Session M3: Spin-Orbit Coupling in Cold Gases

Interacting fermions under spin-orbit coupling in an optical lattice clock

Synthetic gauge fields are a promising tool for creating complex Hamiltonians in ultracold neutral atom systems that may mimic the fractional Quantum Hall effect and other topological states. Interactions are a necessary ingredient for new phases and phenomena. To access the interplay between spin-orbit coupling (SOC) and interactions we study the density-dependent frequency shift in an optical lattice clock. Optical lattice clocks allow the SOC to occur naturally during clock interrogation when the clock laser imparts a lattice-site dependent phase on the atoms that becomes important when the atoms tunnel. For the case of spin polarized fermions, when tunneling is suppressed the differential phase imparted by the laser is irrelevant and only p-wave interaction occur. If tunneling is allowed then the site-dependent phase accumulated by the atoms open up the s-wave interaction channel.   

Spin-orbit-coupled Fermi gases of two-electron ytterbium atoms

Spin-orbit coupling (SOC) has been realized in bosonic and fermionic atomic gases opening an avenue to novel physics associated with spin-momentum locking. In this talk, we will demonstrate all-optical method coupling two hyperfine ground states of $^{173}$Yb fermions through a narrow optical transition $^{1}$S$_0$ $\rightarrow$ $^{3}$P$_1$. An optical AC Stark shift is applied to split the ground hyperfine levels and separate out an effective spin-1/2 subspace from other spin states for the realization of SOC. The spin dephasing dynamics and the asymmetric momentum distribution of the spin-orbit coupled Fermi gas are observed as a hallmark of SOC. The implementation of all-optical SOC for ytterbium fermions should offer a new route to a long-lived spin-orbit coupled Fermi gas and greatly expand our capability in studying novel spin-orbit physics with alkaline-earth-like atoms. Other ongoing experimental works related to SOC will be also discussed.   

Observation of the supersolid stripe phase in spin-orbit coupled Bose-Einstein condensates

Supersolidity combines the property of superfluid flow with long-range spatial periodicity of solids and has not been observed since predicted in condensed matter systems. The concept of supersolidity was then generalized to include other superfluid systems which break continuous translational symmetry. Bose-Einstein condensates with spin-orbit coupling are predicted to possess a stripe phase with supersolid properties. Here we report the first observation of the predicted density modulation of the stripe phase using Bragg reflection -- the evidence for spontaneous long-range order in one direction while maintaining a sharp momentum distribution -- the hallmark of superfluid Bose-Einstein condensates. In our system, the spin-orbit coupling was realized in an optical superlattice as described in [1]. Briefly two lowest bands in the superlattice were used as pseudospins and a Raman process was implemented to provide coupling between pseudospin and momentum. Our work establishes a system with unique continuous symmetry breaking properties, associated Goldstone modes and superfluid behavior.~ References: [1] J. Li \textit{et. al }PRL \textbf{117}.185301 [2] J. Li \textit{et. al }arXiv:1610.08194   

Negative-mass hydrodynamics in a spin-orbit coupled Bose-Einstein condensate

Negative effective mass is peculiar; whereas objects usually accellerate away from a push, negative-mass objects will accelerate $\textit{towards}$ the push. This strange behaviour can be realized in spin-orbit coupled (SOC) BECs where the dispersion relationship can be engineered to exhibit negative curvature. In this talk we will describe an experiment, where trapped $^{87}$Rb atoms expand in the presence of a spin-orbit coupling, demonstrating an interesting array of dynamical phenomena, including the breaking of Galilean covariance, dynamical instabilities, and a slowing down consistent with negative acceleration. We show that these features can be described with a simple theory of negative-mass hydrodynamics, and argue that this also explains a related phenomena of self-trapping seen in optical lattices.   

Dynamics of a spin-orbit coupled BEC in a matching lattice

Spin-orbit coupled Bose-Einstein condensates are a powerful tool to investigate advanced condensed matter phenomena. Recently the generation of a supersolid state in this system has created a lot of interest. In our experiments we investigate a spin-orbit coupled Bose-Einstein condensate in the presence of an optical lattice. The lattice wavevector is chosen such that it is matched to the position of the minima in the spin-orbit dispersion. We show the connection between this system and a supersolid state, and describe its quantum dynamics upon sudden quenches. The current status and future directions of this project will be described.   

