Boson Mott insulators at finite temperatures

We discuss the finite temperature properties of ultracold bosons in optical lattices in the presence of an additional, smoothly varying potential, as in current experiments. Three regimes emerge in the phase diagram: a low-temperature Mott regime similar to the zero-temperature quantum phase, an intermediate regime where MI features persist, but where superfluidity is absent, and a thermal regime where features of the Mott insulator state have disappeared. We obtain the thermodynamic functions of the Mott phase in the latter cases. The results are used to estimate the temperatures achieved by adiabatic loading in current experiments. We point out the crucial role of the trapping potential in determining the final temperature, and suggest a scheme for further cooling by adiabatic decompression

Detecting Chiral Edge States in the Hofstadter Optical Lattice

We propose a realistic scheme to detect topological edge states in an optical lattice subjected to a synthetic magnetic field, based on a generalization of Bragg spectroscopy sensitive to angular momentum. We demonstrate that using a well-designed laser probe, the Bragg spectra provide an unambiguous signature of the topological edge states that establishes their chiral nature. This signature is present for a variety of boundaries, from a hard wall to a smooth harmonic potential added on top of the optical lattice. Experimentally, the Bragg signal should be very weak. To make it detectable, we introduce a "shelving method", based on Raman transitions, which transfers angular momentum and changes the internal atomic state simultaneously. This scheme allows to detect the weak signal from the selected edge states on a dark background, and drastically improves the detectivity. It also leads to the possibility to directly visualize the topological edge states, using in situ imaging, offering a unique and instructive view on topological insulating phases.Comment: 4 pages, 4 figures, Supplementary material (Appendices A-D). Revised version, accepted in the Physical Review Letter

Heating rates for an atom in a far-detuned optical lattice

We calculate single atom heating rates in a far detuned optical lattice, in connection with recent experiments. We first derive a master equation, including a realistic atomic internal structure and a quantum treatment of the atomic motion in the lattice. The experimental feature that optical lattices are obtained by superimposing laser standing waves of different frequencies is also included, which leads to a micromotional correction to the light shift that we evaluate. We then calculate, and compare to experimental results, two heating rates, the "total" heating rate (corresponding to the increase of the total mechanical energy of the atom in the lattice), and the ground bande heating rate (corresponding to the increase of energy within the ground energy band of the lattice).Comment: 11 pages, 3 figures, 1 tabl

Relaxation and hysteresis near Shapiro resonances in a driven spinor condensate

We study the coherent and dissipative aspects of a driven spin-1 Bose-Einstein condensate (BEC) when the Zeeman energy is modulated around a static bias value. Resonances appear when the bias energy matches an integer number of modulation quanta. They constitute the atomic counterpart of Shapiro resonances observed in microwave-driven superconducting Josephson junctions. The population dynamics near each resonance corresponds to slow and non-linear secular oscillations on top of a rapid `micromotion'. At long times and in a narrow window of modulation frequencies around each resonance, we observe a relaxation to asymptotic states that are unstable without drive. These stationary states correspond to phase-locked solutions of the Josephson equations generalized to include dissipation, and are analogous to the stationary states of driven superconducting junctions. We find that dissipation is essential to understand this long-time behavior, and we propose a phenomenological model to explain quantitatively the experimental results. Finally, we demonstrate hysteresis in the asymptotic state of the driven spinor BEC when sweeping the modulation frequency across a Shapiro resonance

Anomalous momentum diffusion in a dissipative many-body system

Decoherence is ubiquitous in quantum physics, from the conceptual foundations to quantum information processing or quantum technologies, where it is a threat that must be countered. While decoherence has been extensively studied for simple, well-isolated systems such as single atoms or ions, much less is known for many-body systems where inter-particle correlations and interactions can drastically alter the dissipative dynamics. Here we report an experimental study of how spontaneous emission destroys the spatial coherence of a gas of strongly interacting bosons in an optical lattice. Instead of the standard momentum diffusion expected for independent atoms, we observe an anomalous sub-diffusive expansion, associated with a universal slowing down $\propto 1/t^{1/2}$ of the decoherence dynamics. This algebraic decay reflects the emergence of slowly-relaxing many-body states, akin to sub-radiant states of many excited emitters. These results, supported by theoretical predictions, provide an important benchmark in the understanding of open many-body systems.Comment: Supplementary material available as ancillary fil

Spin nematic order in antiferromagnetic spinor condensates

Large spin systems can exhibit unconventional types of magnetic ordering different from the ferromagnetic or N\'eel-like antiferromagnetic order commonly found in spin 1/2 systems. Spin-nematic phases, for instance, do not break time-reversal invariance and their magnetic order parameter is characterized by a second rank tensor with the symmetry of an ellipsoid. Here we show direct experimental evidence for spin-nematic ordering in a spin-1 Bose-Einstein condensate of sodium atoms with antiferromagnetic interactions. In a mean field description this order is enforced by locking the relative phase between spin components. We reveal this mechanism by studying the spin noise after a spin rotation, which is shown to contain information hidden when looking only at averages. The method should be applicable to high spin systems in order to reveal complex magnetic phases.Comment: published versio

Interference pattern and visibility of a Mott insulator

We analyze theoretically the experiment reported in [F. Gerbier et al, cond-mat/0503452], where the interference pattern produced by an expanding atomic cloud in the Mott insulator regime was observed. This interference pattern, indicative of short-range coherence in the system, could be traced back to the presence of a small amount of particle/hole pairs in the insulating phase for finite lattice depths. In this paper, we analyze the influence of these pairs on the interference pattern using a random phase approximation, and derive the corresponding visibility. We also account for the inhomogeneity inherent to atom traps in a local density approximation. The calculations reproduce the experimental observations, except for very large lattice depths. The deviation from the measurement in this range is attributed to the increasing importance of non-adiabatic effects.Comment: 6 pages, 4 figure

Phase coherence of an atomic Mott insulator

We investigate the phase coherence properties of ultracold Bose gases in optical lattices, with special emphasis on the Mott insulating phase. We show that phase coherence on short length scales persists even deep in the insulating phase, preserving a finite visibility of the interference pattern observed after free expansion. This behavior can be attributed to a coherent admixture of particle/hole pairs to the perfect Mott state for small but finite tunneling. In addition, small but reproducible ``kinks'' are seen in the visibility, in a broad range of atom numbers. We interpret them as signatures for density redistribution in the shell structure of the trapped Mott insulator