18 research outputs found
Repulsively interacting fermions in a two-dimensional deformed trap with spin-orbit coupling
We investigate a two-dimensional system of with two values of the internal
(spin) degree of freedom. It is confined by a deformed harmonic trap and
subject to a Zeeman field, Rashba or Dresselhaus one-body spin-orbit couplings
and two-body short range repulsion. We obtain self-consistent mean-field
-body solutions as functions of the interaction parameters. Single-particle
Spectra and total energies are computed and compared to the results without
interaction. We perform a statistical analysis for the distributions of nearest
neighbor energy level spacings and show that quantum signatures of chaos are
seen in certain parameters regimes. Furthermore, the effects of two-body
repulsion on the nearest neighbor distributions are investigated. This
repulsion can either promote or destroy the signatures of potential chaotic
behavior depending on relative strengths of parameters. Our findings support
the suggestion that cold atoms may be used to study quantum chaos both in the
presence and absence of interactions.Comment: 12 pages, 9 figures, revised versio
Computation of local exchange coefficients in strongly interacting one-dimensional few-body systems: local density approximation and exact results
One-dimensional multi-component Fermi or Bose systems with strong zero-range
interactions can be described in terms of local exchange coefficients and
mapping the problem into a spin model is thus possible. For arbitrary external
confining potentials the local exchanges are given by highly non-trivial
geometric factors that depend solely on the geometry of the confinement through
the single-particle eigenstates of the external potential. To obtain accurate
effective Hamiltonians to describe such systems one needs to be able to compute
these geometric factors with high precision which is difficult due to the
computational complexity of the high-dimensional integrals involved. An
approach using the local density approximation would therefore be a most
welcome approximation due to its simplicity. Here we assess the accuracy of the
local density approximation by going beyond the simple harmonic oscillator that
has been the focus of previous studies and consider some double-wells of
current experimental interest. We find that the local density approximation
works quite well as long as the potentials resemble harmonic wells but break
down for larger barriers. In order to explore the consequences of applying the
local density approximation in a concrete setup we consider quantum state
transfer in the effective spin models that one obtains. Here we find that even
minute deviations in the local exchange coefficients between the exact and the
local density approximation can induce large deviations in the fidelity of
state transfer for four, five, and six particles.Comment: 12 pages, 7 figures, 1 table, final versio
Tunable self-assembled spin chains of strongly interacting cold atoms for demonstration of reliable quantum state transfer
Energy as a function of dimensionless spin–orbit coupling parameter β for the case where the oscillator potential is deformed
<p><strong>Figure 2.</strong> Energy as a function of dimensionless spin–orbit coupling parameter β for the case where the oscillator potential is deformed. The left panel has \gamma =\frac{\omega _x}{\omega _y} = 2 and the right panel has γ = 3.</p> <p><strong>Abstract</strong></p> <p>We consider a spin–orbit coupled system of particles in an external trap that is represented by a deformed harmonic oscillator potential. The spin–orbit interaction is a Rashba interaction that does not commute with the trapping potential and requires a full numerical treatment in order to obtain the spectrum. The effect of a Zeeman term is also considered. Our results demonstrate that variable spectral gaps occur as a function of strength of the Rashba interaction and deformation of the harmonic trapping potential. The single-particle density of states and the critical strength for superfluidity vary tremendously with the interaction parameter. The strong variations with Rashba coupling and deformation imply that the few- and many-body physics of spin–orbit coupled systems can be manipulated by variation of these parameters.</p
Same as figures 2 and 3 for Îł = 5 (left panel) and Îł = 10 (right panel)
<p><strong>Figure 4.</strong> Same as figures <a href="http://iopscience.iop.org/0953-4075/46/13/134012/article#jpb467366f2" target="_blank">2</a> and <a href="http://iopscience.iop.org/0953-4075/46/13/134012/article#jpb467366f3" target="_blank">3</a> for γ = 5 (left panel) and γ = 10 (right panel). These results approach the limit of an effective one-dimensional system, i.e. γ 1.</p> <p><strong>Abstract</strong></p> <p>We consider a spin–orbit coupled system of particles in an external trap that is represented by a deformed harmonic oscillator potential. The spin–orbit interaction is a Rashba interaction that does not commute with the trapping potential and requires a full numerical treatment in order to obtain the spectrum. The effect of a Zeeman term is also considered. Our results demonstrate that variable spectral gaps occur as a function of strength of the Rashba interaction and deformation of the harmonic trapping potential. The single-particle density of states and the critical strength for superfluidity vary tremendously with the interaction parameter. The strong variations with Rashba coupling and deformation imply that the few- and many-body physics of spin–orbit coupled systems can be manipulated by variation of these parameters.</p