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Theoretical analysis of spin current induced in cold atoms with artificial spin-orbit coupling

Ryohei Sakamoto

Published Mar 25, 2019• 0 citations
OpenAlex

Abstract

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

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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
The novel controllability of a spin current in cold atoms is studied. We show that a mixture of spin-1/2 fermions and spin–orbit (SO) coupled pseudospin-1/2 bosons at zero temperature can form a fermionic spin current, which is experimentally controllable with an external laser applied to the bosons to create the SO coupling. We derive the ground-state phase diagram of the bosons using a variational wave function and identify the magnetic structure of each phase. The spin current of the fermions with the background of the spiral/precessed magnetization of the bosons is calculated as a function of the wave vector and intensity of the external laser. We show that the spin current increases and then decreases, forming a peak, as the wave vector of the laser increases, which indicates the controllability of the spin current with the laser parameters.
We review our recent experimental realization and investigation of a spin-orbit (SO) coupled Bose-Einstein condensate (BEC) and quantum degenerate Fermi gas. By using two counter-propagating Raman lasers and controlling the different frequency of two Raman lasers to engineer the atom-light interaction, we first study the SO coupling in BEC. Then we study SO coupling in Fermi gas. We observe the spin dephasing in spin dynamics and momentum distribution asymmetry of the equilibrium state as hallmarks of SO coupling in a Fermi gas. To clearly reveal the property of SO coupling Fermi gas, we also study the momentum-resolved radio-frequency spectroscopy which characterizes the energy-momentum dispersion and spin composition of the quantum states. We observe the change of fermion surfaces in different helicity branches with different atomic density, which indicates that a Lifshitz transition of the Fermi surface topology change can be found by further cooling the system. At last, we study the momentum-resolved Raman spectroscopy of an ultracold Fermi gas.
The dissertation explores the effects of synthetic spin-orbit coupling on the behaviour of quantum gases in several different contexts. We first study realistic methods to create vortices in spin-orbit-coupled (SOC) Bose-Einstein condensates (BEC). We propose two different methods to induce thermodynamically stable static vortex configurations: (1) to rotate both the Raman lasers and the anisotropic trap; and (2) to impose a synthetic Abelian field on top of synthetic spin-orbit interactions. We solve the Gross-Pitaevskii equation for several experimentally relevant regimes and find new interesting effects such as spatial separation of left- and right-moving spin-orbit-coupled condensates, and the appearance of unusual vortex arrangements. Next we consider cold atoms in an optical lattice with synthetic SOC in the Mott-insulator regime. We calculate the parameters of the corresponding tight-binding model and derive the low-energy spin Hamiltonian which is a combination of Heisenberg model, quantum compass model and Dzyaloshinskii-Moriya interaction. We find that the Hamiltonian supports a rich classical phase diagram with collinear, spiral and vortex phases. Next we study the time evolution of the magnetization in a Rashba spin-orbit-coupled Fermi gas, starting from a fully-polarized initial state. We model the dynamics using a Boltzmann equation, which we solve in the Hartree-Fock approximation. The resulting non-linear system of equations gives rise to three distinct dynamical regimes controlled by the ratio of interaction and spin-orbit-coupling strength λ: for small λ, the magnetization decays to zero. For intermediate λ, it displays undamped oscillations about zero and for large λ, a partially magnetized state is dynamically stabilized. Motivated by an interesting stripe phase which appears in BEC with SOC [Li et al., Phys. Rev. Lett. 108, 225301 (2011)], we study the finite-temperature phase diagram of a pseudospin-1/2 Bose gas with contact interactions. We show that strong inter-spin interactions can lead to the appearance of magnetically ordered phases at temperatures above the superfluid transition. For the case of inter-spin attraction, we also discuss the possibility of a bosonic analogue of the Cooper-paired phase, however this state is not energetically favourable. We extend our calculations to a spin-orbit-coupled Bose gas to investigate the possibility of stripe ordering in the normal phase. However, within our approximations, we do not find an instability towards stripe formation. Finally, we consider a two-dimensional Bose gas at zero temperature with an underlying quartic single-particle dispersion in one spatial direction. This Hamiltonian can be realized using the NIST scheme of spin-orbit coupling [Y.-J. Lin, K. Jimenez-Garcia, and I. B. Spielman, Nature 471, 83 (2011)], or using the shaken lattice scheme of Parker et al. [C. V. Parker, L.-C. Ha and C. Chin, Nature Physics 9, 769 (2013)]. By numerically comparing energies of various trial wave-functions, we show that, at low densities, the ground state is strongly correlated, in contrast to a typical mean-field BEC. The trial wave-function with the lowest energy is of Jastrow-type and it describes a state with finite, but strongly reduced, condensate fraction.
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.
Artificial synthetic gauge field and spin-orbit coupling has been extensively studied following their experimental realization in ultracold atomic systems. Thanks for the versatile controllability, such systems not only provide possibilities to simulate and study important models in multidisciplinary fields of physics, but also work as an excellent platform to engineer novel states of matter and quantum phenomena. This paper reviews some recent progresses on the study of ultracold atomic systems with spin-orbit coupling, focusing on the effects induced by dissipation, novel interaction forms, large symmetry of spins, and long-range interactions. The investigation in these aspects is closely related to the characteristics of ultracold atomic systems, hence can bring new inspirations and perspectives on the understanding of spin-orbit coupling. In this review, we firstly investigate the appearance of a topological superradiant state in a quasi-one-dimensional Fermi gas with cavity-assisted Raman process. A cavity-assisted spin-orbit coupling and a bulk gap opening at half filling will be induced by the superradiant light generated in the transversely driven cavity mode. The topological superradiant state and the corresponding topological phase transition in the system can be driven by this mechanism. Then, symmetry-protected topological states of interacting fermions will be introduced in a quasi-one-dimensional cold gas of alkaline-earth-like atoms. Raman-assisted spin-orbit couplings in the clock states, together with the spin-exchange interactions in the clock-state manifolds will give rise to symmetry-protected topological states for interacting fermions, by taking advantage of the separation of orbital and nuclear-spin degrees of freedom in these alkaline-earth-like atoms. Furthermore, we show that an exotic topological defect, double-quantum spin vortices, which are characterized by doubly quantized circulating spin currents and unmagnetized filled cores, can exist in the ground states of SU(3) spin-orbit-coupled Bose-Einstein condensates. It is found that the combined effects of SU(3) spin-orbit coupling and spin-exchange interaction determine the ground-state phase diagram. Finally, we demonstrate that spin-orbit coupling and soft-core long-range interaction can induce an exotic supersolid phase of Bose gas, with the emergence of spontaneous circulating particle current. This implies that a finite angular momentum can be generated with neither external rotation nor synthetic magnetic field, and the direction of the angular momentum can be altered by adjusting the strength of spin-orbit coupling or interatomic interaction.