BCS-BEC crossover in a system of microcavity polaritons

Keeling, Jonathan; Eastham, P. R.; Szymańska, M. H.; Littlewood, P. B.

doi:10.1103/physrevb.72.115320

Cited by 97 publications

(119 citation statements)

References 56 publications

(93 reference statements)

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“…The resulting polariton condensate can be viewed as a generalization of the BCS state to include coherent photons. Later work on the equilibrium polariton condensate in models of the basic form (1) includes generalisations to include propagating photons [16,17], decoherence [14], and more realistic approaches to disorder [15,19]. The same theoretical framework has also been applied to condensation in atomic gases of fermions [33,34].…”

Section: Background and Basic Modelmentioning

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: Background and Basic Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Eastham¹

2007

J. Phys.: Condens. Matter

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“…On the other hand, the importance of this class of higher order correction terms has been pointed out in Refs. [21,33]. In particular, Ref.…”

Section: Appendix A: Number Equation In the Bcs-bec Crossovermentioning

confidence: 99%

Superfluid density and condensate fraction in the BCS-BEC crossover regime at finite temperatures

et al. 2007

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The superfluid density is a fundamental quantity describing the response to a rotation as well as in two-fluid collisional hydrodynamics. We present extensive calculations of the superfluid density ρ s in the BCS-BEC crossover regime of a uniform superfluid Fermi gas at finite temperatures.We include strong-coupling or fluctuation effects on these quantities within a Gaussian approximation. We also incorporate the same fluctuation effects into the BCS single-particle excitations described by the superfluid order parameter ∆ and Fermi chemical potential µ, using the Nozières and Schmitt-Rink (NSR) approximation. This treatment is shown to be necessary for consistent treatment of ρ s over the entire BCS-BEC crossover. We also calculate the condensate fraction N c as a function of the temperature, a quantity which is quite different from the superfluid density ρ s . We show that the mean-field expression for the condensate fraction N c is a good approximation even in the strong-coupling BEC regime. Our numerical results show how ρ s and N c depend on temperature, from the weak-coupling BCS region to the BEC region of tightly-bound Cooper pair molecules. In a companion paper by the authors (cond-mat/0609187), we derive an equivalent expression for ρ s from the thermodynamic potential, which exhibits the role of the pairing fluctuations in a more explicit manner.

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“…In such a case, an eh pair should be recognized as a Frenkel exciton, and hence, the description is beyond the capability of our model which employs the effective mass approximation. This indicates the need for other theoretical models to treat localized excitons such as the Dicke model [14,15].…”

mentioning

confidence: 99%

“…In this paper, assuming such a situation, we determine the ground state with a fixed excitation density at absolute zero as a function of experimentally variable parameters: excitation density, detuning [13], and ultraviolet cutoff determined by the lattice constant. In past studies, mean-field theories have been used to discuss the two limits-low excitation density [14,15] and high excitation density [16]-by considering two different models. These theories are complementary [17], but their relation is somewhat ambiguous.…”

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confidence: 99%

What Determines the Wave Function of Electron-Hole Pairs in Polariton Condensates?

Kamide

Ogawa

2010

Phys. Rev. Lett.

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The ground state of a microcavity polariton Bose-Einstein condensate is determined by considering experimentally tunable parameters such as excitation density, detuning, and ultraviolet cutoff. During a change in the ground state of Bose-Einstein condensate from excitonic to photonic, which occurs as increasing the excitation density, the origin of the binding force of electron-hole pairs changes from Coulomb to photon-mediated interactions. The change in the origin gives rise to the strongly bound pairs with a small radius, like Frenkel excitons, in the photonic regime. The change in the ground state can be a crossover or a first-order transition, depending on the above-mentionsed parameters, and is outlined by a phase diagram. Our result provides valuable information that can be used to build theoretical models for each regime.PACS numbers: 71.36.+c, 71.35.Lk, 03.75.Hh, 42.50.Gy Microcavity polaritons-photoexcited electrons and holes strongly coupled with photons in a semiconductor microcavity-have been observed to exhibit BoseEinstein condensation (BEC) [1,2]. Due to the lightmatter coupling, the polariton has an extremely small mass about 10 −4 times the free-electron mass; the small mass results in a high critical temperature and low critical density. BEC can be realized even at room temperature [3], which is remarkable considering that it had been difficult to realize BEC in exciton systems for a long time [4]. Microcavity polaritons are dissipative particles due to the short lifetime of photons and inelastic scattering of excitons by phonons. Therefore, the polariton BEC is in a nonequilibrium stationary state with a balance between pumping and losses [5,6,7]. However, the polariton BEC has many similarities with BEC of neutral atoms in a thermal equilibrium [8]. It shows several evidences for the superfluidity: the Goldstone mode [9], the quantized vortices [10], and the collective fluid dynamics [11].Such a stationary state appears to be well described by the ground state of a closed microcavity polariton system, when the polariton lifetime is longer than the thermalization time [6,12]. In this paper, assuming such a situation, we determine the ground state with a fixed excitation density at absolute zero as a function of experimentally variable parameters: excitation density, detuning [13], and ultraviolet cutoff determined by the lattice constant. In past studies, mean-field theories have been used to discuss the two limits-low excitation density [14,15] and high excitation density [16]-by considering two different models. These theories are complementary [17], but their relation is somewhat ambiguous. We investigate the intermediate density region as well, where the electronhole (eh) wave function of the relative motion becomes important. We show that the ground state energy and wavefuction gradually change from those of excitons to photons as the excitation density increases. It is also shown that the change can be a crossover or a first-order transition, depending on the parameters considered. T...

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BCS-BEC crossover in a system of microcavity polaritons

Cited by 97 publications

References 56 publications

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

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

Superfluid density and condensate fraction in the BCS-BEC crossover regime at finite temperatures

What Determines the Wave Function of Electron-Hole Pairs in Polariton Condensates?

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