From Vortex Matter to Quantum Hall States in Anisotropic Rotating Bose Gases

Rapidly rotating atomic gases provide a versatile platform to explore phenomena reminiscent of type-II superconductors and quantum Hall systems. Recent experimental advances—including precise control of trap anisotropy, high-resolution in-situ imaging, and the cooling of complex species such as dipolar gases—have renewed interest in these systems, particularly in the quest to realize fractional quantum Hall (FQH) states. In this work, we present a theoretical study of anisotropic rotating Bose gases projected onto the lowest Landau level (LLL). Starting from the full Hamiltonian, including kinetic, trap, and interaction terms, we derive effective models that capture the interplay of rotation rate, interaction strength, and anisotropy. In the weakly interacting limit, we obtain the Gross-Pitaevskii equation and identify vortex lattice configurations using imaginary-time evolution. At stronger interactions, we employ exact diagonalization and density matrix renormalization group methods to map out a phase diagram featuring both broken-symmetry vortex phases and topologically ordered FQH states, with distinctive edge physics. Our results demonstrate how anisotropy shapes the competition between condensation, vortex matter, and strongly correlated quantum Hall phases, offering a unified framework for future theoretical and experimental exploration of rotating quantum fluids.