrum and lifetime of a biexciton in a semiconductor using Fermis golden rule. Our biexciton wavefunction is obtained using a Quantum Monte Carlo calculation. We consider a recombination process where one of the
excitons within the biexciton annihilates. For hole masses greater than or equal to the electron mass, we find that the surviving exciton is most likely to populate the ground state. We also investigate how the confinement of excitons in a quantum dot would modify the lifetime in the limit of a large quantum dot where confinement principally affects the centre of mass wavefunction. The lifetimes we obtain are in reasonable agreement with experimental values. Our calculation can be used as a benchmark for comparison with approximate methods.
Recent experiments on Bose--Einstein condensates in optical cavities have reported a quantum phase transition to a coherent state of the matter-light system -- superradiance. The time dependent nature of these experiments demands consideration of col
lective dynamics. Here we establish a rich phase diagram, accessible by quench experiments, with distinct regimes of dynamics separated by non-equilibrium phase transitions. We include the key effects of cavity leakage and the back-reaction of the cavity field on the condensate. Proximity to some of these phase boundaries results in critical slowing down of the decay of many-body oscillations. Notably, this slow decay can be assisted by large cavity losses. Predictions include the frequency of collective oscillations, a variety of multi-phase co-existence regions, and persistent optomechanical oscillations described by a damped driven pendulum. These findings open new directions to study collective dynamics and non-equilibrium phase transitions in matter-light systems.
We analyse the spatial and temporal coherence properties of a two-dimensional and finite sized polariton condensate with parameters tailored to the recent experiments which have shown spontaneous and thermal equilibrium polariton condensation in a Cd
Te microcavity [J. Kasprzak, M. Richard, S. Kundermann, A. Baas, P. Jeambrun, J.M.J. Keeling, F.M. Marchetti, M.H. Szymanska, R. Andre, J.L. Staehli, et al., Nature 443 (7110) (2006) 409]. We obtain a theoretical estimate of the thermal length, the lengthscale over which full coherence effectively exists (and beyond which power-law decay of correlations in a two-dimensional condensate occurs), of the order of 5 micrometers. In addition, the exponential decay of temporal coherence predicted for a finite size system is consistent with that found in the experiment. From our analysis of the luminescence spectra of the polariton condensate, taking into account pumping and decay, we obtain a dispersionless region at small momenta of the order of 4 degrees. In addition, we determine the polariton linewidth as a function of the pump power. Finally, we discuss how, by increasing the exciton-photon detuning, it is in principle possible to move the threshold for condensation from a region of the phase diagram where polaritons can be described as a weakly interacting Bose gas to a region where instead the composite nature of polaritons becomes important.
The first realization of a polariton condensate was recently achieved in a CdTe microcavity [Kasprzak et al., Nature 443, 409 (2006)]. We compare the experimental phase boundaries, for various detunings and cryostat temperatures, with those found the
oretically from a model which accounts for features of microcavity polaritons such as reduced dimensionality, internal composite structure, disorder in the quantum wells, polariton-polariton interactions, and finite lifetime.
