Main purpose of this thesis is to present a discussion of the effects \nof artificial spin-orbit coupling and Zeeman fields in fermionic \nultra-cold atoms. Part of the work described here is inspired by \nthe experimental realization of artificial spin-orbit coupling (SOC) in the \nfermionic isotope $^{40}$K using a Raman technique, which was done by NIST group recently. The first aspect investigated is the formation of \ntwo-body bound states of fermions when artificial spin-orbit \ncoupling and artificial Zeeman fields are present. These bound-states \nare analyzed for two-hyperfine-state fermions in free space and \nin a harmonically confining potential. The second aspect explored \nis the study of spectroscopic and thermodynamic properties of \nthree-hyperfine-state fermions. These properties are investigated \nas a function of spin-orbit coupling and Zeeman fields for non-interacting \natoms, but when atom-atom interactions are also included, the many-body \nsystem consisting of three-hyperfine-state fermions \ncan exhibit exotic superfluid phases.
Main purpose of this thesis is to present a discussion of the effects \nof artificial spin-orbit coupling and Zeeman fields in fermionic \nultra-cold atoms. Part of the work described here is inspired by \nthe experimental realization of artificial spin-orbit coupling (SOC) in the \nfermionic isotope 40K using a Raman technique, which was done by NIST group recently. The first aspect investigated is the formation of \ntwo-body bound states of fermions when artificial spin-orbit \ncoupling and artificial Zeeman fields are present. These bound-states \nare analyzed for two-hyperfine-state fermions in free space and \nin a harmonically confining potential. The second aspect explored \nis the study of spectroscopic and thermodynamic properties of \nthree-hyperfine-state fermions. These properties are investigated \nas a function of spin-orbit coupling and Zeeman fields for non-interacting \natoms, but when atom-atom interactions are also included, the many-body \nsystem consisting of three-hyperfine-state fermions \ncan exhibit exotic superfluid phases.
In a recent experiment, a two-dimensional spin-orbit coupling (SOC) was realized for fermions in the continuum [Nat. Phys. 12, 540 (2016)], which represents an important step forward in the study of synthetic gauge fields using cold atoms. In the experiment it was shown that a Raman-induced two-dimensional SOC exists in the dressed-state basis close to a Dirac point of the single-particle spectrum. By contrast, the short-range interatomic interactions of the system are typically expressed in the hyperfine-spin basis. The interplay between synthetic SOC and interactions can potentially lead to interesting few- and many-body phenomena but has so far eluded theoretical attention. Here we study in detail properties of two-body bound states of such a system. We find that, due to the competition between SOC and interaction, the stability region of the two-body bound state is in general reduced. Particularly, the threshold of the lowest two-body bound state is shifted to a positive, SOC-dependent scattering length. Furthermore, the center-of-mass momentum of the lowest two-body bound state becomes nonzero, suggesting the emergence of Fulde-Ferrell pairing states in a many-body setting. Our results reveal the critical difference between the experimentally realized two-dimensional SOC and the more symmetric Rashba or Dresselhaus SOCs in an interacting system, paving the way for future characterizations of topological superfluid states in the experimentally relevant systems.
In this Thesis we discussed ultracold Fermi gas with an s-wave interaction and synthetic spin-orbit coupling under a variety of conditions. We considered the system in both three and two spatial dimensions, with equal-Rashba-Dresselhaus type or Rashba-only type of spin-orbit-coupling, and with or without an artificial Zeeman field. We found competing effects on Fermionic superfluidity from spin-orbit coupling and Zeeman fields, and topologically non-trivial states in the presence of both fields. We gave an outlook on the many-body physics in the last.
Ultra-cold quantum gases subjected to light-induced synthetic gauge potentials have become an emergent field of theoretical and experimental studies. Because of the novel application of two-photon Raman transitions, ultra-cold neutral atoms behave like charged particles in magnetic field. The Raman coupling naturally gives rise to an effective spin-orbit interaction which couples the atom’s center-of-mass motion to its selected pseudo-spin degrees of freedom. Combined with unprecedented controllability of interactions, geometry, disorder strength, spectroscopy, and high resolution measurement of momentum distribution, etc., we are truly in an exciting era of ful- filling and going beyond Richard Feynman’s vision of realizing quantum simulators to better understand the quantum mechanical nature of the universe, manifested immensely in the ultra-cold regimes. In this dissertation, we present a collection of theoretical progresses made by the doctoral candidate and his colleagues and collaborators. From the past few years of work, we mainly address three aspects of the synthetic spin-orbit and light field induced coupling in ultracold quantum gases: a) The ground-state physics of single- particle system, two-body bound states, and many-body systems, all of which are subjected to spin-orbit coupling originated from synthetic gauge potentials; b) The symmetry breaking, topological phase transition and quench dynamics, which are conveniently offered by the realized experimental setup; c) The proposal and impli- cations of light field induced dynamical spin-orbit coupling for atoms inside optical cavity. Our work represents an important advancement of theoretical understanding to the active research frontier of ultra-cold atom physics with spin-orbit coupling.
