Temporal off-diagonal long-range order in polariton condensates

Bosons can populate quantum states macroscopically, forming various kinds of thermal-equilibrium, and quasi-equilibrium condensates [1,2], which exhibit a wide range of collective phenomena including superfluidity and macroscopic coherence in matter. Interferometry has been employed to demonstrate long-range off-diagonal order in cold-atom systems [3], and, recently, in the rapidly developing field of exciton-polariton condensates [4]. However, all such interferometric measurements have been performed on steady-state condensates, unable to access the temporal off-diagonal order and non-equilibrium dynamics. Moreover, in solid-state systems, interference between two separate condensates has not been observed before. Here we use optical injection to resonantly generate two dynamic exciton-polariton condensates with distinct momenta and at different times (Fig. 1(a, b)). We characterize the interference between condensates, demonstrating their long-range temporal order (Fig. 1(c, d)).