Session F41: Rotation, Effective Fields, and Hydrodynamics in Atomic Gases

Hydrodynamics and universality in cold atomic gases

Recent flurry of experiments on out-of-equilibrium dynamics in cold gases (Bosonic and Fermionic) has raised great interest in understanding collective behaviour of interacting particles. Although the dynamics of interacting gases depends on many details of the system, a great insight can be obtained in a rather universal limit of weak non-linearity, dispersion and dissipation. In this limit, using a reductive perturbation method we map many hydrodynamic models relevant to cold atoms to well known chiral one-dimensional equations such as Korteweg-de Vries (KdV), Burgers, KdV-Burgers, and Benjamin-Ono equations. This mapping [1] of rather complicated hydrodynamic equations to known chiral one-dimensional equations is of great experimental and theoretical interest. For instance, this mapping gives a simple way to make estimates for original hydrodynamic equations and to study phenomena such as shock waves, solitons and the interplay between nonlinearity, dissipation and dispersion. All these phenomena have been observed in experiments and are the hallmarks of nonlinear hydrodynamics.\\[4pt] [1] M. Kulkarni, A. G. Abanov, Phys. Rev. A 86, 033614 (2012)   

Time-of-flight expansion dynamics of a circulating ring BEC

We have studied the effect of non--zero circulation on the time--of--flight expansion dynamics of a ring--shaped BEC, under conditions matching recent experiments at the Joint Quantum Institute/NIST in Maryland. We modeled the dynamics of the condensate by first solving the time--independent Gross--Pitaevskii equation (GPE) to obtain the initial condensate wavefunction, with the (quantized) circulation set by imprinting an azimuthal phase gradient. This state was then propagated using the time--dependent GPE in real time, with the trapping potential turned off. In the absence of circulation, the BEC expands and closes the central hole in a few milliseconds, eventually resulting in a density profile with a central peak surrounded by a pedestal modulated by weak concentric fringes. When the ring BEC is circulating, the central hole initially decreases in size but never closes due to the phase singularity. In the long--time limit, the size of the central hole scales nearly linearly with the winding number of the circulation state, in good agreement with the NIST experimental results.   

Driving phase slips in a neutral-atom analog of an RF SQUID

We can deterministically control the quantized circulation state of a toroidal atomic Bose-Einstein condensate by rotating a weak link around the ring above a critical velocity. We vary this critical velocity by controlling the strength of the repulsive optical dipole potential creating the weak link. This system is directly analogous to a superconducting loop in an external magnetic field, where the loop is interrupted by a weak link with a dynamically tunable current-phase relation.   

Observation of hysteresis in a superfluid Bose-Einstein condensate with a weak link

Hysteresis is a common feature of superfluid and superconducting systems with Josephson junctions. We have observed hysteresis in the persistent current state of a toroidally-shaped, Bose-Einstein condensate, stirred with a rotating barrier potential. The barrier, which is modeled as a weak link, induces phase slips in the superfluid between well-defined persistent current states. The rotation frequency at which these phase slips occur differ, depending on whether the phase slip results in an increase or decrease of the persistent current. Such behavior in a toroidal BEC is analogous to an RF SQUID, allowing this device to possibly be used as a sensitive rotation sensor.   

Stirring a ring Bose-Einstein condensate: vortices and overall circulation

We have studied the process whereby stirring a superfluid Bose--Einstein condensate confined in a ring-shaped potential leads to an overall circulation. We solved the time-dependent Gross--Pitaevskii equation under conditions chosen to match those of an experiment recently conducted at NIST. Briefly, 500,000 Na atoms where confined at the ring-shaped intersection of a red-detuned horizontal light sheet and a vertically propagating Laguerre--Gauss beam. Stirring was carried via a blue--detuned gaussian beam. We found that, at first, the stirring spawned a number of vortex--antivortex pairs and then stopped. These vortices displayed a complicated dynamical behavior which slowly reduced the number of vortices pairwise via annihilation and singly via diffusion into surface modes of the condensate. At the end of this dynamics, the set of vortices was replaced by an overall circulation of atoms around the ring. We present examples of this behavior, give a simple model of vortex motion and vortex-vortex interaction, and show how the production and annihilation of vortices gets turned into a overall circulation of the ring Bose--Einstein condensate.   