Time-reversal invariant bilayer spin-orbit coupled Bose-Einstein condensates

The recent experimental realization of spin-orbit coupling for ultra-cold atomic gases provides a new powerful platform for exploring many interesting quantum phenomena. In these experiments, time-reversal symmetry is explicitly broken by the Raman coupling that corresponds to an effective Zeeman field. Here we propose that time-reversal symmetry can be restored in bilayer spin-orbit coupled ultracold atomic gases using opposite Zeeman field in two layers, which can realized easily in experiments. We study the ground phase diagram of such time-reversal invariant BEC and explore the important role of layer-spin coupling.   

Strongly correlated magnetic phases of the spin orbit coupled spin-1 Bose-Hubbard chain

Motivated by the ability to engineer artificial gauge fields in ultra cold atomic gases we consider the strong coupling phases of the one-dimensional spin-1 Bose-Hubbard model in the presence of a spin orbit coupling. We determine the low energy magnetic Hamiltonian that describes the bosonic Mott insulating phases with an odd integer filling, which is a spin-1 ferromagnetic bilinear-biquadratic model in a spiral magnetic field. We solve the effective spin Hamiltonian using the density matrix renormalization group and determine the zero temperature quantum phase diagram.   

Damping of spin-dipole mode and generation of quadrupole mode excitations in a spin-orbit coupled Bose-Einstein condensate

In cold atom systems, spin excitations have been shown to be a sensitive probe of interactions and quantum statistical effects, and can be used to study spin transport in both Fermi and Bose gases. In particular, spin-dipole mode (SDM) is a type of excitation that can generate a spin current without a net mass current. We present recent measurements and analysis of SDM in a disorder-free, interacting three-dimensional (3D) $^{\mathrm{87}}$Rb Bose-Einstein condensate (BEC) by applying spin-dependent synthetic electric fields to actuate head-on collisions between two BECs of different spin states. We experimentally study and compare the behaviors of the system following SDM excitations in the presence as well as absence of synthetic 1D spin-orbit coupling (SOC). We find that in the absence of SOC, SDM is relatively weakly damped, accompanied with collision-induced thermalization which heats up the atomic cloud. However, in the presence of SOC, we find that SDM is more strongly damped with reduced thermalization, and observe excitation of a quadrupole mode that exhibits BEC shape oscillation even after SDM is damped out. Such a mode conversion bears analogies with the Beliaev coupling process or the parametric frequency down conversion of light in nonlinear optics.   

Spin-tensor-momentum-coupled Bose-Einstein condensates

The recent experimental realization of spin-orbit coupling for ultra-cold atomic gases provides a new powerful platform for exploring many interesting quantum phenomena. Here the spin represents spin-vector (spin-1/2 or spin-1) and orbit represents linear momentum. We propose a scheme to realize a new type coupling between spin-tensor and linear momentum in spin-1 ultra-cold atomic gases. We study ground state properties of such spin-tenor-momentum-coupled Bose-Einstein condensates (BECs) and find interesting stripe superfluid phases that have not been explored in previous spin-orbit coupled BECs. A dynamical process to generate stripe phases with a tunable period of spin-density modulations is discussed.   

Negative-Mass Hydrodynamics: Solitons and Shockwaves

In this talk, I will present a microscopic description of the shockwaves and solitons that form when a trapped Bose-Einstein Condensate (BEC) is released and expands in the presence of Spin-Orbit Coupling (SOC). The SOC dispersion has regions of negative curvature $\left(\frac{\partial^2}{\partial k^2}E(k) < 0 \right)$ which emulate an effective negative mass. We seed the edges of the trapped BEC with momentums in the negative mass region, the edges then push against the outward expansion leading to a self-trapping phenomenon. Using negative mass hydrodynamics we see a build up and trapping of shockwaves in the center of the BEC. Although remarkably stable, the shockwaves ultimately decay into trains of solitons which lead to a dynamic instability of the trapped BEC.