Shih-Kuang Tung

Observation of vortex pinning in Bose-Einstein condensates.

We report the observation of vortex pinning in rotating gaseous Bose-Einstein condensates. Vortices are pinned to columnar pinning sites created by a corotating optical lattice superimposed on the rotating Bose-Einstein condensates. We study the effects of two types of optical lattice: triangular and square. In both geometries we see an orientation locking between the vortex and the optical lattices. At sufficient intensity the square optical lattice induces a structural crossover in the vortex lattice.

Vortex-Lattice Dynamics in Rotating Spinor Bose-Einstein Condensates

We observe interlaced square vortex lattices in rotating dilute-gas spinor Bose-Einstein condensates (BEC). After preparing a hexagonal vortex lattice in a one-component BEC in an internal atomic state |1, we coherently transfer a fraction of the superfluid to a different state |2. The subsequent evolution of this pseudo-spin-1/2 superfluid towards a state of offset square lattices involves an intriguing interplay of phase-separation and -mixing dynamics, both macroscopically and on the length scale of the vortex cores, and a stage of vortex turbulence. The stability of the square structure is proved by its response to applied shear perturbations. An interference technique shows the spatial offset between the two vortex lattices. Vortex cores in either component are filled by fluid of the other component, such that the spin-1/2 order parameter forms a Skyrmion lattice.

Vortex Proliferation in the Berezinskii-Kosterlitz-Thouless Regime on a Two-Dimensional Lattice of Bose-Einstein Condensates

We observe the proliferation of vortices in the Berezinskii-Kosterlitz-Thouless regime on a two-dimensional array of Josephson-coupled Bose-Einstein condensates. As long as the Josephson (tunneling) energy J exceeds the thermal energy T, the array is vortex free. With decreasing J/T, vortices appear in the system in ever greater numbers. We confirm thermal activation as the vortex-formation mechanism and obtain information on the size of bound vortex pairs as J/T is varied.

Experimental studies of equilibrium vortex properties in a Bose condensed gas

We characterize several equilibrium vortex effects in a rotating Bose-Einstein condensate. Specifically we attempt precision measurements of the vortex-lattice spacing and vortex-core size over a range of condensate densities and rotation rates. These measurements are supplemented by numerical simulations, and both experimental and numerical data are compared to theory. Finally, we study the effect of the centrifugal weakening of the trapping spring constants on the critical temperature for quantum degeneracy and the effects of finite temperature on vortex contrast00.

Observation of Quantum Criticality with Ultracold Atoms in Optical Lattices

Critically Cold Atoms Unlike classical phase transitions, such as the freezing of water into ice, which is driven by lowering the temperature of the system, quantum phase transitions occur at absolute zero and are driven by other parameters, including magnetic field or pressure. In the vicinity of a quantum phase transition, a critical region forms where physical observables obey scaling laws as a consequence of the self-similarity of the system. Quantum phase transitions and quantum criticality are usually observed in solid state, but Zhang et al. (p. 1070, published online 16 February) used an optical lattice filled with a cold gas of atoms to simulate a quantum phase transition—from an insulator to a superflnuid in two dimensions. They observed the characteristic scaling of the equation of state, a finding that will facilitate the building of a platform in a tunable system for further investigations of quantum criticality. Trapped low-temperature atoms model the transition between insulating and superfluid states in a more complex material. Quantum criticality emerges when a many-body system is in the proximity of a continuous phase transition that is driven by quantum fluctuations. In the quantum critical regime, exotic, yet universal properties are anticipated; ultracold atoms provide a clean system to test these predictions. We report the observation of quantum criticality with two-dimensional Bose gases in optical lattices. On the basis of in situ density measurements, we observe scaling behavior of the equation of state at low temperatures, locate the quantum critical point, and constrain the critical exponents. We observe a finite critical entropy per particle that carries a weak dependence on the atomic interaction strength. Our experiment provides a prototypical method to study quantum criticality with ultracold atoms.As the temperature of a many-body system approaches absolute zero, thermal fluctuations of observables cease and quantum fluctuations dominate. Competition between different energies, such as kinetic energy, interactions or thermodynamic potentials, can induce a quantum phase transition between distinct ground states. Near a continuous quantum phase transition, the many-body system is quantum critical, exhibiting scale invariant and universal collective behavior [1, 2]. Quantum criticality has been actively pursued in the study of a broad range of novel materials [3–6], and can invoke new insights beyond the Landau-Ginzburg-Wilson paradigm of critical phenomena [7]. It remains a challenging task, however, to directly and quantitatively verify predictions of quantum criticality in a clean and controlled system. Here we report the observation of quantum critical behavior in a two-dimensional Bose gas in optical lattices near the vacuum-to-superfluid quantum phase transition. Based on in situ density measurements, we observe universal scaling of the equation of state at sufficiently low temperatures, locate the quantum critical point, and determine the critical exponents. The universal scaling laws also allow determination of thermodynamic observables. In particular, we observe a finite entropy per particle in the critical regime, which only weakly depends on the atomic interaction. Our experiment provides a prototypical method to study quantum criticality with ultracold atoms, and prepares the essential tools for further study on quantum critical dynamics.