Quantum Hall states in rapidly rotating two-component Bose gases

Ultracold atomic gases under rapid rotation offer interesting analogues of quantum Hall systems with variable statistics and spins of constituent particles. Here we study strongly correlated phases of two-component (or pseudo-spin-$1/2$) Bose gases under rapid rotation by means of exact diagonalization. As the ratio of the inter-component contact interaction $g_{\uparrow\downarrow}$ to the intra-component one $g$ increases, the two components are expected to be entangled to form novel ground states. For $g_{\uparrow\downarrow}=g$, we find the formation of gapped spin-singlet states at the filling factors $\nu=k/3+k/3$ (the $k/3$ filling for each component) with integer $k$. In particular, we present numerical evidences that the gapped state with $k=2$ is well described as a non-Abelian spin-singlet (NASS) state, in which excitations feature non-Abelian statistics. Furthermore, we find the phase transition from the product of composite fermion states to the NASS state by changing the interaction ratio $g_{\uparrow\downarrow}/g$. Reference: Phys. Rev. A 86, 031604(R) (2012).   

Vortex formation in a rotating reference frame

We create vortices in a trapped Bose-Einstein condensate by cooling the atomic sample through the phase transition in the presence of a rotating magnetic trapping potential. The thermal cloud remains in quasi-equilibrium during the cooling, ultimately producing condensates in the rotating ground state. We show that the trap rotation frequency at which a vortex first appears agrees closely with theoretical predictions. The number of vortices within the condensate is established by the rotation frequency at the phase transition; once the condensate has started to form, its vortex content is robust against frequency changes. Images of the condensate taken during evaporation suggest that the vortex spatial configuration is similarly determined early on in the growth of the condensate.   

Quantum Monte Carlo study of the drag coefficient for two-component BECs

Groundbreaking advances in experimental techniques for ultracold gases have resulted in considerable interest in multi-component systems, which exhibit richer physics than single species systems. Recent theoretical work has established the strong possibility of ``entrainment'' coupling between components in a two-component BEC. In this talk, we present quantum Monte Carlo simulations of the drag coefficient in a two-component Bose-Hubbard model. Next, we utilize Langevin dynamics to determine manifestations of the intercomponent drag in the ground state structure of vortices in multi-component superfluids.   

Periodically kicked quantum Hall system of cold atoms

The integer quantum Hall state is characterized by chiral edge modes associated with the topological invariant, the Chern number. We numerically study a non-equilibrium, periodically driven quantum hall system of fermionic atoms in a square optical lattice. We show that periodically modulated tunneling gives rise to new edge states inside the quasi-energy band gaps. We present a phase diagram with a zoo of interesting phases as functions of driving parameters, along with the spectral evolution of the edge states through the topological quantum phase transitions.   

Experimental Validation of Interferometry Simulations on an Atom Chip

We report on recent experimental results on manipulating cold atoms trapped on a chip for the development of a compact atom interferometer using a double-well potential. The experiment uses $^{87}$Rb atoms magnetically confined in an atomic waveguide produced by wires on the surface of a lithographically patterned chip. The double-well potential is created by dynamically changing the current configuration on our atom chip.~ By dynamically powering traces on the atom chip while simultaneously varying external bias fields, we offer a means to coherently split the atomic cloud.~ We investigate real-time transformations, both adiabatic and non-adiabatic, between different double-well configurations and study their effects on the initially trapped atoms. We examine the coherence properties of the two atomic wavepackets and evaluate their potential use in an atom interferometer.