Orbital angular momentum (OAM) of light represents a fundamental optical freedom that can be exploited to manipulate quantum state of atoms. In particular, it can be used to realize spinorbital-angular-momentum (SOAM) coupling in cold atoms by inducing an atomic Raman transition using two laser beams with differing OAM. Rich quantum phases are predicted to exist in manybody systems with SOAM coupling. Their observations in laboratory, however, are often hampered by the limited control of the system parameters. In this work we report, for the first time, the experimental observation of the ground-state quantum phase diagram of the SOAM coupled Bose-Einstein condensate (BEC). The discontinuous variation of the spin polarization as well as the vorticity of the atomic wave function across the phase boundaries provides clear evidence of firstorder phase transitions. Our results open up a new way to the study of phase transitions and exotic quantum phases in quantum gases. arXiv:1806.06263v2 [cond-mat.quant-gas]

We investigate the behaviour of a two-component Fermi superfluid in a double-well potential. We numerically solve the time dependent Bogoliubov-de Gennes equations and characterize the regimes of Josephson oscillations and self-trapping for different potential barriers and initial conditions. In the weak link limit the results agree with a two-mode model where the relative population and the phase difference between the two wells obey coupled nonlinear Josephson equations. A more complex dynamics is predicted for large amplitude oscillations and large tunneling.

Theoretical predictions for the dynamic structure factor of a harmonically trapped Fermi superfluid near the Bose-Einstein condensate-Bardeen-Cooper-Schrieffer (BEC-BCS) crossover are compared with recent Bragg spectroscopy measurements at large transferred momenta. The calculations are based on a random-phase (or time-dependent Hartree-Fock-Gorkov) approximation generalized to the strongly interacting regime. Excellent agreement with experimental spectra at low temperatures is obtained, with no free parameters. Theoretical predictions for zero-temperature static structure factor are also found to agree well with the experimental results and independent theoretical calculations based on the exact Tan relations. The temperature dependence of the structure factors at unitarity is predicted.