Extracting density?density correlations from in situ images of atomic quantum gases

We present a complete recipe to extract the density–density correlations and the static structure factor of a two-dimensional (2D) atomic quantum gas from in situ imaging. Using images of non-interacting thermal gases, we characterize and remove the systematic contributions of imaging aberrations to the measured density–density correlations of atomic samples. We determine the static structure factor and report the results on weakly interacting 2D Bose gases, as well as strongly interacting gases in a 2D optical lattice. In the strongly interacting regime, we observe a strong suppression of the static structure factor at long wavelengths.

Strongly interacting two-dimensional Bose gases.

We prepare and study strongly interacting two-dimensional Bose gases in the superfluid, the classical Berezinskii-Kosterlitz-Thouless (BKT) transition, and the vacuum-to-superfluid quantum critical regimes. A wide range of the two-body interaction strength 0.05 < g < 3 is covered by tuning the scattering length and by loading the sample into an optical lattice. Based on the equations of state measurements, we extract the coupling constants as well as critical thermodynamic quantities in different regimes. In the superfluid and the BKT transition regimes, the extracted coupling constants show significant down-shifts from the mean-field and perturbation calculations when g approaches or exceeds one. In the BKT and the quantum critical regimes, all measured thermodynamic quantities show logarithmic dependence on the interaction strength, a tendency confirmed by the extended classical-field and renormalization calculations.

Observation of the presuperfluid regime in a two-dimensional Bose gas.

In complementary images of coordinate-space and momentum-space density in a trapped 2D Bose gas, we observe the emergence of presuperfluid behavior. As phase-space density ρ increases toward degenerate values, we observe a gradual divergence of the compressibility κ from the value predicted by a bare-atom model, κ(ba). κ/κ(ba) grows to 1.7 before ρ reaches the value for which we observe the sudden emergence of a spike at p = 0 in momentum space. Momentum-space images are acquired by means of a 2D focusing technique. Our data represent the first observation of non-mean-field physics in the presuperfluid but degenerate 2D Bose gas.

Exploring quantum criticality based on ultracold atoms in optical lattices

Critical behavior developed near a quantum phase transition, interesting in its own right, offers exciting opportunities to explore the universality of strongly correlated systems near the ground state. Cold atoms in optical lattices, in particular, represent a paradigmatic system, for which the quantum phase transition between the superfluid and Mott insulator states can be externally induced by tuning the microscopic parameters. In this paper, we describe our approach to study quantum criticality of cesium atoms in a two-dimensional (2D) lattice based on in situ density measurements. Our research agenda involves testing critical scaling of thermodynamic observables and extracting transport properties in the quantum critical regime. We present and discuss experimental progress on both fronts. In particular, the thermodynamic measurement suggests that the equation of state near the critical point follows the predicted scaling law at low temperatures.