Collective fluid dynamics of a polariton condensate in a semiconductor microcavity

Abstract

Below a critical temperature, a sufficiently high density of bosons undergoes Bose-Einstein condensation (BEC). Under this condition, the particles collapse into a macroscopic condensate with a common phase, showing collective quantum behaviour like superfluidity, quantised vortices, interferences, etc. Up to recently, BEC was only observed for diluted atomic gases at μK temperatures. Following the recent observations of non-equilibrium BEC in semiconductor microcavities at temperatures of ~10 K, using momentum-1 and real-space 2 trapping, the quest is now towards the observation of the superfluid motion of a polariton BEC. For the same reasons that polaritons benefit from unusually favourable features for condensation, such as very high critical temperatures, it is expected that their superfluid properties would likewise manifest with altogether different magnitudes, such as very high critical velocities. Since they have shown many deviations in their Bose-condensed phase from the cold atoms paradigm, it is not clear a priori to which extent their superfluid properties would coincide or depart from those observed with atoms, among which quantised vortices 6 , frictionless motion 7 , linear dispersion for the elementary excitations 8 , or more recently Čerenkov emission of a condensate flowing at supersonic velocities 9 , are among the clearest signatures of quantum fluid propagation.Microcavity polaritons are two-dimensional bosons of mixed electronic and photonic nature, formed by the strong coupling of excitons-confined in semiconductor quantum wells-with photons trapped in a micron scale resonant cavity. First observed in 1992 10 , these particles have been profusely studied in the last fifteen years due to their unique features. Thanks to their photon fraction, polaritons can easily be excited by an external laser source and detected by light emission in the direction perpendicular to the cavity plane. However, as opposed to photons, they experience strong interparticle interactions owing to their partially electronic fraction. Due to the deep polariton dispersion, the effective mass of these particles is 10 4 -10 5 smaller than the free electron mass, resulting in a very low density of states. This allows for a high state 3 occupancy even at relatively low excitation intensities. However, polaritons live only a few 10 -12 s in a cavity before escaping and therefore thermal equilibrium is never achieved. In this respect, a macroscopically degenerate state of polaritons departs strongly from an atomic Bose-condensed phase. The experimental observations of spectral and momentum narrowing, spatial coherence and long range order-which have been used as evidence for polariton Bose-Einstein condensation-are also present in a pure photonic laser 11 . The recent observation of long range spatial coherence 12 , vortices 4 and the loss of coherence with increasing density in the condensed phase 13,14 , are in accordance with macroscopic phenomena proper of interacting, coherent bosons 15 . But a direct manifestation ...

Vortices in Polariton OPO Superfluids

“…In the case of a superfluid in equilibrium with a typical interaction energy gn (n is the average density) and mass m, the healing length, ξ = 1/ √ 2mgn, is the typical distance over which the condensate wavefunction recovers its 'bulk' value around a perturbation. In particular, for an |m| = 1 vortex (20), ξ is the typical size of the vortex.…”

Four-wave mixing excitations in a dissipative polariton quantum fluid

“…1(b)], the Bogoliubov transformation not only causes the linearization of the dispersion, but also the appearance of a negative energy ghost branch (GB) as a symmetrical image of the normal phononlike dispersion branch (NB) with respect to the condensate. 21,22 Microcavity polaritons, for which superfluidity has first been demonstrated through frictionless measurements, 3,4 appear as a model system to investigate the Bogoliubov excitation spectrum. 13,14,23,24 These composite bosons show indeed unique properties inherited from both their components: a very small mass from the photonic part and Coulomb mediated repulsive interactions from the excitonic one.…”

“…1 This so-called Bogoliubov transformation is at the basis of the superfluid behavior. During the last 15 years, most of the Bose-Einstein condensates that could be realized, both with cold atoms and in the solid state, have shown clear signs of superfluidity such as frictionless flow [2][3][4] or quantized vortices. [5][6][7][8] Still, the most convincing demonstration of superfluidity remains the measurement of the excitation spectrum of the Bose gas.…”

Geometrically locked vortex lattices in semiconductor quantum fluids

“…Polariton condensates have a finite lifetime and need to be constantly pumped, prompting extensive studies of the rich phenomena in out-of-equilibrium condensates 9 . This also makes it simple to shape the condensate flow [11][12][13] and sculpt the confinement potential [12][13][14] using the pump fields.…”