Determination of the Equation of State of a Two-Component Fermi Gas at Unitarity

We report on the measurement of the equation of state of a two-component Fermi gas of $^6$Li atoms with resonant interactions. By analyzing the \textit{in situ} density distributions of a population-imbalanced Fermi mixture reported in the recent experiment [Y. Shin \textit{et al.}, Nature \textbf{451}, 689 (2008)], we determine the energy density of a resonantly interacting Fermi gas as a function of the densities of the two components. We present a method to determine the equation of state directly from the shape of the trapped cloud, where the fully-polarized, non-interacting ideal Fermi gas in the outer region provides the absolute calibration of particle density. From the density profiles obtained at the lowest temperature, we estimate the zero-temperature equation of state.Comment: 4 pages, 3 figures / typo correction / figure replacemen

Observation of Topologically Stable 2D Skyrmions in an Antiferromagnetic Spinor Bose-Einstein Condensate

We present the creation and time evolution of two-dimensional Skyrmion excitations in an antiferromagnetic spinor Bose-Einstein condensate. Using a spin rotation method, the Skyrmion spin textures were imprinted on a sodium condensate in a polar phase, where the two-dimensional Skyrmion is topologically protected. The Skyrmion was observed to be stable on a short time scale of a few tens of ms but to have dynamical instability to deform its shape and eventually decay to a uniform spin texture. The deformed spin textures reveal that the decay dynamics involves breaking the polar phase inside the condensate without having topological charge density flow through the boundary of the finite-sized sample. We discuss the possible formation of half-quantum vortices in the deformation process.Comment: 5 pages, 5 figure

Role of thermal friction in relaxation of turbulent Bose-Einstein condensates

In recent experiments, the relaxation dynamics of highly oblate, turbulent Bose-Einstein condensates (BECs) was investigated by measuring the vortex decay rates in various sample conditions [Phys. Rev. A $\bf 90$, 063627 (2014)] and, separately, the thermal friction coefficient $\alpha$ for vortex motion was measured from the long-time evolution of a corotating vortex pair in a BEC [Phys. Rev. A $\bf 92$, 051601(R) (2015)]. We present a comparative analysis of the experimental results, and find that the vortex decay rate $\Gamma$ is almost linearly proportional to $\alpha$. We perform numerical simulations of the time evolution of a turbulent BEC using a point-vortex model equipped with longitudinal friction and vortex-antivortex pair annihilation, and observe that the linear dependence of $\Gamma$ on $\alpha$ is quantitatively accounted for in the dissipative point-vortex model. The numerical simulations reveal that thermal friction in the experiment was too strong to allow for the emergence of a vortex-clustered state out of decaying turbulence.Comment: 7 pages, 5 figure

Periodic shedding of vortex dipoles from a moving penetrable obstacle in a Bose-Einstein condensate

We investigate vortex shedding from a moving penetrable obstacle in a highly oblate Bose-Einstein condensate. The penetrable obstacle is formed by a repulsive Gaussian laser beam that has the potential barrier height lower than the chemical potential of the condensate. The moving obstacle periodically generates vortex dipoles and the vortex shedding frequency $f_v$ linearly increases with the obstacle velocity $v$ as $f_v=a(v-v_c)$, where $v_c$ is a critical velocity. Based on periodic shedding behavior, we demonstrate deterministic generation of a single vortex dipole by applying a short linear sweep of a laser beam. This method will allow further controlled vortex experiments such as dipole-dipole collisions.Comment: 6 pages, 7 figure

Metastable hard-axis polar state of a spinor Bose-Einstein condensate under a magnetic field gradient

We investigate the stability of a hard-axis polar state in a spin-1 antiferromagnetic Bose-Einstein condensate under a magnetic field gradient, where the easy-plane spin anisotropy is controlled by a negative quadratic Zeeman energy $q<0$. In a uniform magnetic field, the axial polar state is dynamically unstable and relaxes into the planar polar ground state. However, under a field gradient $B'$, the excited spin state becomes metastable down to a certain threshold $q_{th}$ and as $q$ decreases below $q_{th}$, its intrinsic dynamical instability is rapidly recalled. The incipient spin excitations in the relaxation dynamics appear with stripe structures, indicating the rotational symmetry breaking by the field gradient. We measure the dependences of $q_{th}$ on $B'$ and the sample size, and we find that $q_{th}$ is highly sensitive to the field gradient in the vicinity of $B'=0$, exhibiting power-law behavior of $|q_{th}|\propto B'^{\alpha}$ with $\alpha \sim 0.5$. Our results demonstrate the significance of the field gradient effect in the quantum critical dynamics of spinor condensates.Comment: 8 pages, 7 figure

Observation of wall-vortex composite defects in a spinor Bose-Einstein condensate

We report the observation of spin domain walls bounded by half-quantum vortices (HQVs) in a spin-1 Bose-Einstein condensate with antiferromagnetic interactions. A spinor condensate is initially prepared in the easy-plane polar phase, and then, suddenly quenched into the easy-axis polar phase. Domain walls are created via the spontaneous $\mathbb{Z}_2$ symmetry breaking in the phase transition and the walls dynamically split into composite defects due to snake instability. The end points of the defects are identified as HQVs for the polar order parameter and the mass supercurrent in their proximity is demonstrated using Bragg scattering. In a strong quench regime, we observe that singly charged quantum vortices are formed with the relaxation of free wall-vortex composite defects. Our results demonstrate a nucleation mechanism for composite defects via phase transition dynamics.Comment: 10 pages, 11 figures, reference update

Critical Velocity for Vortex Shedding in a Bose-Einstein Condensate

We present measurements of the critical velocity for vortex shedding in a highly oblate Bose-Einstein condensate with a moving repulsive Gaussian laser beam. As a function of the barrier height $V_0$, the critical velocity $v_c$ shows a dip structure having a minimum at $V_0 \approx \mu$, where $\mu$ is the chemical potential of the condensate. At fixed $V_0\approx 7\mu$, we observe that the ratio of $v_c$ to the speed of sound $c_s$ monotonically increases for decreasing $\sigma/\xi$, where $\sigma$ is the beam width and $\xi$ is the condensate healing length. The measured upper bound for $v_c/c_s$ is about 0.4, which is in good agreement with theoretical predictions for a two-dimensional superflow past a circular cylinder. We explain our results with the density reduction effect of the soft boundary of the Gaussian obstacle, based on the local Landau criterion for superfluidity.Comment: 5 pages, 4 figure