70 research outputs found
Phase-space mixing in dynamically unstable, integrable few-mode quantum systems
Quenches in isolated quantum systems are currently a subject of intense
study. Here, we consider quantum few-mode systems that are integrable in their
classical mean-field limit and become dynamically unstable after a quench of a
system parameter. Specifically, we study a Bose-Einstein condensate (BEC) in a
double-well potential and an antiferromagnetic spinor BEC constrained to a
single spatial mode. We study the time dynamics after the quench within the
truncated Wigner approximation (TWA) and find that system relaxes to a steady
state due to phase-space mixing. Using the action-angle formalism and a
pendulum as an illustration, we derive general analytical expressions for the
time evolution of expectation values of observables and their long-time limits.
We find that the deviation of the long-time expectation value from its
classical value scales as , where is the number of atoms in
the condensate. Furthermore, the relaxation of an observable to its steady
state value is a damped oscillation and the damping is Gaussian in time. We
confirm our results with numerical TWA simulations.Comment: 17 pages, 9 figure
Large effective three-body interaction in a double-well optical lattice
We study ultracold atoms in an optical lattice with two local minima per unit
cell and show that the low energy states of a multi-band Bose-Hubbard (BH)
Hamiltonian with only pair-wise interactions is equivalent to an effective
single-band Hamiltonian with strong three-body interactions. We focus on a
double-well optical lattice with a symmetric double well along the axis and
single well structure along the perpendicular directions. Tunneling and
two-body interaction energies are obtained from an exact band-structure
calculation and numerically-constructed Wannier functions in order to construct
a BH Hamiltonian spanning the lowest two bands. Our effective Hamiltonian is
constructed from the ground state of the -atom Hamiltonian for each unit
cell obtained within the subspace spanned by the Wannier functions of two
lowest bands. The model includes hopping between ground states of neighboring
unit cells. We show that such an effective Hamiltonian has strong three-body
interactions that can be easily tuned by changing the lattice parameters.
Finally, relying on numerical mean-field simulations, we show that the
effective Hamiltonian is an excellent approximation of the two-band BH
Hamiltonian over a wide range of lattice parameters, both in the superfluid and
Mott insulator regions.Comment: 9 pages, 7 figure
A semiclassical theory of phase-space dynamics of interacting bosons
We study the phase-space representation of dynamics of bosons in the
semiclassical regime where the occupation number of the modes is large. To this
end, we employ the van Vleck-Gutzwiller propagator to obtain an approximation
for the Green's function of the Wigner distribution. The semiclassical analysis
incorporates interference of classical paths and reduces to the truncated
Wigner approximation (TWA) when the interference is ignored. Furthermore, we
identify the Ehrenfest time after which the TWA fails. As a case study, we
consider a single-mode quantum nonlinear oscillator, which displays collapse
and revival of observables. We analytically show that the interference of
classical paths leads to revivals, an effect that is not reproduced by the TWA
or a perturbative analysis
Optimization of collisional Feshbach cooling of an ultracold nondegenerate gas
We optimize a collision-induced cooling process for ultracold atoms in the
nondegenerate regime. It makes use of a Feshbach resonance, instead of rf
radiation in evaporative cooling, to selectively expel hot atoms from a trap.
Using functional minimization we analytically show that for the optimal cooling
process the resonance energy must be tuned such that it linearly follows the
temperature. Here, optimal cooling is defined as maximizing the phase-space
density after a fixed cooling duration. The analytical results are confirmed by
numerical Monte-Carlo simulations. In order to simulate more realistic
experimental conditions, we show that background losses do not change our
conclusions, while additional non-resonant two-body losses make a lower initial
resonance energy with non-linear dependence on temperature preferable.Comment: 7 pages, 7 figure
Orbital quantum magnetism in spin dynamics of strongly interacting magnetic lanthanide atoms
Laser cooled lanthanide atoms are ideal candidates with which to study strong
and unconventional quantum magnetism with exotic phases. Here, we use
state-of-the-art closed-coupling simulations to model quantum magnetism for
pairs of ultracold spin-6 erbium lanthanide atoms placed in a deep optical
lattice. In contrast to the widely used single-channel Hubbard model
description of atoms and molecules in an optical lattice, we focus on the
single-site multi-channel spin evolution due to spin-dependent contact,
anisotropic van der Waals, and dipolar forces. This has allowed us to identify
the leading mechanism, orbital anisotropy, that governs molecular spin dynamics
among erbium atoms. The large magnetic moment and combined orbital angular
momentum of the 4f-shell electrons are responsible for these strong anisotropic
interactions and unconventional quantum magnetism. Multi-channel simulations of
magnetic Cr atoms under similar trapping conditions show that their
spin-evolution is controlled by spin-dependent contact interactions that are
distinct in nature from the orbital anisotropy in Er. The role of an external
magnetic field and the aspect ratio of the lattice site on spin dynamics is
also investigated.Comment: 5 figure
Quadrature interferometry for nonequilibrium ultracold bosons in optical lattices
We develop an interferometric technique for making time-resolved measurements
of field-quadrature operators for nonequilibrium ultracold bosons in optical
lattices. The technique exploits the internal state structure of magnetic atoms
to create two subsystems of atoms in different spin states and lattice sites. A
Feshbach resonance turns off atom-atom interactions in one spin subsystem,
