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Recent experiments on bosonic atoms, confined in 2D optical lattices and exposed to a leaky optical cavity, have revealed intriguing self-organization phenomena, including the coexistence of phase coherence and charge order characteristic of supersolid phases.
Mean field theories of such systems typically rely on the cavity adiabatic elimination, yielding an effective Bose-Hubbard model with infinite-range interactions. This approximation misses important effects, related to the dissipative nature of the cavity, that we unveiled by performing truncated Wigner simulations of the full quantum dynamics for large 2D lattices [1]. We show that the relaxation of the system towards the steady state is quite slow compared to the timescales of the bosons and phase coherence displays quasi-long range order. Based on an accurate finite-size scaling analysis, we show that in the strong coupling regime the cavity induces a Berezinskii-Kosterlitz-Thouless phase transition, where the supersolid turns into a charge density wave insulator.
[1] G. Orso, J. Zakrzewski and P. Deuar, Self-organized cavity bosons beyond the adiabatic elimination approximation, Physical Review Letters 134, 183405 (2025).
