Finite temperature coherence of the ideal Bose gas in an optical lattice

In current experiments with cold quantum gases in periodic potentials, interference fringe contrast is typically the easiest signal in which to look for effects of non-trivial many-body dynamics. In order better to calibrate such measurements, we analyse the background effect of thermal decoherence as it occurs in the absence of dynamical interparticle interactions. We study the effect of optical lattice potentials, as experimentally applied, on the condensed fraction of a non-interacting Bose gas in local thermal equilibrium at finite temperatures. We show that the experimentally observed decrease of the condensate fraction in the presence of the lattice can be attributed, up to a threshold lattice height, purely to ideal gas thermodynamics; conversely we confirm that sharper decreases in first-order coherence observed in stronger lattices are indeed attributable to many-body physics. Our results also suggest that the fringe visibility 'kinks' observed in F.Gerbier et al., Phys. Rev. Lett. 95, 050404 (2005) may be explained in terms of the competition between increasing lattice strength and increasing mean gas density, as the gaussian profile of the red-detuned lattice lasers also increases the effective strength of the harmonic trap

Physics with Coherent Matter Waves

This review discusses progress in the new field of coherent matter waves, in particular with respect to Bose-Einstein condensates. We give a short introduction to Bose-Einstein condensation and the theoretical description of the condensate wavefunction. We concentrate on the coherence properties of this new type of matter wave as a basis for fundamental physics and applications. The main part of this review treats various measurements and concepts in the physics with coherent matter waves. In particular we present phase manipulation methods, atom lasers, nonlinear atom optics, optical elements, interferometry and physics in optical lattices. We give an overview of the state of the art in the respective fields and discuss achievements and challenges for the future

Dynamical Quasicondensation of Hard-Core Bosons at Finite Momenta

Long-range order in quantum many-body systems is usually associated with equilibrium situations. Here, we experimentally investigate the quasicondensation of strongly-interacting bosons at finite momenta in a far-from-equilibrium case. We prepare an inhomogeneous initial state consisting of one-dimensional Mott insulators in the center of otherwise empty one-dimensional chains in an optical lattice with a lattice constant $d$. After suddenly quenching the trapping potential to zero, we observe the onset of coherence in spontaneously forming quasicondensates in the lattice. Remarkably, the emerging phase order differs from the ground-state order and is characterized by peaks at finite momenta $\pm (\pi/2) (\hbar / d)$ in the momentum distribution function.Comment: See also Viewpoint: Emerging Quantum Order in an Expanding Gas, Physics 8, 99 (2015

Dynamics and statistical mechanics of ultra-cold Bose gases using c-field techniques

We review phase space techniques based on the Wigner representation that provide an approximate description of dilute ultra-cold Bose gases. In this approach the quantum field evolution can be represented using equations of motion of a similar form to the Gross-Pitaevskii equation but with stochastic modifications that include quantum effects in a controlled degree of approximation. These techniques provide a practical quantitative description of both equilibrium and dynamical properties of Bose gas systems. We develop versions of the formalism appropriate at zero temperature, where quantum fluctuations can be important, and at finite temperature where thermal fluctuations dominate. The numerical techniques necessary for implementing the formalism are discussed in detail, together with methods for extracting observables of interest. Numerous applications to a wide range of phenomena are presented.Comment: 110 pages, 32 figures. Updated to address referee comments. To appear in Advances in Physic

Criterion for bosonic superfluidity in an optical lattice

We show that the current method of determining superfluidity in optical lattices based on a visibly sharp bosonic momentum distribution $n({\bf k})$ can be misleading, for even a normal Bose gas can have a similarly sharp $n({\bf k})$. We show that superfluidity in a homogeneous system can be detected from the so-called visibility $(v)$ of $n({\bf k})$ $-$ that $v$ must be 1 within $O(N^{-2/3})$, where $N$ is the number of bosons. We also show that the T=0 visibility of trapped lattice bosons is far higher than what is obtained in some current experiments, suggesting strong temperature effects and that these states can be normal. These normal states allow one to explore the physics in the quantum critical region.Comment: 4 pages, 2 figures; published versio

Theory of correlations between ultra-cold bosons released from an optical lattice

In this paper we develop a theoretical description of the correlations between ultra-cold bosons after free expansion from confinement in an optical lattice. We consider the system evolution during expansion and give criteria for a far field regime. We develop expressions for first and second order two-point correlations based on a variety of commonly used approximations to the many-body state of the system including Bogoliubov, meanfield decoupling, and particle-hole perturbative solution about the perfect Mott-insulator state. Using these approaches we examine the effects of quantum depletion and pairing on the system correlations. Comparison with the directly calculated correlation functions is used to justify a Gaussian form of our theory from which we develop a general three-dimensional formalism for inhomogeneous lattice systems suitable for numerical calculations of realistic experimental regimes.Comment: 18 pages, 11 figures. To appear in Phys. Rev. A. (few minor changes made and typos fixed

Characteristics of Bose-Einstein condensation in an optical lattice

We discuss several possible experimental signatures of the Bose-Einstein condensation (BEC) transition for an ultracold Bose gas in an inhomogeneous optical lattice. Based on the commonly used time-of-flight imaging technique, we show that the momentum-space density profile in the first Brillouin zone, supplemented by the visibility of interference patterns, provides valuable information about the system. In particular, by crossing the BEC transition temperature, the appearance of a clear bimodal structure sets a qualitative and universal signature of this phase transition. Furthermore, the momentum distribution can also be applied to extract the condensate fraction, which may serve as a promising thermometer in such a system.Comment: 12 pages, 13 figures; Revised version with new figures; Phys. Rev. A 77, 043626 (2008