We investigate the effects of interaction for the stripe phase of a homogeneous one-dimensional Bose gas with laser-induced Raman spin-orbit coupling (SOC) and Zeeman splitting, for a wide range of densities.In order to account for quantum fluctuations, important in one dimension for low densities close to the Tonks-Girardeau limit, we use a variational method based on the hypernetted-chain Euler-Lagrange optimization of a Jastrow-Feenberg ansatz for the many-body wave function.For strong coupling we observe significant deviations from mean-field results not only quantitatively but also qualitatively.The main interest of this paper lies in the interplay and competition between interaction-induced pair correlations and the SOC-induced density oscillations of the stripe phase.We explain the increase in wave number of this density oscillation with increasing interaction due to an effective attraction between particles in the many-body system.
We investigate the effects of interaction for the stripe phase of a homogeneous one-dimensional Bose gas with laser-induced Raman spin-orbit coupling (SOC) and Zeeman splitting, for a wide range of densities.In order to account for quantum fluctuations, important in one dimension for low densities close to the Tonks-Girardeau limit, we use a variational method based on the hypernetted-chain Euler-Lagrange optimization of a Jastrow-Feenberg ansatz for the many-body wave function.For strong coupling we observe significant deviations from mean-field results not only quantitatively but also qualitatively.The main interest of this paper lies in the interplay and competition between interaction-induced pair correlations and the SOC-induced density oscillations of the stripe phase.We explain the increase in wave number of this density oscillation with increasing interaction due to an effective attraction between particles in the many-body system.
A Bose gas under the effect of Raman spin-orbit coupling (SOC) is analyzed using the discrete spin T-moves diffusion Monte Carlo method. Upon computing the energy as well as the static structure factor and the superfluid fraction of the system, the emergence of an energetically favorable supersolid stripe state is observed, which is in agreement with recent observations. A significant enhancement of the stability of the stripe phase with respect to the mean-field prediction is observed when the strength of the interatomic correlations is increased. We also quantify and characterize the degree of superfluidity of the stripes and show that this quantity is mostly determined by the ratio between the Raman coupling and the square of the momentum difference between the pair of SOC-inducing laser beams.
The coherence of a quantum system is one of the key signatures of many-body physics. While a three-dimensional Bose-Einstein condensate (BEC) exhibits true long-range coherence, a Bose gas confined in a one-dimensional (1D) potential displays quasi-long-range order. Experimentally, these coherence properties are typically probed via the momentum distribution, which corresponds to the Fourier transform of the one-body correlation function. In two-dimensional (2D) systems, for example, momentum distribution enables the observation of the Berezinskii-Kosterlitz-Thouless (BKT) transition from a thermal cloud to a superfluid. With trimodal distribution fitting, an intermediate quasicondensate phase is also revealed. In 1D systems, the momentum distribution of a quenched Tonks-Girardeau (TG) Bose gas can be mapped to that of a non-interacting Fermi gas at a specific evolution time, achieving the rapidity distribution. On the other hand, spin-orbit coupling (SOC) has emerged as one of the central topics in ultracold atomic physics. In additional to creating an artificial electric or magnetic field, researchers also observe negative-mass dynamics in a spin-orbit-coupled BEC by engineering the curvature of the band dispersion. This phenomenon is directly observable in the density distribution of the system. In 1D systems, SOC also introduces rich physical phenomena; while low-energy 1D quantum systems are conventionally described by Tomonaga-Luttinger liquid (TLL) theory, SOC notably alters the energy-momentum dispersion. This modification gives rise to unconventional Luttinger liquids whose properties are governed by the spin-orbit coupling strength.In this work, we first investigate the qualitative properties of a 1D Bose gas and demonstrate the temperature dependence of the momentum distribution, revealing how the thermal fluctuations destroy the quasi-long-range order. In the second part, we probe the effects of 1D SOC on a 1D Bose gas, focusing on how SOC modifies the energy-momentum dispersion and the resulting momentum distribution. We demonstrate that within a specific parameter regime, the momentum distribution and its associated coherence properties undergo distinct qualitative changes. The occupied higher momentum states induce phase fluctuations and destroy the coherence of the system, showing signals of the non-Luttinger liquid physics. We probe the coherence properties of a 1D system along these two parameter axes.
