Session B6: Vortices and Related Phenomena in Bose-Einstein Condensates

Critical Velocity for Vortex Shedding in a Bose-Einstein Condensate

We present the measurements of the critical velocity for vortex shedding in a highly oblate Bose-Einstein condensate with a moving repulsive Gaussian potential. As a function of the potential barrier height $V_0$, the critical velocity shows a dip structure having a minimum at $V_0=\mu$, where mu is the chemical potential of the condensate. In a condition of $V_0/\mu\approx7$, where the radius of the density-depleted hole by the potential is close to the potential beam waist $\sigma$, we find that the critical velocity monotonically increases and approaches $0.4c$ for vanishing $\sigma/\xi$, where $c$ is the speed of sound and $\xi$ is the healing length of the condensate. The upper bound for the critical velocity is in good quantitative agreement with the theoretical predictions of the critical velocity of a two-dimensional superflow past a circular cylinder. We will also discuss the effects of the beam profile imperfection on the critical velocity.   

Quantized vortices in interacting gauge theories

We consider a two-dimensional weakly interacting ultracold Bose gas whose constituents are two-level atoms. We study the effects of a synthetic density-dependent gauge field that arises from laser-matter coupling in the adiabatic limit with a laser configuration such that the single-particle vector potential corresponds to a constant synthetic magnetic field. We find a new type of current non-linearity in the Gross-Pitaevskii equation which affects the dynamics of the order parameter of the condensate. We investigate on the physical conditions that make the nucleation of a quantized vortex in the system energetically favourable with respect to the non rotating solution. Two different physical interpretations can be given to this new non linearity: firstly it can be seen as a local modification of the mean field coupling constant, whose value depends on the angular momentum of the condensate. Secondly, it can be interpreted as a density modulated angular velocity given to the cloud. We analyze the physical conditions that make a single vortex state energetically favourable. In the Thomas-Fermi limit, we show that the effect of the new nonlinearity is to induce a rotation to the condensate, where the transition from non-rotating to rotating depends on the density of the cloud.   

Half-quantum circulation and optical spin Hall effect in a polariton spinor ring condensate

We have observed half-quantum circulation in a macroscopic polariton spinor condensate in a ring trap. In our experiment, the polaritons come from the strong coupling between photons and electronic excitations (excitons) in quantum wells embedded in a microcavity. The polaritons are repulsively interacting bosons with small effective mass. The ring trap is a combination of a strain-induced harmonic trap and a laser-generated central barrier. By measuring the phase and polarization of the condensate, we find that theres is a phase rotation of $\pi$ in connection with a polarization rotation of $\pi$ around a closed path. In addition, the handedness of the circular polarization component, which gives the spin of the polariton, flips from one side of the ring to the other. Such a state is allowed in a ring geometry but is prohibited in a simply-connected geometry. The direction of circulation of the flow around the ring fluctuates randomly between clockwise and counterclockwise; this corresponds to spontaneous breaking of time-reversal symmetry in the system. In contrast, the polarization pattern of the condensate is very stable which is very likely due to the optical spin Hall effect playing a role as the condensate is generated.   

Deconstruction of excitations in atomtronic systems using phase reference

Laboratory atomtronic systems consisting of a Bose--Einstein--condensed gas with strong horizontal confinement and arbitrary planar potential, such as a ring--plus--disk, are now possible.\footnote{S.\ Eckel, et al., {\em Phys.\ Rev.\ X} {\bf 4}, 031052 (2014)} Perturbing the ring part (e.g., by stirring) can produce excitations such as vortices and solitons. Each excitation uniquely modifies the local condensate phase and these modifications can be probed by overlapping the ring with the unperturbed disk via condensate release. The resulting interference pattern contains signatures of the excitations present at release time. Using the Gross--Pitaevskii equation, we studied whether this interference pattern can be used to determine what excitations were present at release time. We created individual excitations in a ring--plus--disk condensate, released it to see the interference pattern of individual excitations, and created a compendium of these patterns. We also studied whether the individual patterns can be superposed and tested the deconstruction procedure by analyzing the interference of a strongly stirred ring by comparing the deconstruction with the condensate state at release time.   

Cascade of Solitonic Excitations in a Superfluid Fermi Gas: From Solitons and Vortex Rings to Solitonic Vortices

We follow the evolution of a superfluid Fermi gas of $^6$Li atoms following a one-sided $\pi$ phase imprint. Via tomographic imaging, we observe the formation of a planar dark soliton, and its subsequent snaking and decay into a vortex ring. The latter eventually breaks at the boundary of the superfluid, finally leaving behind a single, remnant solitonic vortex. The nodal surface is directly imaged and reveals its decay into a vortex ring via a puncture of the initial soliton plane. At intermediate stages we find evidence for more exotic structures resembling $\Phi$-solitons. The observed evolution of the nodal surface represents dynamics that occurs at the length scale of the interparticle spacing, thus providing new experimental input for microscopic theories of strongly correlated fermions.   

