Exotic Phases and Quantum Dynamics in Spin-Orbit Coupled Bose-Einstein Condensates

In this dissertation, we study a range of exotic quantum phases and dynamics in BoseEinstein condensates (BECs) with spin-orbit (SO) coupling. Firstly, inspired by the recent experimental progresses in engineering supersolid stripe states in a SO-coupled BEC, we conjecture a new quantum state of matter called “superfluid-qausicrystal”, in which quasicrystalline orders form spontaneously in the ground states of the BECs. We propose a realistic setup to prepare and observe this exotic quantum states and confirm its existence through both variational ansatz analysis and direct simulation of mean-field Gross-Pitaevskii equation (GPE). Moreover, we have identified rich phase diagram including superfluid-qausicrystals, supersoilds and plane-wave phases. By utilizing the double-well band structure of a SO-coupled BEC, we propose and investigate a momentum-pace Josephson junction (MSJJ). We show that, under an extra pair of Raman lasers, the two band minimums in momentum space can be weakly coupled. In such a MSJJ, Josephson currents can be induced not only by applying the equivalent of “voltages”, but also by tuning tunneling phases. We characterize the MSJJs through both full mean-field analysis and a concise two-level model and demonstrate the important role of interactions between atoms. Besides, we experimentally demonstrate that this can be a route for realizing a striped BEC, providing an accessible platform to investigate the excitation spectra and other important properties of supersolid-like states. We observe coherent Rabi oscillations in momentum space between two band minima and demonstrate a long lifetime of the ground state, which find good agreements with mean-field simulations. Finally, we theoretically conceive and experimentally demonstrate a non-magnetic one-way spin switch device using a SO-coupled BEC subjected to a moving spin-independent repulsive dipole potential. We show that the physical foundation of this unidirectional device is based on the breakdown of Galilean invariance in the presence of SO coupling. The experimental observation, the numerical simulations and the theoretic interpretations are consistent with the others.