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

Eastham, P. R.; Littlewood, P. B.

doi:10.1103/physrevb.64.235101

Cited by 152 publications

(211 citation statements)

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“…In passing we note that the analogous generalization of the thermodynamic action for fluctuations about the condensate, equation (22) of reference [11], gives the eigenspectrum for the coherent steady-states with a uniform gap and every spin parallel or antiparallel to its effective field, but more generally there are additional terms generated by the components of the spins transverse to the effective fields. A dynamical instability is indicated by the appearance of a complex root in (6).…”

Section: Linear Stability Analysismentioning

confidence: 99%

“…It can be viewed as a generalization of the BCS Hamiltonian to the strong-coupling regime, as is apparent on rewriting the spin operators in terms of two species of fermions. It was applied to polariton condensation by Eastham and Littlewood [11,10,12], who considered its quasi-equilibrium thermodynamics at fixed excitation number…”

Section: Background and Basic Modelmentioning

confidence: 99%

“…The action for fluctuations around the incoherent thermal equilibrium state is equation (23) in reference [11], so the real eigenfrequencies λ are the solutions to…”

Section: Linear Stability Analysismentioning

confidence: 99%

“…The established techniques of many-particle physics can then be applied to model microcavities, and theories developed which allow for issues such as the internal structure of the polaritons, disorder acting on the excitons, and the many-body nature of Bose condensation. This approach has now established phase diagrams and observable properties for polariton condensation in a range of increasingly realistic models [10,11,12,13,14,15,16,17,18,19,20] The problem with the equilibrium theories is linking them to the experiments, which may not be in thermal equilibrium. In principle they are directly applicable if the polariton lifetime is long compared with the thermalization time.…”

Section: Introductionmentioning

confidence: 99%

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

Eastham¹

2007

J. Phys.: Condens. Matter

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Abstract. 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.

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Section: Linear Stability Analysismentioning

confidence: 99%

Section: Background and Basic Modelmentioning

confidence: 99%

“…The action for fluctuations around the incoherent thermal equilibrium state is equation (23) in reference [11], so the real eigenfrequencies λ are the solutions to…”

Section: Linear Stability Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Eastham¹

2007

J. Phys.: Condens. Matter

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“…Figure 2 shows the phase diagram assuming that only a single cavity mode, of energy c , is relevant. The dotted line shows the phase boundary for equilibrium condensation in the same model 27 with a temperature and chemical potential corresponding to the pumped population. We see that one sheet of the nonequilibrium phase boundary extends the equilibrium result to allow for the cavity damping.…”

Section: Phase Diagrammentioning

confidence: 99%

Finite-momentum condensation in a pumped microcavity

Brierley

Eastham

2010

Phys. Rev. B

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We calculate the absorption spectra of a semiconductor microcavity into which a nonequilibrium exciton population has been pumped. We predict strong peaks in the spectrum corresponding to collective modes analogous to the Cooper modes in superconductors and fermionic atomic gases. These modes can become unstable, leading to the formation of off-equilibrium quantum condensates. We calculate a phase diagram for condensation and show that the dominant instabilities can be at a finite momentum. Thus we predict the formation of inhomogeneous condensates, similar to Fulde-Ferrel-Larkin-Ovchinnikov states.

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Some Considerations Concerning the Detection of Excitons by Field Ionization in a Schottky Barrier

Klingshirn

Fleck

Jörger

2002

phys. stat. sol. (b)

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Dedicated to Professor Dr. Roland Zimmermann on the occasion of his 60th birthdayThe possibility of Bose-Einstein condensation of excitons in semiconductors and/or their superfluid transport are long-standing, still controversially discussed problems. In a recent series of experiments by E. Fortin and coworkers [1-3] [phys. stat. sol. (b) 191, 345 (1995); Phys. Rev. Lett. 77, 896 (1996); and Proc. Internat. Conf. Exciton Processes in Condensed Matter, World Scientific, Singapore 2000, respectively], (para-)excitons in Cu 2 O have been detected electrically by their field ionization in a Schottky barrier. We analyze the electric field in the Schottky barrier and its screening by the holes remaining after field ionization and find serious screening and saturation effects of this Schottky-barrier exciton detector under the excitation conditions of the experiment. These findings make a reinterpretation of the data very likely. IntroductionExcitons are the quanta of the collective excitation of the electron system in semiconductors and insulators. This excitation can be described to a very good approximation as a two-particle state, consisting of an electron in the conduction band and of the hole left behind in the valence band plus Coulomb and exchange interaction between these two particles. In so far the problem is closely related to the hydrogen or the positronium atom (see, e.g., [4,5], and references therein). Obviously the exciton is an electrically neutral quasiparticle with integer spin, but it is composed of two fermions, namely electron and hole. As a consequence of this fact, the commutation relations between exciton creation and annihilation operators are those of bosons at low densities, but with a deviation from ideal boson character via a term which increases with the density of excitons [4].The interplay of bosonic character and fermionic constituents triggered a lot of research over several decades about what happens with excitons at the highest densities. In the following we summarize shortly the present situation for bulk semiconductors. It became clear that at the highest densities a transition to a metallic electron-hole plasma (EHP) occurs [4][5][6]. Depending on the material parameters and excitation conditions such as carrier lifetime, excitation density, and carrier temperature, the plasma may even undergo a first-order phase transition to a liquid-like state, the analogon to molten metallic hydrogen. This is even true in CuCl [7] in spite of its large exciton binding energy and small Bohr radius, shifting the density for the occurrence of an EHP (also called Mott density) from values below 10 17 cm À3 , e.g., for Ge to very high values around 10 20 cm À3 . Experimental investigations and the theoretical modelling of the electron-hole plasma have been pushed by many research groups world-wide as can be seen, e.g., from the references in reviews and textbooks like [4,5]. These refer-

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

Cited by 152 publications

References 37 publications

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

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

Finite-momentum condensation in a pumped microcavity

Some Considerations Concerning the Detection of Excitons by Field Ionization in a Schottky Barrier

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