arXiv subjects

P. R. Eastham

Publications and source records attributed to P. R. Eastham.

34 records · Page 2Linked to original sources

arXiv2009

Vortex states of a disordered quantum Hall bilayer

We present and solve a model for the vortex configuration of a disordered quantum Hall bilayer in the limit of strong and smooth disorder. We argue that there is a characteristic disorder strength below which vortices will be rare, and above which they proliferate. We predict that this can be observed tuning the electron density in a given sample. The ground state in the strong-disorder regime can be understood as an emulsion of vortex-antivortex crystals. Its signatures include a suppression of the spatial decay of counterflow currents. We find an increase of at least an order of magnitude in the length scale for this decay compared to a clean system. This provides a possible explanation of the apparent absence of leakage of counterflow currents through interlayer tunneling, even in experiments performed deep in the coherent phase where enhanced interlayer tunneling is observed.

cond-mat.mes-hall↗

arXiv2008

Coherence properties of the microcavity polariton condensate

A theoretical model is presented which explains the dominant decoherence process in a microcavity polariton condensate. The mechanism which is invoked is the effect of self-phase modulation, whereby interactions transform polariton number fluctuations into random energy variations. The model shows that the phase coherence decay, g1(t), has a Kubo form, which can be Gaussian or exponential, depending on whether the number fluctuations are slow or fast. This fluctuation rate also determines the decay time of the intensity correlation function, g2(t), so it can be directly determined experimentally. The model explains recent experimental measurements of a relatively fast Gaussian decay for g1(t), but also predicts a regime, further above threshold, where the decay is much slower.

cond-mat.str-el↗

arXiv2008

Quantum condensation from a tailored exciton population in a microcavity

An experiment is proposed, on the coherent quantum dynamics of a semiconductor microcavity containing quantum dots. Modeling the experiment using a generalized Dicke model, we show that a tailored excitation pulse can create an energy-dependent population of excitons, which subsequently evolves to a quantum condensate of excitons and photons. The population is created by a generalization of adiabatic rapid passage, and then condenses due to a dynamical analog of the BCS instability.

cond-mat.str-el↗

arXiv2008

Mode-locking and mode-competition in a non-equilibrium solid-state condensate

A trapped polariton condensate with continuous pumping and decay is analyzed using a generalized Gross-Pitaevskii model. Whereas an equilibrium condensate is characterized by a macroscopic occupation of a ground state, here the steady-states take more general forms. Some are characterized by a large population in an excited state, and others by large populations in several states. In the latter case, the highly-populated states synchronize to a common frequency above a critical density. Estimates for the critical density of this synchronization transition are consistent with experiments.

cond-mat.other↗

arXiv2007

Quantum corrections to the Ising interactions in LiYHoF4

We systematically derive an effective two-state Hamiltonian for the dipolar Ising magnet LiYHoF4, including quantum corrections which arise from the transverse dipolar and hyperfine interactions. These corrections are derived using a generalised Schrieffer-Wolff transformation to leading order in the small parameters given by the ratio of the interaction energies to the energy of the first excited electronic state of the Holmium ions. The resulting low-energy Hamiltonian involves two-level systems, corresponding to the low-lying electronic states of the Holmiums, which are coupled to one another and to the Holmium nuclei. It differs from that obtained by treating the electronic states of the Holmium as a spin-1/2 with an anisotropic g-factor. It includes effective on-site transverse fields, and both pairwise and three-body interactions among the dipoles and nuclei. We explain the origins of the terms, and give numerical values for their strengths.

cond-mat.str-el↗

arXiv2007

The new physics of non-equilibrium condensates: insights from classical dynamics

We discuss the dynamics of classical Dicke-type models, aiming to clarify the mechanisms by which coherent states could develop in potentially non-equilibrium systems such as semiconductor microcavities. We present simulations of an undamped model which show spontaneous coherent states with persistent oscillations in the magnitude of the order parameter. These states are generalisations of superradiant ringing to the case of inhomogeneous broadening. They correspond to the persistent gap oscillations proposed in fermionic atomic condensates, and arise from a variety of initial conditions. We show that introducing randomness into the couplings can suppress the oscillations, leading to a limiting dynamics with a time-independent order parameter. This demonstrates that non-equilibrium generalisations of polariton condensates can be created even without dissipation. We explain the dynamical origins of the coherence in terms of instabilities of the normal state, and consider how it can additionally develop through scattering and dissipation.

cond-mat.str-el↗

arXiv2006

Mechanism for the failure of the Edwards hypothesis in the SK spin glass

The dynamics of the SK model at T=0 starting from random spin configurations is considered. The metastable states reached by such dynamics are atypical of such states as a whole, in that the probability density of site energies, $p(λ)$, is small at $λ=0$. Since virtually all metastable states have a much larger $p(0)$, this behavior demonstrates a qualitative failure of the Edwards hypothesis. We look for its origins by modelling the changes in the site energies during the dynamics as a Markov process. We show how the small $p(0)$ arises from features of the Markov process that have a clear physical basis in the spin-glass, and hence explain the failure of the Edwards hypothesis.

cond-mat.dis-nn↗

arXiv2006

Finite-size fluctuations and photon statistics near the polariton condensation transition in a single-mode microcavity

We consider polariton condensation in a generalized Dicke model, describing a single-mode cavity containing quantum dots, and extend our previous mean-field theory to allow for finite-size fluctuations. Within the fluctuation-dominated regime the correlation functions differ from their (trivial) mean-field values. We argue that the low-energy physics of the model, which determines the photon statistics in this fluctuation-dominated crossover regime, is that of the (quantum) anharmonic oscillator. The photon statistics at the crossover are different in the high- and low- temperature limits. When the temperature is high enough for quantum effects to be neglected we recover behavior similar to that of a conventional laser. At low enough temperatures, however, we find qualitatively different behavior due to quantum effects.