making it a well-characterized reference state, while atoms in the other
subsystem undergo nonequilibrium dynamics for a variable hold time. Interfering
the subsystems via a second beam-splitting operation, time-resolved quadrature
measurements on the interacting atoms are obtained by detecting relative spin
populations. The technique can provide quadrature measurements for a variety of
Hamiltonians and lattice geometries (e.g., cubic, honeycomb, superlattices),
including systems with tunneling, spin-orbit couplings using artificial gauge
fields, and higher-band effects. Analyzing the special case of a deep lattice
with negligible tunneling, we obtain the time evolution of both quadrature
observables and their fluctuations. As a second application, we show that the
interferometer can be used to measure atom-atom interaction strengths with
super-Heisenberg scaling n^(-3/2) in the mean number of atoms per lattice site
n, and standard quantum limit scaling M^(-1/2) in the number of lattice sites
M. In our analysis, we require M >> 1 and for realistic systems n is small, and
therefore the scaling in total atom number N = nM is below the Heisenberg
limit; nevertheless, measurements testing the scaling behaviors for
interaction-based quantum metrologies should be possible in this system.Comment: Comments welcom
Sudden-quench dynamics of Bardeen-Cooper-Schrieffer states in deep optical lattices
We determine the exact dynamics of an initial Bardeen-Cooper-Schrieffer (BCS)
state of ultra-cold atoms in a deep hexagonal optical lattice. The dynamical
evolution is triggered by a quench of the lattice potential, such that the
interaction strength is much larger than the hopping amplitude . The
quench initiates collective oscillations with frequency in the
momentum occupation numbers and imprints an oscillating phase with the same
frequency on the BCS order parameter . The oscillation frequency of
is not reproduced by treating the time evolution in mean-field theory.
In our theory, the momentum noise (i.e. density-density) correlation functions
oscillate at frequency as well as at its second harmonic. For a
very deep lattice, with zero tunneling energy, the oscillations of momentum
occupation numbers are undamped. Non-zero tunneling after the quench leads to
dephasing of the different momentum modes and a subsequent damping of the
oscillations. The damping occurs even for a finite-temperature initial BCS
state, but not for a non-interacting Fermi gas. Furthermore, damping is
stronger for larger order parameter and may therefore be used as a signature of
the BCS state. Finally, our theory shows that the noise correlation functions
in a honeycomb lattice will develop strong anti-correlations near the Dirac
point
Two-body transients in coupled atomic-molecular BECs
We discuss the dynamics of an atomic Bose-Einstein condensate when pairs of
atoms are converted into molecules by single-color photoassociation. Three main
regimes are found and it is shown that they can be understood on the basis of
time-dependent two-body theory. In particular, the so-called rogue dissociation
regime [Phys. Rev. Lett., 88, 090403 (2002)], which has a density-dependent
limit on the photoassociation rate, is identified with a transient regime of
the two-atom dynamics exhibiting universal properties. Finally, we illustrate
how these regimes could be explored by photoassociating condensates of
alkaline-earth atoms.Comment: 4 pages, 3 figures - typos corrected in formula
Soliton dynamics of an atomic spinor condensate on a Ring Lattice
We study the dynamics of macroscopically-coherent matter waves of an
ultra-cold atomic spin-one or spinor condensate on a ring lattice of six sites
and demonstrate a novel type of spatio-temporal internal Josephson effect.
Using a discrete solitary mode of uncoupled spin components as an initial
condition, the time evolution of this many-body system is found to be
characterized by two dominant frequencies leading to quasiperiodic dynamics at
various sites. The dynamics of spatially-averaged and spin-averaged degrees of
freedom, however, is periodic enabling an unique identification of the two
frequencies. By increasing the spin-dependent atom-atom interaction strength we
observe a resonance state, where the ratio of the two frequencies is a
characteristic integer multiple and the spin-and-spatial degrees of freedom
oscillate in "unison". Crucially, this resonant state is found to signal the
onset to chaotic dynamics characterized by a broad band spectrum. In a
ferromagnetic spinor condensate with attractive spin-dependent interactions,
the resonance is accompanied by a transition from oscillatory- to
rotational-type dynamics as the time evolution of the relative phase of the
matter wave of the individual spin projections changes from bounded to
unbounded
A Hubbard model for ultracold bosonic atoms interacting via zero-point-energy induced three-body interactions
We show that for ultra-cold neutral bosonic atoms held in a three-dimensional
periodic potential or optical lattice, a Hubbard model with dominant,
attractive three-body interactions can be generated. In fact, we derive that
the effect of pair-wise interactions can be made small or zero starting from
the realization that collisions occur at the zero-point energy of an optical
lattice site and the strength of the interactions is energy dependent from
effective-range contributions. We determine the strength of the two- and
three-body interactions for scattering from van-der-Waals potentials and near
Fano-Feshbach resonances. For van-der-Waals potentials, which for example
describe scattering of alkaline-earth atoms, we find that the pair-wise
interaction can only be turned off for species with a small negative scattering
length, leaving the Sr isotope a possible candidate. Interestingly, for
collisional magnetic Feshbach resonances this restriction does not apply and
there often exist magnetic fields where the two-body interaction is small. We
illustrate this result for several known narrow resonances between alkali-metal
atoms as well as chromium atoms. Finally, we compare the size of the three-body
interaction with hopping rates and describe limits due to three-body
recombination
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