Session R03: Synthetic Gauge Fields and Spin-orbit coupling in Cold Gases II

Two-dimensional Fermi gas in antiparallel magnetic fields

Experimental techniques in ultracold atoms allow us to tune parameters of the system at will. In particular, synthetic magnetic fields have been created by using the atom-light coupling and, therefore, it is interesting to study what kinds of quantum phenomena appear in correlated ultracold atoms subjected to synthetic magnetic fields. In this work, we consider a two-dimensional Fermi gas with two spin states in spin-dependent magnetic fields which are assumed to be antiparallel for different spin states~[1]. By studying the ground-state phase diagram within the mean-field approximation, we find quantum spin Hall and superfluid phases separated by a second-order phase transition. We also show that there are regions where the superfluid pairing gap is proportional to the attractive coupling, which is in marked contrast to the usual exponential dependence. Moreover, we elucidate that the universality class of the phase transition belongs to that of the XY model at special points of the phase boundary, while it belongs to that of a dilute Bose gas anywhere else~[2]. [1] M. C. Beeler et al., Nature \textbf{498}, 201 (2013). [2] T. Anzai and Y. Nishida, Phys. Rev. A \textbf{95}, 051603 (2017).   

Quantum field theory of nematic transitions in spin orbit coupled spin-1 polar bosons in one dimension

We will discuss our recent theoretical study of an ultra-cold gas of spin-1 polar bosons in one spatial dimension, which are subject to a quadratic Zeeman field and a Raman induced spin-orbit coupling. We analytically solve the model in its low-energy sector characterizing the relevant phases and the quantum phase transitions between them. Depending on the sign of the effective quadratic Zeeman field $\epsilon$, two superfluid phases with distinct nematic order appear. In addition, we uncover a spin-liquid superfluid state at strong coupling. We employ a combination of renormalization group calculations, duality transformations, and fermionization to access the nature of phase transitions. At $\epsilon = 0$, a line of spin-charge separated pairs of Luttinger liquids divides the two nematic phases and the transition to the spin disordered state at strong coupling is of the Berezinskii-Kosterlitz-Thouless type. In contrast, at $\epsilon \neq 0$, the quantum critical theory separating nematic and strong coupling spin disordered phases maps to a quantum critical Ising model that is coupled to the charge Luttinger liquid. We will discuss the experimental signatures of our findings that are relevant to ongoing experiments in ultra-cold atomic gases of $^{23}$Na.   

Spin exchange-induced spin-orbit coupling in a superfluid mixture

We investigate the ground-state properties of a dual-species spin-1/2 Bose-Einstein condensate. One of the species is subjected to a pair of Raman laser beams that induces spin-orbit (SO) coupling, whereas the other species is not coupled to the Raman laser. In certain limits, analytical results can be obtained. It is clearly shown that, through the inter-species spin-exchange interaction, the second species also exhibits SO coupling. This mixture system displays a very rich phase diagram, with many of the phases not present in an SO coupled single-species condensate. Our work provides a new way of creating SO coupling in atomic quantum gases, and opens up a new avenue of research in SO coupled superfluid mixtures. From a practical point of view, the spin exchange-induced SO coupling may overcome the heating issue for certain atomic species when subjected to the Raman beams.   

Dynamics of a spin-orbit coupled Bose-Einstein condensate in the presence of a moving barrier

The possibility to explore quantum hydrodynamics has been greatly expanded with the application of ultracold atomic gases in the lab. Bose-Einstein condensates have been shown to exhibit both nonviscous and effectively viscous properties depending on the parameters of the experiment. For instance, when a repulsive impenetrable barrier is driven through an elongated BEC, aspects of the dynamics resemble the behavior of a classical viscous fluid. This concept lays the groundwork for our current experiment, where spin-orbit coupling has been introduced in the system. We perform a similar experiment with a modified dispersion relation and observe spin-flip dynamics even when using a spin-independent barrier. We show that these spin dynamics only occur within a finite range of barrier velocities, and that at large barrier speeds, the SOC BEC remains in the ground state of the system, unperturbed by the moving barrier. This work is in loose analogy to spin-orbit qubits in condensed matter systems where qubit manipulation is affected by coupling to the orbital part of the wavefunction. The current status and future directions of this work are discussed.   