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.
Quantum degenerate gases have provided rich systems to simulate engineered Hamiltonians and to explore quantum many-body problems in laboratory-scale experiments. In this work, I focus on spin-orbit-coupled (SOC) Bose-Einstein condensates (BECs) of Rubidium-87 atoms realized using two-photon Raman coupling in which various novel phases are predicted to exist due to competing energies from the atomic internal structure, coupling strength, and many-body collisions. BECs are observed primarily using the interaction between light and matter, where it is common to probe the atoms with near-resonant light and image their shadow on a camera. This absorption imaging technique measures the integrated column density of the atoms and it is crucial to focus the imaging system. I present a systematic method to bring the ultracold atom systems into an optimal focus using the power spectral density (PSD) of the atomic density-density correlation function. The spatial frequency at which the defocus-induced artifacts first appear in the PSD is maximized at the focus. The focusing process thus identifies the range of spatial frequencies over which the PSD is uncontaminated by finite-thickness effects. Next, I describe magnetic phases which exist in spin-1 spin-orbit-coupled condensates at a near-zero temperature. I observe ferromagnetic and unmagnetized phases which are stabilized by the locking between the spin and linear momentum of the system. Our measurements of both the first- and second-order transitions are in agreement with theory. Finally, I discuss the stripe-ordered phase that occurs in SOC Bose gases favoring the miscibility configuration. The stripe phase is theoretically predicted to have an excitation spectrum analogous to that of a supersolid and to exhibit spatial density modulation within specific regions of parameter space. I used optical Bragg scattering to probe the small density modulation present in the atomic spatial distribution. I present for the very first time observation of the stripe phase in a Raman SOC Bose gas and its phase diagram in various parameter space. Our observations of the phase boundaries are consistent with theory and previous work.
We theoretically investigate a three-dimensional weakly interacting Bose gas with one-dimensional Raman-type spin-orbit coupling at zero temperature. By employing an improved ansatz, including high-order harmonics in the stripe phase, we show that the critical transition from the stripe to the plane-wave phases is shifted to a relatively larger Rabi frequency compared to the prediction by previous work [Li et al., Phys. Rev. Lett. 108, 225301 (2012)] using a first-order stripe ansatz. We also determine the quantum depletion and superfluid density over a large range of Rabi frequency in different phases. The depletion exhibits an intriguing behavior with a discontinuous jump at the transition between the stripe and plane-wave phases, and a maximum at the transition between the plane-wave and zero-momentum phases. The superfluid density is derived through a phase-twist method. In the plane-wave and zero-momentum phases, it is significantly suppressed along the spin-orbit-coupling direction and vanishes at the transition, consistent with a recent work [Zhang et al., Phys. Rev. A 94, 033635 (2016)], while in the stripe phase, it smoothly decreases with increasing Rabi frequency. Our predictions would be useful for further theoretical and experimental studies of the exotic supersolid stripe phase.
We investigate the phases of a Bose-Einstein condensate of dipolar atoms restricted to move in a two-dimensional plane. The dipole moments are all aligned in a direction tilted with respect to the plane normal. As a result of the attractive and repulsive components of the dipole-dipole interaction, the dipolar gas has a self-bound phase, which is stabilized by quantum fluctuations. Tilting the dipoles tunes the anisotropy of the dipole-dipole interaction, which can trigger a spatial density modulation. In this work we study these two aspects and investigate the conditions for the formation of a self-bound and striped phase, which has been realized in experiments with dipolar droplets. We use a variational method based on the hypernetted-chain Euler-Lagrange optimization of a Jastrow-Feenberg ansatz for the many-body wave function to study the ground-state properties. This method takes into account quantum fluctuations in a nonperturbative way and thus can be used also for strongly correlated systems.