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arXiv:1311.6177 · Physical Review A

Raman-dressed spin-1 spin-orbit-coupled quantum gas

Zhihao Lan, Patrik Öhberg

Published Feb 24, 2014• 90 citations
arXivHTMLPDF

Abstract

The recently realized spin-orbit-coupled quantum gases [Lin et al., Nature (London) 471, 83 (2011); Wang et al., Phys. Rev. Lett. 109, 095301 (2012); Cheuk et al., Phys. Rev. Lett. 109, 095302 (2012)] mark a breakthrough in the cold atom community. In these experiments, two hyperfine states are selected from a hyperfine manifold to mimic a pseudospin-1/2 spin-orbit-coupled system by the method of Raman dressing, which is applicable to both bosonic and fermionic gases. In this paper, we show that the method used in these experiments can be generalized to create any large pseudospin spin-orbit-coupled gas if more hyperfine states are coupled equally by the Raman lasers. As an example, we study, in detail, a quantum gas with three hyperfine states coupled by the Raman lasers and show, when the state-dependent energy shifts of the three states are comparable, triple-degenerate minima will appear at the bottom of the band dispersions, thus, realizing a spin-1 spin-orbit-coupled quantum gas. A novel feature of this three-minima regime is that there can be two different kinds of stripe phases with different wavelengths, which has an interesting connection to the ferromagnetic and polar phases of spin-1 spinor Bose-Einstein condensates without spin-orbit coupling.

DOI
10.1103/physreva.89.023630

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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.
Excited-state quantum phase transitions depend on and reveal the structure of the whole spectrum of many-body systems. While they are theoretically well understood, finding suitable signatures and detecting them in actual experiments remains challenging. For instance, in spinor gases, excited-state phases have been identified and characterized through a topological order parameter that is challenging to measure in experiments. Here we propose the Raman-dressed spin-orbit-coupled gas as a novel platform to explore excited-state quantum phase transitions. In a weakly coupled regime, the dressed system is equivalent to a spinor gas with tunable spin-spin interactions. Through this equivalence we are able to identify excited-state phases in the Raman-dressed Bose gas. The phases are characterized by the behavior of the spatial density modulations, or stripes, induced by spin-orbit coupling, and can in principle be measured in current state-of-the-art experiments with ultracold atoms. Conversely, we show that the properties of the excited phase can be exploited to prepare stripe states with large and stable density modulations.
An experimental proposal for realizing spin-orbit (SO) coupling of pseudospin 1 in the ground manifold ${}^{1}\mathrm{\ensuremath{\Sigma}}(\ensuremath{\upsilon}=0)$ of (bosonic) bialkali polar molecules is presented. The three spin components are composed of the ground rotational state and two substates from the first excited rotational level. Using hyperfine resolved Raman processes through two select excited states resonantly coupled by a microwave, an effective coupling between the spin tensor and linear momentum is realized. The properties of Bose-Einstein condensates for such SO-coupled molecules exhibiting dipolar interactions are further explored. In addition to the SO-coupling-induced stripe structures, the singly and doubly quantized vortex phases are found to appear, implicating exciting opportunities for exploring novel quantum physics using SO-coupled rotating polar molecules with dipolar interactions.
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.
Spin-orbit coupling (SOC) can give rise to interesting physics, from spin Hall to topological insulators, in condensed matter systems. Recently, this topical area has extended into atomic quantum gases in searching for artificial or synthetic gauge potentials. The prospects of tunable interaction and quantum state control promote neutral atoms as nature's quantum emulators for SOC. Lin et al. recently demonstrated a special form of the SOC ${k}_{x}{\ensuremath{\sigma}}_{y}$, which they interpret as an equal superposition of Rashba and Dresselhaus couplings in Bose-condensed atoms [Lin, Jim\'enez-Garc\'{\i}a, and Spielman, Nature (London) 471, 83 (2011)]. This work reports a method of implementing arbitrary forms of SOC by switching between two pairs of Raman laser pulses like the method used by Lin et al. While one pair affects ${k}_{x}{\ensuremath{\sigma}}_{y}$ for some time, a second pair creates ${k}_{y}{\ensuremath{\sigma}}_{y}$ at other times with Raman pulses from different directions and a subsequent spin rotation into $\ifmmode\pm\else\textpm\fi{}{k}_{y}{\ensuremath{\sigma}}_{x}$. With a sufficient number of pulses, the effective actions from different durations are small and accumulate in the same exponent despite the fact that ${k}_{x}{\ensuremath{\sigma}}_{y}$ and $\ifmmode\pm\else\textpm\fi{}{k}_{y}{\ensuremath{\sigma}}_{x}$ do not commute. Our scheme involves no added complication and can be demonstrated within current experiments. It applies equally to bosonic or fermionic atoms.
In spinor Bose-Einstein condensates, spin-changing collisions are a remarkable proxy to coherently realize macroscopic many-body quantum states. These processes have been, e.g., exploited to generate entanglement, to study dynamical quantum phase transitions, and proposed for realizing nematic phases in atomic condensates. In the same systems dressed by Raman beams, the coupling between spin and momentum induces a spin dependence in the scattering processes taking place in the gas. Here we show that, at weak couplings, such modulation of the collisions leads to an effective Hamiltonian which is equivalent to the one of an artificial spinor gas with spin-changing collisions that are tunable with the Raman intensity. By exploiting this dressed-basis description, we propose a robust protocol to coherently drive the spin-orbit-coupled condensate into the ferromagnetic stripe phase via crossing a quantum phase transition of the effective low-energy model in an excited state.