Exciting BEC's with Spin Orbit Coupling

In this talk, I will discuss the theory behind several techniques for exciting and manipulating Bose Einstein Condensates (BECs) with Spin-Orbit Coupling (SOC). In particular, I shall discuss how the SOC can be used to engineer a dispersion relationship to realize a system with negative-mass hydrodynamics, and then how to probe properties of this unique system by dynamically varying the SOC parameters and manipulating the optical potentials so as to produce shockwaves, solitons, and turbulence. This theory will be compared with experimental results from P. Engels group, and features of their experiment will be explained.   

Shockwaves in Spin-Orbit Coupled BECs

Spin-Orbit Coupling (SOC) allows for a great deal of control over BECs. For example, you can experimentally engineer the dispersion relationship to realize regions of negative effective mass. In this presentation, I will discuss how the shape of the dispersion affects the structure and behavior of dispersive shockwaves and how a time-dependent dispersion is analogous to motion in a moving reference frame. The time-dependent dispersion is compared to simulations of a BEC in a moving optical bucket.   

Synthesizing 1D Dirac dispersion and unidirectional spin flow for cold atoms

We describe a spin dependent bipartite [1] Floquet lattice [2], in which the dispersion relation is linear for all points in the Brillouin zone. The Floquet spectrum of our periodically-driven Hamiltonian features: perfect spin-momentum locking, a linear Dirac dispersion, and unidirectional spin-motion. These experiments are performed in ${87}Rb$ Bose-Einstein condensates subject to simultaneous RF and Optical couplings. [1] H.-I Lu, M. Schemmer, L. Aycock, D. Genkina, S. Sugawa, and I. Spielman, Phys Rev Lett 116, 200402 (2016) [2] J.C. Budich, Y Hu, P. Zoller, Phys Rev Lett 118, 105302 (2017)   

Abstract moved to U07.5

This abstract has been moved to session U07.5.   

A tunneling assisted, spin-orbit coupled Bose-Einstein condensate exhibiting stripe-phase-like behavior

We investigate a spin-orbit coupled Bose-Einstein condensate in which the two spin-orbit dispersion minima are coupled by additional lattice-assisted tunneling. This system is expected to display stripe-phase-like behavior, such as a pronounced fine-grained density modulation. We observe coherent Rabi oscillations between the relevant momentum states and experimentally verify the ground state phase diagram as a function of tunneling strength and spin-orbit detuning. This arrangement provides a flexible experimental platform for further investigation of the properties of the stripe-phase in the context of a spin-orbit coupled Bose-Einstein condensate.   

Scissors mode and rotational properties of a spin-orbit coupled Bose-Einstein condensate

The rotational properties of a Bose-Einstein condensate (BEC) are important to study its superfluidity. Recent studies have found that spin-orbit (SO) coupling can change a BEC's superfluid properties. In addition, the scissors mode of a BEC, where the condensate's angle oscillates with respect to trap axes, has been demonstrated to be important for probing rotational properties and superfluidity. Here, we study the scissors mode of a Raman-induced SO coupled BEC of $^{\mathrm{87}}$Rb atoms in a synthetic magnetic field $B$. A SO coupled BEC is first prepared in the presence of $B$ field generated by a spatially-varying Raman coupling. We then quench the Raman coupling or detuning to apply a spatially-varying synthetic force, which pushes and shears the BEC. After such a quench, both the dipole and scissors modes are excited in the trap, and their dynamical evolutions are studied in the presence of SO coupling and $B$ field. We experimentally find that the measured scissors frequency does not agree with the prediction based on effective masses. The GPE simulations reveal the existence of two scissors frequency components, which are important to understand the measured results. Our work may allow us to study how SO coupling modify the BEC's rotational properties.