Temporal and thermal dependence of a persistent, quantized current in a BEC

We study the decay dynamics of a persistent, quantized current in a ring-shaped Bose-Einstein condensate (BEC), to compare with the behaviors seen in a recent theoretical study that predicts that thermally activated phase slips play a role in persistent current decays [{\it Phys. Rev. A}, {\bf 90}, 023604 (2014)] . After inserting a persistent current into the ring, we raise a barrier potential to attempt to interrupt the flow. When the local flow velocity inside this barrier region, or ``weak link,'' exceeds the critical velocity of the superfluid, a phase slip occurs and the flow ceases. We investigate the time needed for this phase slip to occur and the role of temperature in this process. We find that the maximum barrier height at which we can sustain a persistent current changes as we vary the temperature but keep the chemical potential and trapping parameters constant. This behavior is similar to that observed in recent theoretical work.   

Impurity and Dislocation Mediated Vortex Lattice Melting in Bose-Einstein Condensate

We present a numerical study of a Bose condensed gas in a harmonic trap potential in presence of impurities and dislocations in two-dimensions at zero temperature. The impurity is modeled by a Gaussian function and the line dislocation is modeled by a 'Dirac comb' potential. Such potentials can be created experimentally by laser light. We solve the time-dependent Gross-Pitaevskii equation in two-dimensions using split-step Crank-Nicolson method. To characterize the melting of the vortex lattice we calculate the structure factor and from this the angular distortion of the vortex lattice. We also calculate the histogram of distances between each pair of vortices. The angular distortion of the vortex lattice shows large variations with changes in the impurity or dislocation positions. Also, the angular distortion of the vortex lattice increases with increase in the strength of the impurity and dislocation potentials and shows a jumps to a higher value at a particular strength indicating vortex lattice melting. Large distortion of the vortex lattice is also seen with variations of the number of dislocations and their positions with respect to the Abrikosov lattice. The histogram shows absence of separated peaks indicating the melting of the vortex lattice.   

Rotation of quantum impurities in the presence of a many-body environment

Pioneered by the seminal works of Wigner and Racah, the quantum theory of angular momentum evolved into a powerful machinery, commonly used to classify the states of isolated quantum systems and perturbations to their structure due to electromagnetic or crystalline fields. In ``realistic'' experiments, however, quantum systems are almost inevitably coupled to a many-particle environment and a field of elementary excitations associated with it, which is capable of fundamentally altering the physics of the system. We present the first systematic treatment of quantum rotation coupled to a many-particle environment. By using a series of canonical transformations on a generic microscopic Hamiltonian, we single out the conserved quantities of the problem. Using a variational ansatz accounting for an infinite number of many-body excitations, we characterize the spectrum of angular momentum eigenstates and identify the regions of instability, accompanied by emission of angular Cerenkov radiation. The developed technique can be applied to a wide range of systems described by the angular momentum algebra, from Rydberg atoms immersed into BEC's, to cold molecules solvated in helium droplets, to ultracold molecular ions.   

Thermal and quantum fluctuation effects in rotational hysteresis of ring Bose--Einstein condensates

In a recent experiment~\footnote{S.\ Eckel, et al., {\em Nature} {\bf 506}, 200 (2014)} a ring Bose--Einstein condensate (BEC) with zero circulation (with winding number $m=0$) and stirred by a barrier jumped to an $m=1$ state when stirred faster than a certain critical speed, $\Omega_{+c}$. Conversely an $m=1$ condensate dropped to $m=0$ when stirred below a critical speed, $\Omega_{?c}$, which was lower than $\Omega_{+c}$. The hysteresis loop areas, $\Omega_{+c}-\Omega_{-c}$, disagreed significantly with the predictions of the zero--temperature Gross--Pitaevskii equation. We report the results of simulating this experiment with both the Zaremba--Nikuni--Griffin (ZNG) theory and the Truncated Wigner Approximation (TWA). The ZNG theory can account for thermal fluctuations while the TWA can also account for quantum fluctations of the gas. We compare the results of these simulations with the experimental data and describe how the dynamics of vortex/antivortex pairs formed in the barrier region during the stirring is modified by the presence of a thermal cloud and by quantum fluctuations beyond the mean field.   

Black--hole lasing action in laboratory Bose--Einstein condensates

A recent experiment \footnote{J. Steinhauer, {\em Nature Physics} {\bf 11}, 864 (2014)} infers the the production of Hawking radiation in an analogue black-hole laser, which consists of a Bose-Einstein condensate of about 5,000 $^{87}$Rb atoms in a trap with a translating potential step. In the co-moving reference frame the flow velocity of the condensate exceeds the sound speed in a region confined between two sonic points, the analogue black and white hole horizons. We report simulations of that experiment based on the zero-temperature Gross-Pitaevskii (GP) equation that are consistent with the reported experimental results. The simulations show exponential growth of oscillatory modes trapped between the horizons, with a power spectrum consistent with expectations from the Bogoliubov dispersion relation, which saturates after an initial period. Quantum Hawking radiation occurs spontaneously in the vacuum, but in the presence of a coherent state of phonons it takes on a classical form captured by the zero-temperature GP equation. The growth of the trapped modes results from repeated super-radiant scattering from the black hole horizon, associated with emission of Hawking radiation to the exterior that is not well-resolved in the simulation.