273 research outputs found
Bose-Einstein Condensates in Superlattices
We consider the Gross--Pitaevskii (GP) equation in the presence of periodic and quasi-periodic superlattices to study cigar-shaped Bose--Einstein condensates (BECs) in such potentials. We examine spatially extended wavefunctions in the form of modulated amplitude waves (MAWs). With a coherent structure ansatz, we derive amplitude equations describing the evolution of spatially modulated states of the BEC. We then apply second-order multiple scale perturbation theory to study harmonic resonances with respect to a single lattice substructure as well as ultrasubharmonic resonances that result from interactions of both substructures of the superlattice. In each case, we determine the resulting system's equilibria, which represent spatially periodic solutions, and subsequently examine the stability of the corresponding wavefunctions by direct simulations of the GP equation, identifying them as typically stable solutions of the model. We then study subharmonic resonances using Hamiltonian perturbation theory, tracing robust spatio-temporally periodic patterns
Strong correlations in quantum vortex nucleation of ultracold atomic gases
We review some recent developments in the theory of rotating atomic gases.
These studies have thrown light on the process of nucleation of vortices in
regimes where mean-field methods are inadequate. In our review we shall
describe and compare quantum vortex nucleation of a dilute ultracold bosonic
gas trapped in three different configurations: a one-dimensional ring lattice,
a one-dimensional ring superlattice and a two-dimensional asymmetric harmonic
trap. In all of them there is a critical rotation frequency, at which the
particles in the ground state exhibit strong quantum correlations. However, the
entanglement properties vary significantly from case to case. We explain these
differences by characterizing the intermediate states that participate in the
vortex nucleation process. Finally, we show that noise correlations are
sensitive to these differences. These new studies have, therefore, shown how
novel quantum states may be produced and probed in future experiments with
rotating neutral atom systems.Comment: 17 pages, 5 figure
Quasiperiodic Dynamics in Bose-Einstein Condensates in Periodic Lattices and Superlattices
We employ KAM theory to rigorously investigate quasiperiodic dynamics in
cigar-shaped Bose-Einstein condensates (BEC) in periodic lattices and
superlattices. Toward this end, we apply a coherent structure ansatz to the
Gross-Pitaevskii equation to obtain a parametrically forced Duffing equation
describing the spatial dynamics of the condensate. For shallow-well,
intermediate-well, and deep-well potentials, we find KAM tori and Aubry-Mather
sets to prove that one obtains mostly quasiperiodic dynamics for condensate
wave functions of sufficiently large amplitude, where the minimal amplitude
depends on the experimentally adjustable BEC parameters. We show that this
threshold scales with the square root of the inverse of the two-body scattering
length, whereas the rotation number of tori above this threshold is
proportional to the amplitude. As a consequence, one obtains the same dynamical
picture for lattices of all depths, as an increase in depth essentially only
affects scaling in phase space. Our approach is applicable to periodic
superlattices with an arbitrary number of rationally dependent wave numbers.Comment: 29 pages, 6 figures (several with multiple parts; higher-quality
versions of some of them available at
http://www.its.caltech.edu/~mason/papers), to appear very soon in Journal of
Nonlinear Scienc
Modulated amplitude waves with nonzero phases in Bose-Einstein condensates
In this paper we give a frame for application of the averaging method to
Bose-Einstein condensates (BECs) and obtain an abstract result upon the
dynamics of BECs. Using aver- aging method, we determine the location where the
modulated amplitude waves (periodic or quasi-periodic) exist and we also study
the stability and instability of modulated amplitude waves (periodic or
quasi-periodic). Compared with the previous work, modulated amplitude waves
studied in this paper have nontrivial phases and this makes the problem become
more diffcult, since it involves some singularities.Comment: 17 pages, 2 figure
Tunneling of ultracold atoms in time-independent potentials
We present theoretical as well as experimental results on resonantly enhanced
quantum tunneling of Bose-Einstein condensates in optical lattices both in the
linear case of single particle dynamics and in the presence of atom-atom
interactions. Our results demonstrate the usefulness of condensates in optical
lattices for the dynamical control of tunneling and for simulating Hamiltonians
originally used for describing solid state phenomena.Comment: slightly amended version published as ch. 11 of a book edited by S.
Keshavamurthy and P. Schlagheck with the title "Dynamical Tunneling: Theory
and Experiment
Spin-Orbit Coupling and Spin Textures in Optical Superlattices
We proposed and demonstrated a new approach for realizing spin orbit coupling
with ultracold atoms. We use orbital levels in a double well potential as
pseudospin states. Two-photon Raman transitions between left and right wells
induce spin-orbit coupling. This scheme does not require near resonant light,
features adjustable interactions by shaping the double well potential, and does
not depend on special properties of the atoms. A pseudospinor Bose-Einstein
condensate spontaneously acquires an antiferromagnetic pseudospin texture which
breaks the lattice symmetry similar to a supersolid
Quantum walk of a Bose-Einstein condensate in the Brillouin zone
We propose a realistic scheme to implement discrete-time quantum walks in the
Brillouin zone (i.e., in quasimomentum space) with a spinor Bose-Einstein
condensate. Relying on a static optical lattice to suppress tunneling in real
space, the condensate is displaced in quasimomentum space in discrete steps
conditioned upon the internal state of the atoms, while short pulses
periodically couple the internal states. We show that tunable twisted boundary
conditions can be implemented in a fully natural way by exploiting the
periodicity of the Brillouin zone. The proposed setup does not suffer from
off-resonant scattering of photons and could allow a robust implementation of
quantum walks with several tens of steps at least. In addition, onsite
atom-atom interactions can be used to simulate interactions with infinitely
long range in the Brillouin zone.Comment: 9 pages, 4 figures; in the new version, added a discussion about
decoherence in the appendi
Nonlinear Phenomena of Ultracold Atomic Gases in Optical Lattices: Emergence of Novel Features in Extended States
The system of a cold atomic gas in an optical lattice is governed by two
factors: nonlinearity originating from the interparticle interaction, and the
periodicity of the system set by the lattice. The high level of controllability
associated with such an arrangement allows for the study of the competition and
interplay between these two, and gives rise to a whole range of interesting and
rich nonlinear effects. This review covers the basic idea and overview of such
nonlinear phenomena, especially those corresponding to extended states. This
includes "swallowtail" loop structures of the energy band, Bloch states with
multiple periodicity, and those in "nonlinear lattices", i.e., systems with the
nonlinear interaction term itself being a periodic function in space.Comment: 39 pages, 21 figures; review article to be published in a Special
Issue of Entropy on "Non-Linear Lattice
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