First-order transition into a topological superfluid state in an atom-cavity system

We propose to combine Bose-Einstein condensation in higher Bloch bands and a driven-dissipative cavity-BEC system into a hybrid light-matter platform. Specifically, the condensate is trapped in a bipartite $s$-$p_x$-$p_y$-lattice, with a tunable energy offset. This enables a controlled population transfer from the $s$-orbital to the nearly degenerate $p_x$ and $p_y$ orbitals. The system forms a chiral ground state with $p_x \pm i p_y$ symmetry, with staggered orbital currents. By increasing the transverse pump strength, we drive the system into the superradiant phase, resulting in a self-organized, density checkerboard, which rectifies the staggered chiral order into a topological superfluid state. Using truncated Wigner simulations and complementary mean-field analysis, we determine the phase transition into this state as first order. Our results show that higher-band condensates coupled to a cavity provide a promising platform for engineering non-trivial orbital order and topological superfluid phases in quantum optical many-body systems.