In cold atom, the coupling between "spin" (atomic internal hyperfine states) and "orbit" (atomic center-of-mass motion) can be induced by Raman transition, where different hyperfine states are coupled by a pair of Raman lasers. In recent years, this synthetic spin-orbit coupling has received tremendous attention, as it leads to a variety of novel quantum phenomena in precisely controllable cold atom systems. In this thesis, we first present a comprehensive analysis of one-, two- and many- particle physics of harmonically trapped atoms with spin-orbit coupling, followed by the study of "novel spin-orbit coupling" in two different systems: (1) cold atom spinor mixtures and (2) cold atoms in an optical cavity. In the first system, we consider a spinor mixture consisting of two species of cold atoms, where the spin-orbit coupling can be transmitted from one species to the other, and we discuss novel topological properties and the supersolid stripe phase in this mixture. In the second system, we consider the coupling among three parts: the cavity photon field, the atomic internal hyperfine states, and the atomic external center-of-mass motion, and we discuss how this coupling affects familiar quantum optical phenomena, such as Rabi oscillation and Dicke superradiance phase transition. Our novel systems contribute new and practical platforms for the research field of synthetic spin-orbit coupling in cold atoms.
We develop a theory for interacting fermions in the presence of spin-orbit coupling and Zeeman fields, and show that many new superfluids phases, which are topological in nature, emerge. Depending on values of spin-orbit coupling, Zeeman fields, and interactions, initially gapped s-wave superfluids acquire p-wave, d-wave, f-wave and higher angular momentum components, which produce zeros in the excitation spectrum, rendering the superfluid gapless. Several multi-critical points, which separate topological superfluid phases from normal or non-uniform, are accessible depending on spin-orbit coupling, Zeeman fields or interactions, setting the stage for the study of tunable topological superfluids.
Atomtronics, a technique to control atoms for an application of devices, has been studied in recent years.The purpose of this thesis is to propose a novel method to control atoms for the application to the atomtronics.To achieve this purpose, we use a spin current in a spin-orbit (SO) coupled cold atoms.The spin current, that is a counterflow of particles with different spins, has attracted attention as a method to control electrons.On the other hand, the artificial SO coupled cold atoms were experimentally realized in 2011 and have been studied theoretically and experimentally.We can expect that a spin current can be formed in the SO coupled cold atoms because the SO coupling is known to induce a spin current and controlled because the cold atoms have various experimentally controllable parameters.However, little has been studied so far on the spin current in the cold atom.Therefore, we studied novel controllability of the spin current in the SO coupled cold atom.An SO coupled Bose-Einstein condensate (BEC) was experimentally realized in 2011 and then an SO coupled degenerate fermions became available in 2012.In these systems, since the SO coupling was engineered in a neutral atom by dressing two atomic spin states with a pair of Raman lasers and an external magnetic field, it is called artificial SO coupling.In addition, some parameters such as intensity of the SO coupling can be experimentally tuned by the lasers and the external magnetic field in the artificial SO coupled cold atoms.Therefore, by investigating parameter dependence of the spin currents, we reveal controllability of the atoms in the artificial SO coupled Bose and Fermi systems.As a result, in the SO coupled Bose system, the spin current changes discontinuously and non-smoothly across the phase boundaries, while in the SO coupled Fermi system, the spin current changes continuously and smoothly at zero temperature.On the other hand, Bose-Fermi mixture was experimentally realized and have been studied from different viewpoints.Therefore, we can expect to realize an artificial SO coupled Bose-Fermi mixture in near future.In this system, since atoms of different quantum statistics coexist under an influence of the SO coupling, novel phenomena can be expected.Based on these ideas, we investigate a ground state and a spin current in a mixture of fermions and SO coupled bosons.The ground states are calculated in the SO coupled Bose-Fermi mixture with high density or low density of the atoms by using a variational method and some approximations such as tight-binding approximation.For the high density, the fermions have a large influence on the Bose system, while, for the low density, the fermions have little influence although the relative amounts of the bosons and the fermions are comparable in the two cases.In addition, we show that the spin current of the i