Periodically-driven cold atoms: the role of the phase

Numerous theoretical and experimental studies have investigated the dynamics of cold atoms subjected to time periodic fields. Novel effects dependent on the amplitude and frequency of the driving field, such as Coherent Destruction of Tunneling have been identified and observed. However, in the last year or so, three distinct types of experiments have demonstrated for the first time, interesting behaviour associated with the driving phase: i.e. for systems experiencing a driving field of general form $V(x)\sin (\omega t + \phi)$, different types of large scale oscillations and directed motion were observed. We investigate and explain the phenomenon of Super-Bloch Oscillations (SBOs) in relation to the other experiments and address the role of initial phase in general. We analyse and compare the role of $\phi$ in systems with homogeneous forces ($V'(x)= const$), such as cold atoms in shaken or amplitude-modulated optical lattices, as well as non-homogeneous forces ($V'(x)\neq const$), such as the sloshing of atoms in driven traps, and clarify the physical origin of the different $\phi$-dependent effects.Comment: 10 pages, 1 figur

Superfluid-insulator transition in a periodically driven optical lattice

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.Comment: 4 pages, 4 figures, RevTe

Second-order calculation of the local density of states above a nanostructured surface

We have numerically implemented a perturbation series for the scattered electromagnetic fields above rough surfaces, due to Greffet, allowing us to evaluate the local density of states to second order in the surface profile function. We present typical results for thermal near fields of surfaces with regular nanostructures, investigating the relative magnitude of the contributions appearing in successive orders. The method is then employed for estimating the resolution limit of an idealized Near-Field Scanning Thermal Microscope (NSThM).Comment: 10 pages, 7 figure

Theory of Coherent Time-dependent Transport in One-dimensional Multiband Semiconductor Superlattices

We present an analytical study of one-dimensional semiconductor superlattices in external electric fields, which may be time-dependent. A number of general results for the (quasi)energies and eigenstates are derived. An equation of motion for the density matrix is obtained for a two-band model, and the properties of the solutions are analyzed. An expression for the current is obtained. Finally, Zener-tunneling in a two-band tight-binding model is considered. The present work gives the background and an extension of the theoretical framework underlying our recent Letter [J. Rotvig {\it et al.}, Phys. Rev. Lett. {\bf 74}, 1831 (1995)], where a set of numerical simulations were presented.Comment: 15 pages, Revtex 3.0, uses epsf, 2 ps figures attache

Bose Condensation and the BTZ Black Hole

Although all popular approaches to quantum gravity are able to recover the Bekenstein-Hawking entropy-area law in the thermodynamic limit, there are significant differences in their descriptions of the microstates and in the application of statistics. Therefore they can have significantly different phenomenological implications. For example, requiring indistinguishability of the elementary degrees of freedom should lead to changes in the black hole's radiative porperties away from the thermodynamic limit and at low temperatures. We demonstrate this for the Ba\~nados-Teitelboim-Zanelli (BTZ) black hole. The energy eigenstates and statistical entropy in the thermodynamic limit of the BTZ black hole were obtained earlier by us via symmetry reduced canonical quantum gravity. In that model the BTZ black hole behaves as a system of Bosonic mass shells moving in a one dimensional harmonic trap. Bose condensation does not occur in the thermodynamic limit but this system possesses a finite critical temperature, $T_c$, and exhibits a large condensate fraction below $T_c$ when the number of shells is finite.Comment: 5 pages, 5 figures. Published versio

