Coherent zero-state and p-state in an exciton-polariton condensate array

The effect of quantum statistics in quantum gases and liquids results in observable collective properties among many-particle systems. One prime example is Bose-Einstein condensation, whose onset in a quantum liquid leads to phenomena such as superfluidity and superconductivity. A Bose-Einstein condensate is generally defined as a macroscopic occupation of a single-particle quantum state, a phenomenon technically referred to as off-diagonal long-range order due to non-vanishing off-diagonal components of the single-particle density matrix(1-3). The wave-function of the condensate is an order parameter whose phase is essential in characterizing the coherence and superfluid phenomena(4-11). The long-range spatial coherence leads to the existence of phase-locked multiple condensates in an array of superfluid helium(12), superconducting Josephson junctions(13-15) or atomic Bose-Einstein condensates(15-18). Under certain circumstances, a quantum phase difference of p is predicted to develop among weakly coupled Josephson junctions(19). Such a meta-stable pi-state was discovered in a weak link of superfluid 3 He, which is characterized by a 'p-wave' order parameter(20). The possible existence of such a pi-state in weakly coupled atomic Bose-Einstein condensates has also been proposed(21), but remains undiscovered. Here we report the observation of spontaneous build-up of in-phase ('zero-state') and antiphase ('pi-state') 'superfluid' states in a solid-state system; an array of exciton-polariton condensates connected by weak periodic potential barriers within a semiconductor microcavity. These in-phase and antiphase states reflect the band structure of the one-dimensional polariton array and the dynamic characteristics of metastable exciton-polariton condensates.