3,756 research outputs found
Josephson dynamics of a spin-orbit coupled Bose-Einstein condensate in a double well potential
We investigate the quantum dynamics of an experimentally realized spin-orbit
coupled Bose-Einstein condensate in a double well potential. The spin-orbit
coupling can significantly enhance the atomic inter-well tunneling. We find the
coexistence of internal and external Josephson effects in the system, which are
moreover inherently coupled in a complicated form even in the absence of
interatomic interactions. Moreover, we show that the spin-dependent tunneling
between two wells can induce a net atomic spin current referred as spin
Josephson effects. Such novel spin Josephson effects can be observable for
realistically experimental conditions.Comment: 8 page
Superfluid and magnetic states of an ultracold Bose gas with synthetic three-dimensional spin-orbit coupling in an optical lattice
We study ultracold bosonic atoms with the synthetic three-dimensional
spin-orbit (SO) coupling in a cubic optical lattice. In the superfluidity
phase, the lowest energy band exhibits one, two or four pairs of degenerate
single-particle ground states depending on the SO-coupling strengths, which can
give rise to the condensate states with spin-stripes for the weak atomic
interactions. In the deep Mott-insulator regime, the effective spin Hamiltonian
of the system combines three-dimensional Heisenberg exchange interactions,
anisotropy interactions and Dzyaloshinskii-Moriya interactions. Based on Monte
Carlo simulations, we numerically demonstrate that the resulting Hamiltonian
with an additional Zeeman field has a rich phase diagram with spiral, stripe,
vortex crystal, and especially Skyrmion crystal spin-textures in each xy-plane
layer. The obtained Skyrmion crystals can be tunable with square and hexagonal
symmetries in a columnar manner along the z axis, and moreover are stable
against the inter-layer spin-spin interactions in a large parameter region.Comment: 9 pages, 4 figures; title modified, references and discussions added;
accepted by PR
Quantum simulation of exotic PT-invariant topological nodal loop bands with ultracold atoms in an optical lattice
Since the well-known PT symmetry has its fundamental significance and
implication in physics, where PT denotes the combined operation of
space-inversion P and time-reversal T, it is extremely important and intriguing
to completely classify exotic PT-invariant topological metals and to physically
realize them. Here we, for the first time, establish a rigorous classification
of topological metals that are protected by the PT symmetry using KO-theory. As
a physically realistic example, a PT-invariant nodal loop (NL) model in a 3D
Brillouin zone is constructed, whose topological stability is revealed through
its PT-symmetry-protected nontrivial Z2 topological charge. Based on these
exact results, we propose an experimental scheme to realize and to detect
tunable PT-invariant topological NL states with ultracold atoms in an optical
lattice, in which atoms with two hyperfine spin states are loaded in a
spin-dependent 3D OL and two pairs of Raman lasers are used to create
out-of-plane spin-flip hopping with site-dependent phase. Such a realistic
cold-atom setup can yield topological NL states, having a tunable ring-shaped
band-touching line with the two-fold degeneracy in the bulk spectrum and
non-trivial surface states. The states are actually protected by the combined
PT symmetry even in the absence of both P and T symmetries, and are
characterized by a Z2-type invariant (a quantized Berry phase). Remarkably, we
demonstrate with numerical simulations that (i) the characteristic NL can be
detected by measuring the atomic transfer fractions in a Bloch-Zener
oscillation; (ii) the topological invariant may be measured based on the
time-of-flight imaging; and (iii) the surface states may be probed through
Bragg spectroscopy. The present proposal for realizing topological NL states in
cold atom systems may provide a unique experimental platform for exploring
exotic PT-invariant topological physics.Comment: 11 pages, 6 figures; accepted for publication in Phys. Rev.
