Matter Waves In Optical Lattices Research Articles

Instabilities of interacting matter waves in optical lattices with Floquet driving

Instabilities of interacting matter waves in optical lattices with Floquet driving

Negative refraction of ultra-cold atoms in optical lattices with nonuniform artificial gauge fields

We theoretically study the reflection and refraction of ultra-cold atoms in optical lattices exposed to a nonuniform artificial magnetic field. The introduction of the nonuniform artificial magnetic field to the optical lattice for suitable designer magnetic potential barrier can lead to a series of intriguing reflection and refraction phenomena of atoms, including reflection, positive refraction, negative refraction and atomic matter wave splitting. Both the occurrence and the distribution of these reflection and refraction scenarios can be coherently controlled by the nonuniform artificial magnetic field. In particular, the regions close to the boundary of reflection demonstrate two more interesting propagation modes, i.e., a reflected branch of atoms comprising a positive or negative refracted branch of atoms with almost same atom population will be excited simultaneously at the magnetic potential barrier. The results can be a guide for the coherent control of the matter waves in optical lattices and the design of new atom optics devices.

NONLINEAR WAVE PROPAGATION IN PHOTONIC CRYSTAL FIBERS

Wave propagation is a fundamental phenomenon occurring in several physical systems. The spectra have been used by others to develop optical frequency standards. The process can potentially be used for frequency conversion in fiber optic network. In this system the dispersive properties can be controlled by the optical lattice making it possible to achieve phase-matched four wave mixing, like look the process taking place in the photonic crystal fibers (PCFs). In this paper will focus on two such systems the propagation nonlinear wave in photonic crystal fibers and the propagation of matter waves in optical lattices.

Localization-delocalization transition in self-dual quasi-periodic lattices

Within the framework of the Aubry-André model, one kind of self-dual quasi-periodic lattice, it is known that a sharp transition occurs from all eigenstates being extended to all being localized. The common perception for this type of quasi-periodic lattice is that the self-duality excludes the appearance of a finite critical energy separating localized from extended states. In this work, we propose a multi-chromatic quasi-periodic lattice model retaining the self-duality identical to the Aubry-André model. In this model we find numerically a well-defined localization-delocalization transition at the mobility edges in contrast with the Aubry-André model. As a result, the diffusion of wave packet exhibits a transition from ballistic to diffusive motion, and back to ballistic motion. We point out that experimental realizations of the predicted transition can be accessed with light waves in photonic lattices and matter waves in optical lattices.

Intrinsic localized modes in coupled DNLS equations from the anti-continuum limit

In the present work, we generalize earlier considerations for intrinsic localized modes consisting of a few excited sites, as developed in the one-component discrete nonlinear Schrödinger equation model, to the case of two-component systems. We consider all the different combinations of “up” (zero phase) and “down” (π phase) site excitations and are able to compute not only the corresponding existence curves, but also the eigenvalue dependence of the small eigenvalues potentially responsible for instabilities, as a function of the nonlinear parameters of the model representing the self/cross phase modulation in optics and the scattering length ratios in the case of matter waves in optical lattices. We corroborate these analytical predictions by means of direct numerical computations. We infer that all the modes which bear two adjacent nodes with the same phase are unstable in the two component case and the only solutions that may be linear stable are ones where each set of adjacent nodes, in each component is out of phase.

Controlled engineering of extended states in disordered systems

We describe how to engineer wavefunction delocalization in disordered systems modelled by tight-binding Hamiltonians in d>1 dimensions. We show analytically that a simple product structure for the random onsite potential energies, together with suitably chosen hopping strengths, allows a resonant scattering process leading to ballistic transport along one direction, and a controlled coexistence of extended Bloch states and anisotropically localized states in the spectrum. We demonstrate that these features persist in the thermodynamic limit for a continuous range of the system parameters. Numerical results support these findings and highlight the robustness of the extended regime with respect to deviations from the exact resonance condition for finite systems. The localization and transport properties of the system can be engineered almost at will and independently in each direction. This study gives rise to the possibility of designing disordered potentials that work as switching devices and band-pass filters for quantum waves, such as matter waves in optical lattices.

