Spatial and spectral shape of inhomogeneous nonequilibrium exciton-polariton condensates

Abstract

We develop a mean-field theory of the spatial profile and the spectral properties of polariton condensates in nonresonantly pumped semiconductor microcavities in the strong coupling regime. Predictions are obtained for both the continuous-wave and the pulsed excitation regimes and the specific signatures of the non-equilibrium character of the condensation process are pointed out. A striking sensitivity of the condensate shape on the optical pump spot size is demonstrated by analytical and numerical calculations, in good quantitative agreement with recent experimental observations. PACS numbers: 03.75. Kk, 71.36.+c, 42.65.Sf, 05.70.Ln First evidences of Bose-Einstein condensation (BEC) in a solid-state system have been recently reported in a gas of exciton-polaritons in a semiconductor microcavity in the strong coupling regime [1,2,3,4,5,6]. In addition of being a remarkable example of an exciton condensate, this system opens interesting perspectives towards the study of the BEC phenomenon in completely new regimes. Polariton condensates differ in several fundamental aspects from the ideal case generally considered in textbooks: polariton-polariton interactions are significant and the system is far from thermodynamical equilibrium. While the separate effect on condensation of the interactions and of the non-equilibrium condition is already well understood from either ultracold atom [7] or laser [8] theory, not much is yet known about the interplay of the two effects when simultaneously present. In this case, the Bose gas is in fact a quantum degenerate, interacting many-body system whose stationary state does not correspond to a thermal equilibrium state, but rather originates from a dynamical balance of pumping and losses [9,10,11] Some striking consequences of the non-equilibrium condition on the elementary excitations have been recently predicted, the propagating sound mode of equilibrium condensate being e.g. replaced by a diffusive mode [10,11]. Even more remarkably, an unexpectedly rich behavior has been observed in recent experiments in the spatial and spectral shapes of the condensate depending on the size of the pump spot [1,2]. While at equilibrium, BEC generally occurs at zero momentum and the trapping potential is only responsible for the k-space broadening due to finite size [7], the first experimental studies of polariton condensates performed with a relatively small pump laser spot showed BoseEinstein condensation into a ring of momentum states with a non-zero wave vector [1]; mutual coherence of different k-states was however interferometrically demonstrated, which proved that a true condensate was created, and not a fragmented one [12]. Standard condensation around k = 0 was then recovered in later experiments using a much wider excitation spot [2,3]. So far, most of these experimental observations have challenged theoretical understanding [13]: the purpose of the present Letter is to propose a complete and unified theoretical model able to explain them in a simple and physically transparent ...

Polariton lasing in high-quality selenide-based micropillars in the strong coupling regime

“…Therefore, under spatially inhomogeneous excitation, polaritons generated at the center of the excitation spot experience a repulsive potential gradient (due to a stronger blueshift in the center) that pushes them away from the laser spot center. 8,29,32 The polaritonic field effectively driving the stimulated relaxation is thus lowered by this mechanism. In micropillars, this loss channel is increasingly suppressed for decreasing diameter since non-zero momentum states (i.e., excited states) are split away from the ground state by an increasing energy gap.…”

Spontaneous formation and optical manipulation of extended polariton condensates

“…This condensate undergoes a local blueshift E b owing to repulsive interaction with the high-density exciton cloud photogenerated in the excitation area. As there are no photogenerated excitons outside the small pump area, this blueshift is spatially limited and creates a force tending to expel polaritons from the excitation area: the polariton condensate undergoes a lateral acceleration and acquires a finite in-plane wave vector 26 . The far-field emission measured on each side of the excitation spot indicates the spontaneous generation of condensed polaritons with well-defined wave vectors given by k y = ± √ 2 m * E b /h when approximating the polariton dispersion by a parabola 26 .…”

“…As there are no photogenerated excitons outside the small pump area, this blueshift is spatially limited and creates a force tending to expel polaritons from the excitation area: the polariton condensate undergoes a lateral acceleration and acquires a finite in-plane wave vector 26 . The far-field emission measured on each side of the excitation spot indicates the spontaneous generation of condensed polaritons with well-defined wave vectors given by k y = ± √ 2 m * E b /h when approximating the polariton dispersion by a parabola 26 . Note that at high excitation powers, pair scattering of two polaritons in the pump spot into two polaritons exiting in the left and right directions at the same energy and opposite k could also contribute to the observed feature.…”

Compactons and bistability in exciton-polariton condensates

“…7 and 15), as well as in the justification of the mean-field models written for the polariton order parameter (like in the models used, e.g., in Ref. 18), obviously the respective mean-field models cannot capture the effects related to variations of the relative fractions of the quasiparticles. Remarkably, Fig.…”

“…All such solitons reported so far were detected only on a broad constant background due to the use of very extended pump beams, whose width is comparable with the cavity size 17 or considerably exceeds a width of localized excitation propagating on a broad background. 3 However, in experiment the pump beam may be inhomogeneous and strongly localized in space, which leads to a highly nontrivial collective dynamics of polaritons within the pump spot 18 which can be used for observation of rich dynamical phenomena, such as direct visualization of quantum field patterns 19 or switching in polaritonic transistors. 20 The possibility of formation of strongly localized nonlinear excitations in condensates supported by a narrow pump beam and the impact of the pump beam width on the localization degree of stationary states have not been explored, so far.…”