| The ultracold atomic gas attracts extensive interests of the physics community in recent years, for its feasible controllability to study quantum theory of many-body sys-tems and associated novel quantum states. In ultracold atomic gases, alkali atoms are loaded in magneto-optical trap (MOT), and can be tuned and measured via various laser techniques. Meanwhile, the tunable interaction between two alkali atoms can be intro-duced via Feshbach resonances. Due to those experimental advantages, the ultracold atomic gas offers an ideal platform to simulate various condensed matter systems such as strongly correlated ones, and reveal exotic quantum phenomena.The superconductivity/superfluidity, with an intriguing behavior that particles flow without friction, has attracted tremendous investigations, but challenges perfect theo-retic explanations. It is first discovered in mercury by Onnes in 1911. In 1957, Bardeen, Cooper, and Schrieffer (hereafter BCS) developed a mean-field theory and successfully made a first effort to explain the microscopic mechanics of the conventional supercon-ductors. They introduced the concept, the Cooper pair, which consists in two fermions with opposite spins and momentum, to characterize the superconductivity. However, for new discovery of unconventional superconductors such as heavy-fermion super-conductors (CeCoIn5), organic superconductors ((TMTSF)2PF2), and topological su-perconductors (Kitaev chain), there still exist obstacles to explain their existence via the BCS theory. Exotic superfluid states, for example the Fulde-Ferrell superfluid state (Cooper pairs with non-zero momentum) and the p-wave superfluid state, provide an alternative way to understand those unconventional superconductors. However, the ex-perimental signature of those exotic superfluid states still lacks.The research on topological materials and associated topological phase transitions is another new direction that has attracted much recent attention. Basically, The topo-logical properties of many-body systems is characterized in terms of the time-reverse symmetry, particle-hole symmetry, and chiral symmetry. The topological materials can host edge states which is distinct from nontopological ones. Investigations on topolog-ical materials can provide theoretic explanation for novel quantum states such as quan-tum Hall effect, topological insulators, and topological superconductors. Due to the evidence of chiral Majorana-fermion edge states, topological superconductors provide a promising experimental platform for topological quantum computation and quantum memory, and potential applications in fault-tolerant topological quantum computation.Motivated by those earlier works, in this thesis we focus on the realization of exotic superfluid states in ultracold atomic gases, and investigate their theoretic explanation and topological properties. We organize the thesis as following:I. Fulde-Ferrell superfluids in a spin-orbital coupled Fermi gas.In cold atom experiments, the hyperfine states of alkali atoms can be coupled via Raman lasers. The alkali atom will earn an additional momentum from Raman lasers when it hops from the initial hyperfine state to another one. If we denote the hyperfine states as the atom spins (i.e. pseudo-spins), the Raman transition gives rise to synthetic spin-orbit couplings. Meanwhile, the detune between the coupled hyperfine states be-haves as Zeeman fields. Therefore in a ultracold atomic gas, we can study the influence of the spin-orbit couplings and Zeeman fields on the collective mode of the many-body system. This work consists in three parts:(i) We search the evidence of the Fulde-Ferrell superfluids and explain the mechanics of its existence, (ii) We investigate the topologi-cal property of the Fulde-Ferrell superfluids, and find the evidence of Majorana-fermion states. The origin of the topological property is also discussed, (iii) We study the effect of spin-orbit couplings and Zeeman fields on thermodynamic properties.II. Floquet Fulde-Ferrell superfluids in a shaken fermionic optical lattice.The shaken optical lattice has been experimental realized, and open a new avenue to study Floquet states for time-periodic systems. When the shaking frequency is tuned to match the gap between two orbital bands, the two bands will be hybridized and it induces a change of the single-particle dispersion. Our work relies on the band hybrida-tion caused by the shaken optical lattice. If we denote the orbits as the pseudo-spins, the interaction will introduce the Cooper pairing between two orbits, simulating a superfluid state, i.e. the Floquet superfluid. The band inversion between two bands (pseudo-spins) thus gives rise to Cooper pairs with non-zero momentum, i.e. the Floquet Fulde-Ferrell superfluids. The topological phase transition in such a shaken lattice system is also studied.III. Fulde-Ferrell superfluids in a driven fermionic optical lattice.Motivated by the shaken optical lattice technique, we study a lattice system with an additional moving lattice. When the moving frequency is tuned to match the gap be-tween two orbital bands, the two bands will be hybridized and the symmetry of single-particle dispersion will be broken. In the presence of interactions, the Cooper pair will naturally host a non-zero momentum, indicating the Fulde-Ferrell superfluids. Our pro-posal is simple and reliable. All lasers are far detuned and spin-orbit couplings are absent, hence the heating effect, which is detrimental to superfluids, is obviously sup-pressed. As the spin degeneracy is not broken, the system is spin-balanced. That is completely distinct from earlier works in which the Fulde-Ferrell superfluids originated from spin imbalance. Hence our work provide a new proposal to find the Fulde-Ferrell superfluids whose origination is totally different.Ⅳ. Effective p-wave superfluids in a spin-dependent optical lattice.The spin-dependent optical lattice can be realized via lasers with opposite polar-izations. It can introduce a polarization-dependent A.C. Stark shift and, consequently, gives rise to a hyperfine-state-dependent lattice trap. When the two sublattice in differ-ent spins hosts a spaitial offset, each alkali atom in one sublattice can interplay with two adjacent atoms in the other sublattice. In such a spin-dependent lattice system, we can synthesize effective p-wave superfluids. The p-wave superfluids can hosts Majorana-fermion states, which plays a critical role in research on elemental particles and dark matters. In contrast of earlier works to realize p-wave superfluids via p-wave Feshbach resonance or p-orbital parity, our work offer a more experimental feasible proposal. |
PDF Full Text Request