Non-perturbative electron dynamics in crossed fields

Intense AC electric fields on semiconductor structures have been studied in photon-assisted tunneling experiments with magnetic field applied either parallel (B_par) or perpendicular (B_per) to the interfaces. We examine here the electron dynamics in a double quantum well when intense AC electric fields F, and tilted magnetic fields are applied simultaneously. The problem is treated non-perturbatively by a time-dependent Hamiltonian in the effective mass approximation, and using a Floquet-Fourier formalism. For B_par=0, the quasi-energy spectra show two types of crossings: those related to different Landau levels, and those associated to dynamic localization (DL), where the electron is confined to one of the wells, despite the non-negligible tunneling between wells. B_par couples parallel and in-plane motions producing anti-crossings in the spectrum. However, since our approach is non-perturbative, we are able to explore the entire frequency range. For high frequencies, we reproduce the well known results of perfect DL given by zeroes of a Bessel function. We find also that the system exhibits DL at the same values of the field F, even as B_par non-zero, suggesting a hidden dynamical symmetry in the system which we identify with different parity operations. The return times for the electron at various values of field exhibit interesting and complex behavior which is also studied in detail. We find that smaller frequencies shifts the DL points to lower field F, and more importantly, yields poorer localization by the field. We analyze the explicit time evolution of the system, monitoring the elapsed time to return to a given well for each Landau level, and find non-monotonic behavior for decreasing frequencies.Comment: REVTEX4 + 11 eps figs, submitted to Phys. Rev.

Dynamical control of correlated states in a square quantum dot

In the limit of low particle density, electrons confined to a quantum dot form strongly correlated states termed Wigner molecules, in which the Coulomb interaction causes the electrons to become highly localized in space. By using an effective model of Hubbard-type to describe these states, we investigate how an oscillatory electric field can drive the dynamics of a two-electron Wigner molecule held in a square quantum dot. We find that, for certain combinations of frequency and strength of the applied field, the tunneling between various charge configurations can be strongly quenched, and we relate this phenomenon to the presence of anti-crossings in the Floquet quasi-energy spectrum. We further obtain simple analytic expressions for the location of these anti-crossings, which allows the effective parameters for a given quantum dot to be directly measured in experiment, and suggests the exciting possibility of using ac-fields to control the time evolution of entangled states in mesoscopic devices.Comment: Replaced with version to be published in Phys. Rev.

Ground-state energy and depletions for a dilute binary Bose gas

When calculating the ground-state energy of a weakly interacting Bose gas with the help of the customary contact pseudopotential, one meets an artifical ultraviolet divergence which is caused by the incorrect treatment of the true interparticle interactions at small distances. We argue that this problem can be avoided by retaining the actual, momentum-dependent interaction matrix elements, and use this insight for computing both the ground-state energy and the depletions of a binary Bose gas mixture. Even when considering the experimentally relevant case of equal masses of both species, the resulting expressions are quite involved, and no straightforward generalizations of the known single-species formulas. On the other hand, we demonstrate in detail how these latter formulas are recovered from our two-species results in the limit of vanishing interspecies interaction.Comment: 11 pages, Phys. Rev. A in pres

Time Dependent Floquet Theory and Absence of an Adiabatic Limit

Quantum systems subject to time periodic fields of finite amplitude, lambda, have conventionally been handled either by low order perturbation theory, for lambda not too large, or by exact diagonalization within a finite basis of N states. An adiabatic limit, as lambda is switched on arbitrarily slowly, has been assumed. But the validity of these procedures seems questionable in view of the fact that, as N goes to infinity, the quasienergy spectrum becomes dense, and numerical calculations show an increasing number of weakly avoided crossings (related in perturbation theory to high order resonances). This paper deals with the highly non-trivial behavior of the solutions in this limit. The Floquet states, and the associated quasienergies, become highly irregular functions of the amplitude, lambda. The mathematical radii of convergence of perturbation theory in lambda approach zero. There is no adiabatic limit of the wave functions when lambda is turned on arbitrarily slowly. However, the quasienergy becomes independent of time in this limit. We introduce a modification of the adiabatic theorem. We explain why, in spite of the pervasive pathologies of the Floquet states in the limit N goes to infinity, the conventional approaches are appropriate in almost all physically interesting situations.Comment: 13 pages, Latex, plus 2 Postscript figure

Engineered quantum tunnelling in extended periodic potentials

Quantum tunnelling from a tilted, but otherwise periodic potential is studied. Our theoretical and experimental results show that, by controlling the system's parameters, we can engineer the escape rate of a Bose-Einstein condensate to an exceptional degree. Possible applications of this atom-optics realization of the open Wannier-Stark system are discussed.Comment: 6 pp, proceedings DICE 11-15 September 2006, Castello di Piombino, Tuscany, Ital