Microcavity electron-hole-photon systems are long anticipated to exhibit a crossover from Bose-Einstein condensate (BEC) to Bardeen-Cooper-Schrieffer (BCS) superfluid, when carrier density is tuned to reach the Mott transition density. Yet, theoretical understanding of such a BEC-BCS crossover largely relies on the mean-field framework and the nature of the carriers at the crossover remains unclear to some extent. The BEC-BCS crossover is also known to occur in ultracold atoms confined in optical traps. In this talk, I will introduce some recent results on the universal BEC-BCS crossover physics from the theory group at Swinburne University.
In the first part of the talk, motivated by the recent demonstration of a BCS polariton laser , I will discuss the properties of a strongly interacting BCS polariton condensate at thermal equilibrium . Based on a simplified short-range description of the electron-hole attraction, we examine the role of quantum fluctuations in an exciton-polariton condensate and determine the number of different type carriers at the crossover beyond mean-field. Near Mott density and with ultra-strong light-matter coupling, we find an unexpectedly large phase window for the strongly correlated BCS polariton condensate, where both fermionic Bogoliubov quasi-particles and bosonic excitons are significantly populated and strongly couple to photons. We predict its absorption spectrum and show that the upper polariton energy gets notably renormalized, giving rise to a high-energy side-peak at large carrier density, as observed in recent experiments.
In the second part, I will talk about spin-1/2 ultracold Fermi gases confined in two dimensions with a tight harmonic trapping potential along the z-direction. Here, virtual excitations along the tightly-confined direction play the same role of photons in microcavities. In the case of an additional harmonic trap added on the xy-plane, the Fermi cloud shows an interesting violation of a classical scale invariance (i.e., the so-called quantum anomaly), as indicated by its breathing mode frequency. We present theoretical understanding of such a quantum anomaly from both few-body  and many-body perspective . We also find the formation of cluster states at a positive interaction range , similar to biexcitons, triexcitons and bipolaritons observed in microcavities.
 J. Hu, Z. Wang, S. Kim, H. Deng, S. Brodbeck, C. Schneider, S. Höfling, N. H. Kwong, and R. Binder, Signatures of a Bardeen-Cooper-Schrieffer Polariton Laser, arXiv:1902.00142v1.
 H. Hu and X.-J. Liu, Quantum fluctuations in a strongly interacting BCS polariton condensate at thermal equilibrium, arXiv:1910.06494v1.
 X.-Y. Yin, H. Hu, and X.-J. Liu, Few-body perspective of quantum anomaly in two-dimensional interacting Fermi gases, arXiv:1907.10195v1.
 H. Hu, B. C. Mulkerin, U. Toniolo, L. He, and X.-J. Liu, Phys. Rev. Lett. 122, 070401 (2019).
 X.-Y. Yin, H. Hu, and X.-J. Liu, Phys. Rev. Lett. 123, 073401 (2019).