80 research outputs found
Tunable Wigner States with Dipolar Atoms and Molecules
We study the few-body physics of trapped atoms or molecules with electric or
magnetic dipole moments aligned by an external field. Using exact numerical
diagonalization appropriate for the strongly correlated regime, as well as a
classical analysis, we show how Wigner localization emerges with increasing
coupling strength. The Wigner states exhibit non-trivial geometries due to the
anisotropy of the interaction. This leads to transitions between different
Wigner states as the tilt angle of the dipoles with the confining plane is
changed. Intriguingly, while the individual Wigner states are well described by
a classical analysis, the transitions between different Wigner states are
strongly affected by quantum statistics. This can be understood by considering
the interplay between quantum-mechanical and spatial symmetry properties.
Finally, we demonstrate that our results are relevant to experimentally
realistic systems.Comment: 4 pages, 6 figure
Vortices in Bose-Einstein condensates - finite-size effects and the thermodynamic limit
For a weakly-interacting Bose gas rotating in a harmonic trap we relate the
yrast states of small systems (that can be treated exactly) to the
thermodynamic limit (derived within the mean-field approximation). For a few
dozens of atoms, the yrast line shows distinct quasi-periodic oscillations with
increasing angular momentum that originate from the internal structure of the
exact many-body states. These finite-size effects disappear in the
thermodynamic limit, where the Gross-Pitaevskii approximation provides the
exact energy to leading order in the number of particles N. However, the exact
yrast states reveal significant structure not captured by the mean-field
approximation: Even in the limit of large N, the corresponding mean-field
solution accounts for only a fraction of the total weight of the exact quantum
state.Comment: Phys Rev A, in pres
Vortices in fermion droplets with repulsive dipole-dipole interactions
Vortices are found in a fermion system with repulsive dipole-dipole
interactions, trapped by a rotating quasi-two-dimensional harmonic oscillator
potential. Such systems have much in common with electrons in quantum dots,
where rotation is induced via an external magnetic field. In contrast to the
Coulomb interactions between electrons, the (externally tunable) anisotropy of
the dipole-dipole interaction breaks the rotational symmetry of the
Hamiltonian. This may cause the otherwise rotationally symmetric exact
wavefunction to reveal its internal structure more directly.Comment: 5 pages, 5 figure
Transport and interaction blockade of cold bosonic atoms in a triple-well potential
We theoretically investigate the transport properties of cold bosonic atoms
in a quasi one-dimensional triple-well potential that consists of two large
outer wells, which act as microscopic source and drain reservoirs, and a small
inner well, which represents a quantum-dot-like scattering region. Bias and
gate "voltages" introduce a time-dependent tilt of the triple-well
configuration, and are used to shift the energetic level of the inner well with
respect to the outer ones. By means of exact diagonalization considering a
total number of six atoms in the triple-well potential, we find diamond-like
structures for the occurrence of single-atom transport in the parameter space
spanned by the bias and gate voltages. We discuss the analogy with Coulomb
blockade in electronic quantum dots, and point out how one can infer the
interaction energy in the central well from the distance between the diamonds.Comment: 18 pages, 6 figure
Rotating Bose-Einstein condensates: Closing the gap between exact and mean-field solutions
When a Bose-Einstein condensed cloud of atoms is given some angular momentum,
it forms vortices arranged in structures with a discrete rotational symmetry.
For these vortex states, the Hilbert space of the exact solution separates into
a "primary" space related to the mean-field Gross-Pitaevskii solution and a
"complementary" space including the corrections beyond mean-field. Considering
a weakly-interacting Bose-Einstein condensate of harmonically-trapped atoms, we
demonstrate how this separation can be used to close the conceptual gap between
exact solutions for systems with only a few atoms and the thermodynamic limit
for which the mean-field is the correct leading-order approximation. Although
we illustrate this approach for the case of weak interactions, it is expected
to be more generally valid.Comment: 8 pages, 5 figure
Spin-orbit-enhanced Wigner localization in quantum dots
We investigate quantum dots with Rashba spin-orbit coupling in the
strongly-correlated regime. We show that the presence of the Rashba interaction
enhances the Wigner localization in these systems, making it achievable for
higher densities than those at which it is observed in Rashba-free quantum
dots. Recurring shapes in the pair-correlated densities of the yrast spectrum,
which might be associated with rotational and vibrational modes, are also
reported.Comment: 5 pages, 4 figure
Test of a Jastrow-type wavefunction for a trapped few-body system in one dimension
For a system with interacting quantum mechanical particles in a
one-dimensional harmonic oscillator, a trial wavefunction with simple structure
based on the solution of the corresponding two-particle system is suggested and
tested numerically. With the inclusion of a scaling parameter for the distance
between particles, at least for the very small systems tested here the ansatz
gives a very good estimate of the ground state energy, with the error being of
the order of ~1% of the gap to the first excited state
Signatures of Wigner Localization in Epitaxially Grown Nanowires
It was predicted by Wigner in 1934 that the electron gas will undergo a
transition to a crystallized state when its density is very low. Whereas
significant progress has been made towards the detection of electronic Wigner
states, their clear and direct experimental verification still remains a
challenge. Here we address signatures of Wigner molecule formation in the
transport properties of InSb nanowire quantum dot systems, where a few
electrons may form localized states depending on the size of the dot (i.e. the
electron density). By a configuration interaction approach combined with an
appropriate transport formalism, we are able to predict the transport
properties of these systems, in excellent agreement with experimental data. We
identify specific signatures of Wigner state formation, such as the strong
suppression of the antiferromagnetic coupling, and are able to detect the onset
of Wigner localization, both experimentally and theoretically, by studying
different dot sizes.Comment: 4 pages, 4 figure
Vortex arrays in neutral trapped Fermi gases through the BCS–BEC crossover
Vortex arrays in type-II superconductors reflect the translational symmetry of an infinite system. There are cases, however, such as ultracold trapped Fermi gases and the crust of neutron stars, where finite-size effects make it complex to account for the geometrical arrangement of vortices. Here, we self-consistently generate these arrays of vortices at zero and finite temperature through a microscopic description of the non-homogeneous superfluid based on a differential equation for the local order parameter, obtained by coarse graining the Bogoliubov–de Gennes (BdG) equations. In this way, the strength of the inter-particle interaction is varied along the BCS–BEC crossover, from largely overlapping Cooper pairs in the Bardeen–Cooper–Schrieffer (BCS) limit to dilute composite bosons in the Bose–Einstein condensed (BEC) limit. Detailed comparison with two landmark experiments on ultracold Fermi gases, aimed at revealing the presence of the superfluid phase, brings out several features that make them relevant for other systems in nature as well
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