cond-mat.mes-hall↗

arXiv2005

Condensation and Lasing of Microcavity Polaritons: Comparison between two Models

Condensation of microcavity polaritons and the substantial influence of pair-breaking disorder and decoherence leading to a laser regime has been recently considered using two different models: a model for direct two band excitons in a disordered quantum well coupled to light and a model where the cavity mode couples instead to a medium of localised excitons, represented by two-level oscillators in the presence of dephasing processes. Even if complementary from the point of view of assumptions, the models share most of the main conclusions and show similar phase diagrams. The issue whether excitons are propagating or localised seems secondary for the polariton condensation and the way in which pair-breaking disorder and decoherence processes influence the condensation and drive the microcavity into a lasing regime is, within the approximations used in each model, generic. The reasons for the similarities between the two physical situations are analysed and explained.

cond-mat.mes-hall↗

arXiv2005

BCS-BEC crossover in a system of microcavity polaritons

We investigate the thermodynamics and signatures of a polariton condensate over a range of densities, using a model of microcavity polaritons with internal structure. We determine a phase diagram for this system including fluctuation corrections to the mean-field theory. At low densities the condensation temperature, T_c, behaves like that for point bosons. At higher densities, when T_c approaches the Rabi splitting, T_c deviates from the form for point bosons, and instead approaches the result of a BCS-like mean-field theory. This crossover occurs at densities much less than the Mott density. We show that current experiments are in a density range where the phase boundary is described by the BCS-like mean-field boundary. We investigate the influence of inhomogeneous broadening and detuning of excitons on the phase diagram.

cond-mat.str-el↗

arXiv2004

Polariton condensation with localised excitons and propagating photons

We estimate the condensation temperature for microcavity polaritons, allowing for their internal structure. We consider polaritons formed from localised excitons in a planar microcavity, using a generalised Dicke model. At low densities, we find a condensation temperature T_c \propto ρ, as expected for a gas of structureless polaritons. However, as T_c becomes of the order of the Rabi splitting, the structure of the polaritons becomes relevant, and the condensation temperature is that of a B.C.S.-like mean field theory. We also calculate the excitation spectrum, which is related to observable quantities such as the luminescence and absorption spectra.

cond-mat.str-el↗

arXiv2004

Models of coherent exciton condensation

That excitons in solids might condense into a phase-coherent ground state was proposed about 40 years ago, and has been attracting experimental and theoretical attention ever since. Although experimental confirmation has been hard to come by, the concepts released by this phenomenon have been widely influential. This tutorial review discusses general aspects of the theory of exciton and polariton condensates, focussing on the reasons for coherence in the ground state wavefunction, the BCS to Bose crossover(s) for excitons and for polaritons, and the relationship of the coherent condensates to standard lasers.

cond-mat.str-el↗

arXiv2003

Phase locking in quantum and classical oscillators: polariton condensates, lasers, and arrays of Josephson junctions

We connect three phenomena in which a coherent electromagnetic field could be generated: polariton condensation, phase-locking in arrays of underdamped Josephson junctions, and lasing. All these phenomena have been described using Dicke-type models of spins coupled to a single photon mode. These descriptions may be distinguished by whether the spins are quantum or classical, and whether they are strongly or weakly damped.

cond-mat.mes-hall↗

arXiv2003

Steady states of a chi-three parametric oscillator with coupled polarisations

Polarisation effects in the microcavity parametric oscillator are studied using a simple model in which two chi-three optical parametric oscillators are coupled together. It is found that there are, in general, a number of steady states of the model under continuous pumping. There are both continuous and discontinuous thresholds, at which new steady-states appear as the driving intensity is increased: at the continuous thresholds, the new state has zero output intensity, whereas at the discontinuous threshold it has a finite output intensity. The discontinuous thresholds have no analog in the uncoupled device. The coupling also generates rotations of the linear polarisation of the output compared with the pump, and shifts in the output frequencies as the driving polarisation or intensity is varied. For large ratios of the interaction between polarisations to the interaction within polarisations, of the order of 5, one of the thresholds has its lowest value when the pump is elliptically polarised. This is consistent with recent experiments in which the maximum output was achieved with an elliptically polarised pump.

cond-mat.mes-hall↗

arXiv2001

Bose condensation of cavity polaritons beyond the linear regime: the thermal equilibrium of a model microcavity

We consider a generalization of the Dicke model. It describes localized, physically separated, saturable excitations, such as excitons bound on impurities, coupled to a single long-lived mode of an optical cavity. We consider the thermal equilibrium of the model at a fixed total number of excitons and photons. We find a phase in which both the cavity field and the excitonic polarization are coherent. This phase corresponds to a Bose condensate of cavity polaritons, generalized to allow for the fermionic internal structure of the excitons. It is separated from the normal state by an unusual reentrant phase boundary. We calculate the excitation energies of the model, and hence the optical absorption spectra of the cavity. In the condensed phase the absorption spectrum is gapped. The presence of a gap distinguishes the polariton condensate from the normal state and from a conventional laser, even when the inhomogeneous linewidth is so large that there is no observable polariton splitting in the normal state.

cond-mat.str-el↗

arXiv2000

Bose condensation in a model microcavity

We study the equilibrium properties of a system of dipole-active excitons coupled to a single photon mode at fixed total excitation. Treating the presence or absence of a trapped exciton as a two-level system produces a model that is exactly soluble. It gives a simple description of the physics of polariton condensation in optical cavities beyond the low-density bosonic regime.

cond-mat.str-el↗