Robust dynamical recurrences based on Floquet spectrum

Recurrence behavior of wave packets in coupled higher dimensional systems and periodically driven systems is analyzed, which takes place in the realm of higher coupling/modulation strength. We analyze the wave packet dynamics close to nonlinear resonances developed in the systems and provide the analytical understanding of recurrence times.We apply these analytical results to investigate the recurrence times of matter waves in optical lattice in the presence of external periodic forcing. The obtained analytical results can experimentally be observed using currently available experimental setups.

Self-guiding of matter waves in optical lattices

It is shown numerically that Bose-Einstein condensates in optical lattices may be localized as self-induced waveguides and that these waveguides may take complex forms, including bends and X junctions. The waveguides are found to support continuous condensate flow, even around multiple right-angle bends. It is demonstrated that pulsed matter-wave transport may also occur along single-site waveguides in the form of solitons and that these solitons may propagate around bends and collide without change of shape or dependence on phase. A scheme based on single-site addressability techniques and the Kibble-Zurek mechanism is proposed for observing these effects.

Observation of Stückelberg oscillations in accelerated optical lattices

We report the experimental observation of St\"{u}ckelberg oscillations of matter waves in optical lattices. Extending previous work on Landau-Zener tunneling of Bose-Einstein condensates in optical lattices, we study the effects of the accumulated phase between two successive crossings of the Brillouin zone edge. Our results agree well with a simple model for multiple Landau-Zener tunneling events taking into account the band structure of the optical lattice.

Counterpropagating Matter Waves in Optical Lattices

An investigation of Bose–Einstein condensate in two-dimensional optical lattice potentials, formed by laser beams, is carried out. We are interested in the dynamics of Bose–Einstein condensate in a square optical lattice, where the periodic potential can lead to the stabilization of an otherwise unstable Bose–Einstein condensate. The behavior of Bose–Einstein condensate in optical lattices is described by the nonlinear Gross–Pitaevskii equation, which we treat numerically. By applying the Petviashvili iteration method, we demonstrate the existence of solitonic solutions in the case of counterpropagating matter waves, and analyze their stability.

One-dimensional delocalizing transitions of matter waves in optical lattices

We investigate, both analytically and numerically, the conditions for the occurrence of the delocalizing transition phenomenon of one-dimensional localized modes of several nonlinear continuous periodic and discrete systems of the nonlinear Schrödinger type. We show that either non-existence of solitons in the small amplitude limit or the loss of stability along existence branches can lead to delocalizing transitions, which occur following different scenarios. Examples of delocalizing transitions of both types are provided for a class of equations which describe single component and binary mixtures of Bose–Einstein condensates trapped in linear and nonlinear optical lattices.

Long-Living Bloch Oscillations of Matter Waves in Periodic Potentials

The dynamics of matter waves in linear and nonlinear optical lattices subject to a spatially uniform linear force is studied both analytically and numerically. It is shown that by properly designing the spatial dependence of the scattering length it is possible to induce long-living Bloch oscillations of gap-soliton matter waves in optical lattices. This occurs when the effective nonlinearity and the effective mass of the soliton have opposite signs for all values of the crystal momentum in the Brillouin zone. The results apply to all systems modeled by the periodic nonlinear Schrödinger equation, including propagation of light in photonic and photorefractive crystals with tilted band structures.

Management of matter waves in optical lattices by means of the Feshbach resonance

The mean-field dynamics of Bose-Einstein condensates loaded in an optical lattice, confined by a parabolic potential, and subjected to a change of scattering length by means of the Feshbach resonance is considered. The system is described by the Gross-Pitaevskii (GP) equation with varying nonlinearity, which in a number of cases is reduced to one-dimensional (1D) perturbed nonlinear Schr\"odinger (NLS) equations, the particular form of which depends on the relation among the parameters of the problem. We analytically describe the adiabatic dynamics of periodic solutions of the respective NLS equations, provide a numerical study of 1D models confined by a parabolic trap, and carry out numerical simulations of the matter-wave dynamics within the framework of the radially symmetric 3D GP equation. Special attention is paid to processes of generation of trains of bright and dark matter solitons from initially periodic waves. The results of the 1D approximation are compared with direct numerical simulation of the original 3D GP eqation, showing remarkable coincidence for definite regions of parameters.