The observation of the superfluid to Mott insulator phase transition of ultracold atoms in optical lattices was an enabling discovery in experimental many-body physics, providing the first tangible example of a quantum phase transition (one that occurs even at zero temperature) in an ultracold atomic gas. For a trapped gas, the spatially varying local chemical potential gives rise to multiple quantum phases within a single sample, complicating the interpretation of bulk measurements. Here we report spatially resolved, in-situ imaging of a two-dimensional ultracold atomic gas as it crosses the superfluid to Mott insulator transition, providing direct access to individual characteristics of the insulating, superfluid and normal phases. We present results for the local compressibility in all phases, observing a strong suppression in the insulator domain and suppressed density fluctuations for the Mott insulator, in accordance with the fluctuation-dissipation theorem. Furthermore, we obtain a direct measure of the finite temperature of the system. Taken together, these methods enable a complete characterization of multiple phases in a strongly correlated Bose gas, and of the interplay between quantum and thermal fluctuations in the quantum critical regime.

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-KosterlitzThouless (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][6][7][8][9][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.PACS numbers: 64.60.F-,05.70. Jk,67.10.Ba, In 2D Bose gases, critical behavior develops in the BKT transition regime, where an ordered phase with finite-ranged coherence competes with thermal fluctuations and induces a continuous phase transition from normal gas to superfluid with quasi-long range order [3]. In this fluctuation region, a universal and scale-invariant description for the system is expected through the powerlaw scaling of thermodynamic quantities with respect to the coupling strength and a characteristic length scale [12,14], e.g., thermal de Broglie wavelength (Fig. 1a). For weakly interacting gases at finite temperatures, in particular, the scale invariance prevails over the normal, fluctuation, and superfluid regions because of the densityindependent coupling constant[15] and the symmetry of underlying Hamiltonian [4].In this letter, we verify the scale invariance and universality of interacting 2D Bose gases, and identify BKT critical points. We test scale invariance of in situ density and density fluctuations of 133 Cs 2D gases at various temperatures. We study the universality near the BKT transition by tuning the atomic scattering length using a magnetic Feshbach resonance [16] and observing a universal scaling behavior of the equation of state and the quasi-condensate density. Finally, by comparing the local density fluctuations and the compressibility derived from the density profiles, we provide strong evidence of a growing density-density correlation in the fluctuation regime.We begin the experiment by loading a nearly pure 133 Cs Bose condensate of N = 2 × 10 ...

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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 adiabatic, 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 loss pulses to analyze the occupancy distribution, we observe similarly slow-evolving dynamics, and a lower effective temperature at the center of the sample.

We demonstrate a simple scheme to achieve fast, accelerating ͑runaway͒ 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 of vibration frequencies on trap depth, which preserves atomic density during the evaporation process. Using this scheme, we show that Bose-Einstein condensation with ϳ10 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.The possibility to manipulate Bose-Einstein condensates ͑BECs͒ and degenerate Fermi gases of cold atoms in optical traps opens up a wide variety of exciting research; prominent examples include spinor condensates ͓1͔, Feshbach resonance in cold collisions ͓2͔, and BECs of molecules ͓3,4͔. In many early experiments, condensates were first created in a magnetic trap and subsequently transferred to an optical dipole trap. These experiments could be greatly simplified after direct evaporation to BEC in optical traps as demonstrated in ͓5͔. In this paper, we describe a further improvement on dipole-trap based evaporation, which allows for runaway cooling without significant increase in trap complexity.Evaporative cooling proceeds by lowering the depth of a confining potential, which allows atoms with high kinetic energy to escape and the remaining particles to acquire a lower temperature and higher phase space density through rethermalization. Starting from a sample of precooled atoms in a dipole trap, one can perform forced evaporative cooling on optically trapped atoms by constantly reducing the trap depth until quantum degeneracy is reached. This method has been successful in creating rubidium BEC in a dipole trap ͓5͔, and has become a critical component in recent experiments on quantum gases of Cs ͓6͔, Li ͓7͔, K ͓8͔, and Yb ͓9͔. In all of these experiments, forced evaporative cooling in the dipole trap is realized by reducing the intensity of the trapping beam, and consequently also the restoring forces. In a later discussion, we will refer to this approach as the trapweakening scheme.Evaporative cooling in optical traps remains one of the most time consuming and technically challenging steps in condensate production. Fundamentally, this is due to the fact that cooling by weakening the trapping potential inevitably reduces the collision rate. Here runaway ͑accelerating͒ evaporation is essentially impossible even with perfect evaporation efficiency and purely elastic collisions ͓10͔. Within experimentally accessible times, the trap-weakening method puts a severe limit on the maximum gain in phase space density that one can reach. Several auxiliary schemes have been successfully implemented in order to increase the evaporation speed, including the dimple trap ͓6͔ and a zoom lens system ͓11͔. These methods often increase the complexity of the apparatus o...