Coherent control of a self-trapped Bose-Einstein condensate

We study the behavior of a Bose-Einstein condensate held in an optical lattice. We first show how a self-trapping transition can be induced in the system by either increasing the number of atoms occupying a lattice site, or by raising the interaction strength above a critical value. We then investigate how applying a periodic driving potential to the self-trapped state can be used to coherently control the emission of a precise number of correlated bosons from the trapping-site. This allows the formation and transport of entangled bosonic states, which are of great relevance to novel technologies such as quantum information processing.Comment: 4 pages, 5 EPS figure

Phase dependence of localization in the driven two-level model

A two-level system subjected to a high-frequency driving field can exhibit an effect termed ``coherent destruction of tunneling'', in which the tunneling of the system is suppressed at certain values of the frequency and strength of the field. This suppression becomes less effective as the frequency of the driving field is reduced, and we show here how the detailed form of its fall-off depends on the phase of the driving, which for certain values can produce small local maxima (or revivals) in the overall decay. By considering a squarewave driving field, which has the advantage of being analytically tractable, we show how this surprising behavior can be interpreted geometrically in terms of orbits on the Bloch sphere. These results are of general applicability to more commonly used fields, such as sinusoidal driving, which display a similar phenomenology.Comment: 4 pages,4 eps figures. V2: minor changes, this version to be published in Europhysics Letter

Coherent ratchets in driven Bose-Einstein condensates

We study the response of a Bose-Einstein condensate to an unbiased periodic driving potential. By controlling the space and time symmetries of the driving we show how a directed current can be induced, producing a coherent quantum ratchet. Weak driving induces a regular behavior that is strongly governed by the interparticle interaction. Breaking both space and time symmetries is required to produce current flow. For strong driving the behavior becomes chaotic. The resulting effective irreversibility renders the space asymmetry sufficient to produce the ratchet effect, although the system is completely coherent.Comment: 5 pages, 4 eps figures. Minor changes, this version to be published in PR

Generation of uniform synthetic magnetic fields by split driving of an optical lattice

We describe a method to generate a synthetic gauge potential for ultracold atoms held in an optical lattice. Our approach uses a time-periodic driving potential based on two quickly alternating signals to engineer the appropriate Aharonov-Bohm phases, and permits the simulation of a uniform tunable magnetic field. We explicitly demonstrate that our split driving scheme reproduces the behavior of a charged quantum particle in a magnetic field over the complete range of field strengths, and obtain the Hofstadter butterfly band-structure for the Floquet quasienergies at high fluxes.Comment: 5 pages, 3 eps figure

Controlled generation of coherent matter-currents using a periodic driving field

We study the effect of a strong, oscillating driving field on the dynamics of ultracold bosons held in an optical lattice. Modeling the system as a Bose-Hubbard model, we show how the driving field can be used to produce and maintain a coherent atomic current by controlling the phase of the intersite tunneling processes. We investigate both the stroboscopic and time-averaged behavior using Floquet theory, and demonstrate that this procedure provides a stable and precise method of controlling coherent quantum systems.Comment: 4.1 pages, 4 eps figure

Optimum pinning of the vortex lattice in extremely type-II layered superconductors

The two-dimensional (2D) vortex lattice in the extreme type-II limit is studied by Monte Carlo simulation of the corresponding 2D Coulomb gas, with identical pins placed at sites coinciding with the zero-temperature triangular vortex lattice. At weak pinning we find evidence for 2D melting into an intermediate hexatic phase. The strong pinning regime shows a Kosterlitz-Thouless transition, driven by interstitial vortex/anti-vortex excitations. A stack of such identical layers with a weak Josephson coupling models a layered superconductor with a triangular arrangement of columnar pins at the matching field. A partial duality analysis finds that layer decoupling of the flux-line lattice does not occur at weak pinning for temperatures below 2D melting.Comment: 5 pgs., 4 figs. To appear in PRB. Added size study of hexatic phas

Instability and control of a periodically-driven Bose-Einstein condensate

We investigate the dynamics of a Bose-Einstein condensate held in an optical lattice under the influence of a strong periodic driving potential. Studying the mean-field version of the Bose-Hubbard model reveals that the condensate becomes highly unstable when the effective intersite tunneling becomes negative. We further show how controlling the sign of the tunneling can be used as a powerful tool to manage the dispersion of an atomic wavepacket, and thus to create a pulsed atomic soliton laser.Comment: 4 pages, 3 eps figure

Tuning the Mott transition in a Bose-Einstein condensate by multi-photon absorption

We study the time-dependent dynamics of a Bose-Einstein condensate trapped in an optical lattice. Modeling the system as a Bose-Hubbard model, we show how applying a periodic driving field can induce coherent destruction of tunneling. In the low-frequency regime, we obtain the novel result that the destruction of tunneling displays extremely sharp peaks when the driving frequency is resonant with the depth of the trapping potential (``multi-photon resonances''), which allows the quantum phase transition between the Mott insulator and the superfluid state to be controlled with high precision. We further show how the waveform of the field can be chosen to maximize this effect.Comment: Minor changes, this version to be published in Phys. Rev. Let

Relativistic motion of an Airy wavepacket in a lattice potential

We study the dynamics of an Airy wavepacket moving in a one-dimensional lattice potential. In contrast to the usual case of propagation in a continuum, for which such a wavepacket experiences a uniform acceleration, the lattice bounds its velocity, and so the acceleration cannot continue indefinitely. Instead, we show that the wavepacket's motion is described by relativistic equations of motion, which surprisingly, arise naturally from evolution under the standard non-relativistic Schr\"odinger equation. The presence of the lattice potential allows the wavepacket's motion to be controlled by means of Floquet engineering. In particular, in the deep relativistic limit when the wavepacket's motion is photon-like, this form of control allows it to mimic both standard and negative refraction. Airy wavepackets held in lattice potentials can thus be used as powerful and flexible simulators of relativistic quantum systems.Comment: 9 pages, 8 figures. Higher resolution versions of Figs. 7a, 7b, 7c can be supplied on reques

Perturbative analysis of coherent quantum ratchets in cold atom systems

We present a perturbative study of the response of cold atoms in an optical lattice to a weak time- and space-asymmetric periodic driving signal. In the noninteracting limit, and for a finite set of resonant frequencies, we show how a coherent, long lasting ratchet current results from the interference between first and second order processes. In those cases, a suitable three-level model can account for the entire dynamics, yielding surprisingly good agreement with numerically exact results for weak and moderately strong driving.Comment: 8 pages, 6 figure