Session N5: Synthetic Gauge Fields and Spin-Orbit Coupling

Realizing the Harper Hamiltonian and Spin-Orbit Coupling with Laser-Assisted Tunneling in an Optical Lattice

The study of charged particles in a magnetic field has led to paradigm shifts in condensed matter physics including the discovery of topologically ordered states like the quantum Hall and fractional quantum Hall states. Quantum simulation of such systems using neutral atoms has drawn much interest recently in the atomic physics community due to the versatility and defect-free nature of such systems. We discuss our recent experimental realization of the Harper Hamiltonian and strong, uniform effective magnetic fields for neutral particles in an optical lattice [1]. Additionally, our scheme represents a promising system to realize spin-orbit coupling and the quantum spin Hall states without flipping atomic spin states and thus without the intrinsic heating that comes with near-resonant Raman lasers [2]. We point out that our scheme can be implemented all optically through the use of a period-tripling superlattice, offering faster switching times and more precise control than with magnetic field gradients. Finally, we show that this method is very general for engineering novel single particle spectra in an optical lattice and can be used to map out Hofstadter's butterfly. \\[4pt] [1] H. Miyake, et al., Phys. Rev. Lett., 111, 185302\\[0pt] [2] C.J. Kennedy, et al., Phys. Rev. Lett., 111, 225301   

Observing artificial-field-driven vortex nucleation in a BEC via bulk response

By exploiting the quantum mechanical phase's relationship to velocity, we extracted information about a Bose-Einstein condensate's (BEC's) order parameter through time-of-flight (TOF) imaging. In these experiments, trapped BECs were equilibrated in Raman-induced artificial gauge fields, then released and imaged. The removal of the artificial field at the moment of release caused a shearing of the atomic distribution as the BEC evolved in field-free TOF. The quantitative measure of the cloud's shear increased suddenly at magnetic fields sufficient to nucleate vortices. Using superfluid hydrodynamics and Gross-Pitaevskii equation calculations, we confirmed the critical field for this structural phase transition from the vortex-free state. We discuss the relationship between the apparatus and the vector potential's ``natural gauge'' in quantum gas experiments with artificial magnetic fields.   

Spin Transport in Spin-Orbit Coupled BECs

We measure spin transport induced by synthetic spin-dependent electric fields in spin-orbit coupled (SOC) Bose Einstein Condensates (BECs). The 1D SOC is created with counter propagating Raman lasers which couple hyperfine spins ($m_F=-1$ and 0, of F=1) and momentum states of $^{87}Rb$, allowing us to engineer spin dependent vector potentials. Quickly decreasing the spin-orbit Raman coupling strength ($\Omega_R$) separates the spin vector potentials and applies opposite synthetic electric fields to the two dressed spin BECs. We allow them to oscillate in opposite directions within the optical trap (exhibiting a spin dipole mode) and measure the time evolution of their momentum and density after time-of-flight (TOF). The oscillations damp as the spin BECs collide and the damping drastically increases as the Raman coupling is increased, possibly related to the Raman coupling dressing and increasing the effective spin interactions. Over longer time scales, thermalization accompanies the damping of the bare spins' oscillations. However, with Raman coupling, the overdamped dressed spins' oscillations are accompanied by rich excitations in the BEC but less thermalization. The measured damping and its dependence on Raman coupling and detuning agree well with GPE simulations.   

Experimental progress towards non-abelian spin-orbit coupling of neutral ultracold bosons

Spin-orbit coupling can be created in ultracold gases by linking a change in state to a change in momentum, for example using Raman transitions. When two or more eigenstates of the spin-orbit coupling interaction are degenerate, a geometric phase associated with a closed loop in momentum may exist. Rashba spin-orbit coupling (present for free electrons in the presence of a uniform electric field, such as in asymmetric semiconductor heterostructures), is perhaps the simplest of these 2D spin-orbit couplings associated with a non-trivial geometric phase. To date it has not been realized in ultracold neutral gases. We will discuss experimental progress toward realizing Rashba spin-orbit coupling in ultracold $^{87}Rb$ gases.   

