Spatial quantization of exciton-polariton condensates in optically induced traps

We study the formation of exciton-polariton condensates in potlike traps created by optical pumping in a planar microcavity with embedded quantum wells. The trap is formed by a repulsive reservoir of incoherent excitons excited by a ring-shaped nonresonant laser beam. Polariton condensates confined in a trapping potential are subject to spatial confinement leading to energy quantization. We reveal experimentally the discrete spectrum of polariton eigenstates in an optical trap that can be characterized by a pair of quantum numbers, azimuthal and radial quantum numbers, that correspond to the number of nodes of a condensate wave function in the corresponding directions. The occupation numbers of the eigenstates of a polariton condensate are determined by the overlap integral of the condensate wave function and the exciton reservoir spatial density distribution. The nonresonant pumping scheme enables engineering the shape and size of the trap, that allows to selectively excite specific superpositions of the eigenstates of a polariton condensate in each experiment. We demonstrate both single-and multiple-mode polariton lasing in an optical trap.