Collective state transitions of exciton-polaritons loaded into a periodic potential

Abstract

We study the loading of a nonequilibrium, dissipative system of composite bosons -exciton polaritons -into a one dimensional periodic lattice potential. Utilizing momentum resolved photoluminescence spectroscopy, we observe a transition between an incoherent Bose gas and a polariton condensate, which undergoes further transitions between different energy states in the band-gap spectrum of the periodic potential with increasing pumping power. We demonstrate controlled loading into distinct energy bands by modifying the size and shape of the excitation beam. The observed effects are comprehensively described in the framework of a nonequilibrium model of polariton condensation. In particular, we implement a stochastic treatment of quantum and thermal fluctuations in the system and confirm that polariton-phonon scattering is a key energy relaxation mechanism enabling transitions from the highly nonequilibrium polariton condensate in the gap to the ground band condensation for large pump powers.Introduction.-Since the initial demonstration of Bose-Einstein condensation of microcavity exciton polaritons [1], one particular direction of research has been focused on engineering the potential landscape of polaritons. These potentials have been created by deposition of metal on the microcavity surface [2], interference of surface acoustic waves [3], deep etching of micropillars [4], fabrication of shallow mesas [5], and deposition of semiconductor micro-rods on a silicon grating [6]. Periodic arrangements of these potentials have been used to study the formation of gap solitons [7,8] and graphene-like band spectra (including Dirac cones) [4,9], are predicted to be prime candidates for the generation of topological polariton states [10][11][12], and hold high promise for implementation of quantum simulators in solid state systems [13].

Spatiotemporal coherence of non-equilibrium multimode photon condensates

“…Net gain (the difference between drive and dissipation) saturates only locally, leaving gain available for modes which have not already condensed. Since those conditions are natural for trapped polaritons [9,51] or might be engineered even for atoms [52], the observed fragmentation is by no means specific to the system at hand, but rather is expected to be observable in a variety of condensates. Since photons interact only indirectly and incoherently, but many other condensed particles have direct coherent interactions, coherence properties are a feature in which fragmented photon condensates might deviate from other condensates.…”

Multivalley engineering in semiconductor microcavities

“…Here we begin by considering the behavior of the system under non-resonant excitation under which polariton condensation can be expected in the lattice14. Due to their finite lifetime, exciton-polaritons are non-equilibrium systems and so would not necessarily form in the ground state42, however, at high densities energy relaxation is typically enhanced to the ground state23. In this section, we consider qualitative arguments in the limit of thermal equilibrium43.…”

Talbot effect for exciton-polaritons

“…Recently, experimental investigations of macroscopic coherent quantum states (bosonic condensates) of microcavity exciton-polaritons [18][19][20] in one-dimensional (1D) periodic potentials has received a lot of attention [21][22][23][24][25]. Exciton-polaritons are quasiparticles arising due to hybridisation of an electron-hole pair (exciton) and photon in a strong light-matter coupling regime.…”

“…The detailed description of the model, which describes transition between different energy states occupied by the condensate in the mesa traps can be found in [24]. It consists of the open-dissipative Gross-Pitaevskii equation for the condensate wavefunction incorporating stochastic fluctuations and coupled to the rate equation for the excitonic reservoir created by the off-resonant cw pump [24,36].…”

“…To achieve the strong coupling, the exciton is spatially confined in a 2D quantum well grown in an optically pumped semiconductor microcavity, the latter ensuring resonance with a long-lived photon mode. Periodic potentials for polaritons can be formed by surface metal deposition on arXiv:1603.05056v1 [cond-mat.quant-gas] 16 Mar 2016 the semiconductor microcavity [21,26,27], acousting wave modulation [23,28], deep etching of micropillars [22,25] or microstructuring of buried mesa traps [24,29] (see [30] and references therein). These potentials act as a solid-state superlattice: when a microcavity is optically pumped, the exciton-polaritons populate the energy bands of the resulting periodic potentials.…”