We demonstrate that the transition from a superfluid to a Mott insulator in the Bose-Hubbard model can be induced by an oscillating force through an effective renormalization of the tunneling matrix element. The mechanism involves adiabatic following of Floquet states, and can be tested experimentally with Bose-Einstein condensates in periodically driven optical lattices. Its extension from small to very large systems yields nontrivial information on the condensate dynamics.

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We present measurements of the near-field heat transfer between the tip of a thermal profiler and planar material surfaces under ultrahigh vacuum conditions. For tip-sample distances below 10 −8 m our results differ markedly from the prediction of fluctuating electrodynamics. We argue that these differences are due to the existence of a material-dependent small length scale below which the macroscopic description of the dielectric properties fails, and discuss a corresponding model which yields fair agreement with the available data. These results are of importance for the quantitative interpretation of signals obtained by scanning thermal microscopes capable of detecting local temperature variations on surfaces.PACS numbers: 44.40.+a, 03.50.De, 78.20.Ci Radiative heat transfer between macroscopic bodies increases strongly when their spacing is made smaller than the dominant wavelength λ th of thermal radiation. This effect, caused by evanescent electromagnetic fields existing close to the surface of the bodies, has been studied theoretically already in 1971 by Polder and van Hove for the model of two infinitely extended, planar surfaces separated by a vacuum gap [1], and re-investigated later by Loomis and Maris [2] and Volokitin and Persson [3,4]. While early pioneering measurements with flat chromium bodies had to remain restricted to gap widths above 1 µm [5], and later studies employing an indium needle in close proximity to a planar thermocouple remained inconclusive [6], an unambiguous demonstration of near-field heat transfer under ultrahigh vacuum conditions and, thus, in the absence of disturbing moisture films covering the surfaces, could be given in Ref. [7].The theoretical treatment of radiative near-field heat transfer is based on fluctuating electrodynamics [8]. Within this framework, the macroscopic Maxwell equations are augmented by fluctuating currents inside each body, constituting stochastic sources of the electric and magnetic fields E and H. The individual frequency components j(r, ω) of these currents are considered as Gaussian stochastic variables. According to the fluctuationdissipation theorem, their correlation function reads [9]where E(ω, β) = ω/ exp(β ω) − 1 , with the usual inverse temperature variable β = 1/(k B T ); the angular brackets indicate an ensemble average. Moreover, ǫ ′′ (ω) denotes the imaginary part of the complex dielectric function ǫ(ω) = ǫ ′ (ω) + iǫ ′′ (ω). It describes the dissipative properties of the material under consideration, which is assumed to be homogeneous and non-magnetic. Thus, Eq. (1) contains the idealization that stochastic sources residing at different points r, r ′ are uncorrelated, no matter how small their distance may be. Applied to a material occupying the half-space z < 0, facing the vacuum in the complementary half-space z > 0, these propositions can be evaluated to yield the electromagnetic energy density in the distance z above the surface, giving [10]dκ ρ E (ω, κ, β, z) + ρ H (ω, κ, β, z)

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We report on the experimental observation of dynamic localization of a Bose-Einstein condensate in a shaken optical lattice, both for sinusoidal and square-wave forcing. The formulation of this effect in terms of a quasienergy band collapse, backed by the excellent agreement of the observed collapse points with the theoretical predictions, suggests the feasibility of systematic quasienergy band engineering

A primer on the Floquet theory of periodically time-dependent quantum systems is provided, and it is shown how to apply this framework for computing the quasienergy band structure governing the dynamics of ultracold atoms in driven optical cosine lattices. Such systems are viewed here as spatially and temporally periodic structures living in an extended Hilbert space, giving rise to spatio-temporal Bloch waves whose dispersion relations can be manipulated at will by exploiting ac-Stark shifts and multiphoton resonances. The elements required for numerical calculations are introduced in a tutorial manner, and some example calculations are discussed in detail, thereby illustrating future prospects of Floquet engineering.

We study the transition from a Mott insulator to a superfluid in both the two- and the three-dimensional Bose-Hubbard model at zero temperature, employing the method of the effective potential. Converting Kato's perturbation series into an algorithm capable of reaching high orders, we obtain accurate critical parameters for any integer filling factor. Our technique allows us to monitor both the approach to the mean-field limit by considering spatial dimensionalities $d > 3$, and to the quantum rotor limit of high filling, which refers to an array of Josephson junctions.Comment: 4 pages, 4 figure

We investigate the localization properties of single-particle eigenstates in bichromatic one-dimensional optical lattices. Whereas such a lattice with a sufficiently deep primary component and a suitably adjusted incommensurate secondary component provides an approximate realization of the Harper model, the system's self-duality is broken when the lattice is comparatively shallow. As a consequence, the sharp metal-insulator transition exhibited by Harper's model is replaced by a sequence of mobility edges in realistic bichromatic optical lattices that do not reach the tight-binding regime.