In this paper we study the transient dynamics of a Bose superfluid subsequent to an interaction quench. Essential for equilibration is a source of dissipation which we include following the approach of Caldeira and Leggett. Here we solve the equation
s of motion exactly by integrating out an environmental bath. We thereby derive precisely the time dependent density correlation functions with the appropriate analytic and asymptotic properties. The resulting structure factor exhibits the expected damping and thereby differs from that of strict Bogoliubov theory. These damped sound modes, which reflect the physics beyond mean field approaches, are characterized and the structure factors are found to compare favorably with experiment.
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 st
rength 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.
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 cite{Coleman05Nat, Sachdev99QPT}. Quantum criticality has been actively pursued in the study of a broad range of novel materials cite{vdMarel03Nat, Lohneysen07rmp, G08NatPhys, Sachdev08NatPhys}, and can invoke new insights beyond the Landau-Ginzburg-Wilson paradigm of critical phenomena cite{Senthil04prb}. 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 textit{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.
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 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.
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 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.
The collective behavior of a many-body system near a continuous phase transition is insensitive to the details of its microscopic physics[1]. Characteristic features near the phase transition are that the thermodynamic observables follow generalized
scaling laws[1]. The Berezinskii-Kosterlitz-Thouless (BKT) phase transition[2,3] in two-dimensional (2D) Bose gases presents a particularly interesting case because the marginal dimensionality and intrinsic scaling symmetry[4] result in a broad fluctuation regime which manifests itself in an extended range of universal scaling behavior. Studies on BKT transition in cold atoms have stimulated great interest in recent years[5-10], clear demonstration of a critical behavior near the phase transition, however, has remained an elusive goal. Here we report the observation of a scale-invariant, universal behavior of 2D gases through in-situ density and density fluctuation measurements at different temperatures and interaction strengths. The extracted thermodynamic functions confirm a wide universal region near the BKT phase transition, provide a sensitive test to the universality prediction by classical-field theory[11,12] and quantum Monte Carlo (MC) calculations[13], and point toward growing density-density correlations in the fluctuation region. Our assay raises new perspectives to explore further universal phenomena in the realm of classical and quantum critical physics.
We study transport dynamics of ultracold cesium atoms in a two-dimensional optical lattice across the superfluid-Mott insulator transition based on in situ imaging. Inducing the phase transition with a lattice ramping routine expected to be locally a
diabatic, we observe a global mass redistribution which requires a very long time to equilibrate, more than 100 times longer than the microscopic time scales for on-site interaction and tunneling. When the sample enters the Mott insulator regime, mass transport significantly slows down. By employing fast recombination pulses to analyze the occupancy distribution, we observe similarly slow-evolving dynamics, and a lower effective temperature at the center of the sample.
We study near-equilibrium thermodynamics of bosonic atoms in a two-dimensional optical lattice by ramping up the lattice depth to convert a superfluid into an inhomogeneous mixture of superfluid and Mott insulator. Detailed study of in situ density p
rofiles shows that, first, locally adiabatic ramps do not guarantee global thermal equilibrium. Indeed, full thermalization for typical parameters only occurs for experiment times which exceed one second. Secondly, ramping non-adiabatically to the Mott insulator regime can result in strong localized cooling at short times and global cooling once equilibrated. For an initial temperature estimated as 20 nK, we observe local temperatures as low as 1.5 nK, and a final global temperature of 9 nK. Possible cooling mechanisms include adiabatic decompression, modification of the density of states near the quantum critical regime, and the Joule-Thomson effect. **NOTE: Following submission of arXiv:0910.1382v1, a systematic correction was discovered in the density measurement, stemming from three-body losses during the imaging process. New measurements were performed, and the result is in support of the claim on the slow global dynamics. Due to the substantially altered methods and analysis, a new text has been posted as arXiv:1003.0855.
A universal characterization of interactions in few- and many-body quantum systems is often possible without detailed description of the interaction potential, and has become a defacto assumption for cold atom research. Universality in this context i
s defined as the validity to fully characterize the system in terms of two-body scattering length. We discuss universality in the following three contexts: closed-channel dominated Feshbach resonance, Efimov physics near Feshbach resonances, and corrections to the mean field energy of Bose-Einstein condensates with large scattering lengths. Novel experimental tools and strategies are discussed to study universality in ultracold atomic gases: dynamic control of interactions, run-away evaporative cooling in optical traps, and preparation of few-body systems in optical lattices.
We demonstrate a simple scheme to achieve fast, runaway evaporative cooling of optically trapped atoms by tilting the optical potential with a magnetic field gradient. Runaway evaporation is possible in this trap geometry due to the weak dependence o
f vibration frequencies on trap depth, which preserves atomic density during the evaporation process. Using this scheme, we show that Bose-Einstein condensation with ~10^5 cesium atoms can be realized in 2~4 s of forced evaporation. The evaporation speed and energetics are consistent with the three-dimensional evaporation picture, despite the fact that atoms can only leave the trap in the direction of tilt.