Static and dynamical properties of topological Fulde-Ferrell states in spin-orbit-coupled Fermi gases

Motivated by recent experimental breakthroughs in generating spin-orbit coupling in ultracold Fermi gases using Raman beams, we present a systematic study of spin-orbit-coupled Fermi gases in the presence of an in-plane Zeeman field (which can be realized using a finite two-photon Raman detuning). We find that a topological Fulde-Ferrell state with finite-momentum Cooper pairing will emerge in a one-dimensional harmonic trap. The topological nature of the system is manifested by the Majorana modes localized near the trap edges. We investigate the dynamics of the system by solving the time-dependent Bogoliubov-de Gennes equations. We will explore the possibility of exploiting the dynamical properties to probe the topological phase.   

Energy spectrum of trapped two-atom system with spin-orbit coupling

Ultracold atomic gases provide a novel platform with which to study spin-orbit coupling, a mechanism that plays a central role in the nuclear shell model, atomic fine structure and two-dimensional electron gases. We introduce a theoretical framework that allows for the efficient determination of the eigenenergies and eigenstates of a harmonically trapped two-atom system with short-range interaction subject to spin-orbit coupling. Energy spectra for experimentally relevant parameter combinations will be presented and future extensions will be discussed.   

Tunable miscibility and thermalization in a spin-orbit coupled BEC

The commonly used relation for the miscible-immiscible transition for two-component Bose-Einstein condensates is reconsidered. Our study goes beyond the Thomas-Fermi approximation by considering the kinetic energy term in mean field theory [1]. Numerical solution of the time-dependent and time-independent Gross-Pitaevskii equations in the spin-orbit coupled BEC suggests a new phase boundary for the miscible-immiscible transition when kinetic energy becomes important. The possible implications of this kinetic energy effect on the thermalization of a binary BEC based on this miscibility transition are also discussed. \\[4pt] [1] L. Wen et al., Phys. Rev. A, 85, 043602 (2012).   

Spin Orbit Coupling in a Spin-1 System

Using a three frequency Raman coupling scheme, we create a system that provides independent control of the bare energy states of a spin orbit coupled $^{87}$Rb Bose-Einstein Condensate in the $F=1$ hyperfine state. The independent energy level control given by the three frequency coupling scheme leads to tunable effective quadratic Zeeman shift which is used to create a spin-1 spin orbit coupled system. In this work we study the energy dispersion under various spin orbit coupling and effective quadratic Zeeman shift magnitudes. In addition, we explore the modified many-body interactions in the spin orbit coupled system.   

Synthetic gauge fields can stabilize exotic phases in alkaline earth atoms

Alkaline earth atoms in an optical lattice have been predicted to harbor exotic topological quantum phases of matter, for example a chiral spin liquid, at very low temperatures, due to their large nuclear spin $I\le 9/2$, and high symmetry, SU($N=2I+1$). We have previously shown that strong correlations and quantum magnetism can persist to surprisingly high temperatures in these systems, due to the enhanced symmetry. Here we show that the application of an artificial gauge field can greatly expand the parameter regime where these exotic phases occur, pushing them one step closer to experimental reality.   

Prospects for generating large synthetic gauge fields in dysprosium quantum gases

Highly magnetic atoms such as dysprosium offer large, possibly non-perturbative, dipolar interactions concomitant with extraordinarily large SU(2) spinors and novel atomic structure. Such properties are promising additions to the toolbox of quantum gas-based many-body physics. We will discuss a recent theory proposal [1] that points to exciting prospects for generating strong synthetic gauge fields in such gases, as well as for observing novel many-body states arising from spin-orbit coupling. We will report on experimental progress toward generating these fields in dysprosium.