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

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

Comment on "Creating artificial magnetic fields for cold atoms by photon-assisted tunneling" by Kolovsky A.R

We comment briefly on the scheme proposed in EPL 93, 20003 (2011) to produce synthetic gauge fields by means of photon-assisted tunneling.Comment: 2 pages, EPL forma

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

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

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

Finding zeros of the Riemann zeta function by periodic driving of cold atoms

The Riemann hypothesis, which states that the non-trivial zeros of the Riemann zeta function all lie on a certain line in the complex plane, is one of the most important unresolved problems in mathematics. Inspired by the P\'olya-Hilbert conjecture, we propose a new approach to finding a physical system to study the Riemann zeros, which in contrast to previous examples, is based on applying a time-periodic driving field. This driving allows us to mould the quasienergies of the system (the analogue of the eigenenergies in the absence of driving), so that they are directly governed by the zeta function. We further show by numerical simulations that this allows the Riemann zeros to be measured in currently accessible cold atom experiments.Comment: 6 pages, accepted for publication in Phys. Rev.

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