Delocalization of relativistic Dirac particles in disordered one-dimensional systems and its implementation with cold atoms
We study theoretically the localization of relativistic particles in
disordered one-dimensional chains. It is found that the relativistic particles
tend to dislocation in comparison with the non-relativistic particles with the
same disorder strength. More intriguingly, we reveal that the massless Dirac
particles are entirely delocalized for any energy due to the inherent chiral
symmetry, leading to a well-known result that particles are always localized in
one-dimensional system for arbitrary weak disorders to break down. Furthermore,
we propose a feasible scheme to simulate and detect the delocalization feature
of the Dirac particles with cold atoms..Comment: The version to be published in Phys. Rev. Lett.. many typos
corrected; the suggested experiment was clarified
Modelling uncertainty using stochastic transport noise in a 2-layer quasi-geostrophic model
The stochastic variational approach for geophysical fluid dynamics was
introduced by Holm (Proc Roy Soc A, 2015) as a framework for deriving
stochastic parameterisations for unresolved scales. This paper applies the
variational stochastic parameterisation in a two-layer quasi-geostrophic model
for a beta-plane channel flow configuration. We present a new method for
estimating the stochastic forcing (used in the parameterisation) to approximate
unresolved components using data from the high resolution deterministic
simulation, and describe a procedure for computing physically-consistent
initial conditions for the stochastic model. We also quantify uncertainty of
coarse grid simulations relative to the fine grid ones in homogeneous (teamed
with small-scale vortices) and heterogeneous (featuring horizontally elongated
large-scale jets) flows, and analyse how the spread of stochastic solutions
depends on different parameters of the model. The parameterisation is tested by
comparing it with the true eddy-resolving solution that has reached some
statistical equilibrium and the deterministic solution modelled on a
low-resolution grid. The results show that the proposed parameterisation
significantly depends on the resolution of the stochastic model and gives good
ensemble performance for both homogeneous and heterogeneous flows, and the
parameterisation lays solid foundations for data assimilation
Numerically Modelling Stochastic Lie Transport in Fluid Dynamics
We present a numerical investigation of stochastic transport in ideal fluids.
According to Holm (Proc Roy Soc, 2015) and Cotter et al. (2017), the principles
of transformation theory and multi-time homogenisation, respectively, imply a
physically meaningful, data-driven approach for decomposing the fluid transport
velocity into its drift and stochastic parts, for a certain class of fluid
flows. In the current paper, we develop new methodology to implement this
velocity decomposition and then numerically integrate the resulting stochastic
partial differential equation using a finite element discretisation for
incompressible 2D Euler fluid flows. The new methodology tested here is found
to be suitable for coarse graining in this case. Specifically, we perform
uncertainty quantification tests of the velocity decomposition of Cotter et al.
(2017), by comparing ensembles of coarse-grid realisations of solutions of the
resulting stochastic partial differential equation with the "true solutions" of
the deterministic fluid partial differential equation, computed on a refined
grid. The time discretization used for approximating the solution of the
stochastic partial differential equation is shown to be consistent. We include
comprehensive numerical tests that confirm the non-Gaussianity of the stream
function, velocity and vorticity fields in the case of incompressible 2D Euler
fluid flows.Comment: 41 pages, 26 figures Minor changes -- updated figures to improve
readability. Corrected typos. Shifted Remark 7 to just after Assumption A1.
Added Remark
Theoretical analysis and numerical approximation for the stochastic thermal quasi-geostrophic model
This paper investigates the mathematical properties of a stochastic version
of the balanced 2D thermal quasigeostrophic (TQG) model of potential vorticity
dynamics. This stochastic TQG model is intended as a basis for parametrisation
of the dynamical creation of unresolved degrees of freedom in computational
simulations of upper ocean dynamics when horizontal buoyancy gradients and
bathymetry affect the dynamics, particularly at the submesoscale (250m-10km).
Specifically, we have chosen the SALT (Stochastic Advection by Lie Transport)
algorithm introduced in [25] and applied in [11,12] as our modelling approach.
The SALT approach preserves the Kelvin circulation theorem and an infinite
family of integral conservation laws for TQG. The goal of the SALT algorithm is
to quantify the uncertainty in the process of up-scaling, or coarse-graining of
either observed or synthetic data at fine scales, for use in computational
simulations at coarser scales. The present work provides a rigorous
mathematical analysis of the solution properties of the thermal
quasigeostrophic (TQG) equations with stochastic advection by Lie transport
(SALT) [27,28].Comment: 38 page
Efficiency optimization in a correlation ratchet with asymmetric unbiased fluctuations
The efficiency of a Brownian particle moving in periodic potential in the
presence of asymmetric unbiased fluctuations is investigated. We found that
there is a regime where the efficiency can be a peaked function of temperature,
which proves that thermal fluctuations facilitate the efficiency of energy
transformation, contradicting the earlier findings (H. kamegawa et al. Phys.
Rev. Lett. 80 (1998) 5251). It is also found that the mutual interplay between
asymmetry of fluctuation and asymmetry of the potential may induce optimized
efficiency at finite temperature. The ratchet is not most efficiency when it
gives maximum current.Comment: 10 pages, 7 figure
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