Temporal long-range order in exciton-polariton condensates

We demonstrate temporal long-range off-diagonal order in microcavity exciton-polariton dynamic condensation, by interference between two separate condensates, generated at different times and with different momenta. In our pulsed resonantly-injected condensates, stimulated polariton-polariton scattering results in spectral narrowing of the dynamic condensates and thus in longer coherence times. We study the temporal decay of the long-range order by monitoring the interference visibility between the condensates. We show that it strongly depends on the excitonic fraction of the polaritons and the corresponding polariton-polariton interaction strength, as well as on the temperature and pump intensity. Moreover, polariton interaction yields a blue shift of the condensate energy, which appears as a time-dependent shift in the interference pattern. These results show a direct evidence of temporal long-range order in dynamic condensates as well as demonstrate a new method for probing their ultrafast dynamics, opening new directions in the fundamental study of coherence in matter.