4,217 research outputs found
Vortices in Bose-Einstein Condensate Dark Matter
If dark matter in the galactic halo is composed of bosons that form a
Bose-Einstein condensate then it is likely that the rotation of the halo will
lead to the nucleation of vortices. After a review of the Gross-Pitaevskii
equation, the Thomas-Fermi approximation and vortices in general, we consider
vortices in detail. We find strong bounds for the boson mass, interaction
strength, the shape and quantity of vortices in the halo, the critical
rotational velocity for the nucleation of vortices and, in the Thomas-Fermi
regime, an exact solution for the mass density of a single, axisymmetric
vortex.Comment: 10 pages, 3 figures; minor corrections, references adde
Competing Orders in a Dipolar Bose-Fermi Mixture on a Square Optical Lattice: Mean-Field Perspective
We consider a mixture of a two-component Fermi gas and a single-component
dipolar Bose gas in a square optical lattice and reduce it into an effective
Fermi system where the Fermi-Fermi interaction includes the attractive
interaction induced by the phonons of a uniform dipolar Bose-Einstein
condensate. Focusing on this effective Fermi system in the parameter regime
that preserves the symmetry of , the point group of a square, we explore,
within the Hartree-Fock-Bogoliubov mean-field theory, the phase competition
among density wave orderings and superfluid pairings. We construct the matrix
representation of the linearized gap equation in the irreducible
representations of . We show that in the weak coupling regime, each matrix
element, which is a four-dimensional (4D) integral in momentum space, can be
put in a separable form involving a 1D integral, which is only a function of
temperature and the chemical potential, and a pairing-specific "effective"
interaction, which is an analytical function of the parameters that
characterize the Fermi-Fermi interactions in our system. We analyze the
critical temperatures of various competing orders as functions of different
system parameters in both the absence and presence of the dipolar interaction.
We find that close to half filling, the d_{x^{2}-y^{2}}-wave pairing with a
critical temperature in the order of a fraction of Fermi energy (at half
filling) may dominate all other phases, and at a higher filling factor, the
p-wave pairing with a critical temperature in the order of a hundredth of Fermi
energy may emerge as a winner. We find that tuning a dipolar interaction can
dramatically enhance the pairings with - and g-wave symmetries but not
enough for them to dominate other competing phases.Comment: 18 pages, 9 figure
Bistability in Feshbach Resonance
A coupled atom-molecule condensate with an intraspecies Feshbach resonance is
employed to explore matter wave bistability both in the presence and in the
absence of a unidirectional optical ring cavity. In particular, a set of
conditions are derived that allow the threshold for bistability, due both to
two-body s-wave scatterings and to cavity-mediated two-body interactions, to be
determined analytically. The latter bistability is found to support, not only
transitions between a mixed (atom-molecule) state and a pure molecular state as
in the former bistability, but also transitions between two distinct mixed
states.Comment: 6 pages + 3 figures; To appear in Jounal of Modern Optics, Special
Issue - Festschrift in Honor of Lorenzo Narducc
Singlet and Triplet Superfluid Competition in a Mixture of Two-Component Fermi and One-Component Dipolar Bose Gases
We consider a mixture of two-component Fermi and (one-component) dipolar Bose
gases in which both dipolar interaction and s-wave scattering between fermions
of opposite spins are tunable. We show that in the long wavelength limit, the
anisotropy in the Fermi-Fermi interaction induced by phonons of the dipolar
condensate can strongly enhance the scattering in the triplet channel. We
investigate in detail the conditions for achieving optimal critical temperature
at which the triplet superfluid begins to compete with the singlet superfluid.Comment: 5 pages, 2 figure
Topological study of a Bogoliubov-de Gennes system of pseudo spin- bosons with conserved magnetization in a honeycomb lattice
We consider a Bogolibov-de Geenes (BdG) Hamiltonian, which is a non-Hermitian
Hamiltonian with pseudo-Hermiticity, for a system of (pseudo) spin- bosons
in a honeycomb lattice under the condition that the population difference
between the two spin components, i.e., magnetization, is a constant. Such a
system is capable of acting as a topological amplifier, under time-reversal
symmetry, with stable bulk bands but unstable edge modes which can be populated
at an exponentially fast rate. We quantitatively study the topological
properties of this model within the framework of the 38-fold way for
non-Hermitian systems. We find, through the symmetry analysis of the Bloch
Hamiltonian, that this model is classified either as two copies of symmetry
class AIII+ or two copies of symmetry class A+ depending on
whether the (total) system is time-reversal-symmetric, where is the
matrix representing pseudo-Hermiticity and indicates that
pseudo-Hermiticity and chiral symmetry operators anticommute. We prove, within
the context of non-Hermitian physics where eigenstates obey the
bi-orthonormality relation, that a stable bulk is characterized by a single
topological invariant, the Chern number for the Haldane model, independent of
pairing interactions. We construct a convenient analytical description for the
edge modes of the Haldane model in semi-infinite planes, which is expected to
be useful for models built upon copies of the Haldane model across a broad
array of disciplines. We adapt the theorem in our recent work [Phys. Rev. A
104, 013305 (2021)] to pseudo-Hermitian Hamiltonians that are less restrictive
than BdG Hamiltonians and apply it to highlight that the vanishing of an
unconventional commutator between number-conserving and number-nonconserving
parts of the Hamiltonian indicates whether a system can be made to act as a
topological amplifier.Comment: 20 pages, 7 figure
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