44 research outputs found
Behaviour of the energy gap in a model of Josephson coupled Bose-Einstein condensates
In this work we investigate the energy gap between the ground state and the
first excited state in a model of two single-mode Bose-Einstein condensates
coupled via Josephson tunneling. The energy gap is never zero when the
tunneling interaction is non-zero. The gap exhibits no local minimum below a
threshold coupling which separates a delocalised phase from a self-trapping
phase which occurs in the absence of the external potential. Above this
threshold point one minimum occurs close to the Josephson regime, and a set of
minima and maxima appear in the Fock regime. Analytic expressions for the
position of these minima and maxima are obtained. The connection between these
minima and maxima and the dynamics for the expectation value of the relative
number of particles is analysed in detail. We find that the dynamics of the
system changes as the coupling crosses these points.Comment: 12 pages, 5 .eps figures + 4 figs, classical analysis, perturbation
theor
Integrable atomtronic interferometry
High sensitivity quantum interferometry requires more than just access to
entangled states. It is achieved through deep understanding of quantum
correlations in a system. Integrable models offer the framework to develop this
understanding. We communicate the design of interferometric protocols for an
integrable model that describes the interaction of bosons in a four-site
configuration. Analytic formulae for the quantum dynamics of certain
observables are computed. These expose the system's functionality as both an
interferometric identifier, and producer, of NOON states. Being equivalent to a
controlled-phase gate acting on two hybrid qudits, this system also highlights
an equivalence between Heisenberg-limited interferometry and quantum
information. These results are expected to open new avenues for
integrability-enhanced atomtronic technologies.Comment: 6 pages, 4 figures, 1 tabl
Magnetic Susceptibility of an integrable anisotropic spin ladder system
We investigate the thermodynamics of a spin ladder model which possesses a
free parameter besides the rung and leg couplings. The model is exactly solved
by the Bethe Ansatz and exhibits a phase transition between a gapped and a
gapless spin excitation spectrum. The magnetic susceptibility is obtained
numerically and its dependence on the anisotropy parameter is determined. A
connection with the compounds KCuCl3, Cu2(C5H12N2)2Cl4 and (C5H12N)2CuBr4 in
the strong coupling regime is made and our results for the magnetic
susceptibility fit the experimental data remarkably well.Comment: 12 pages, 12 figures included, submitted to Phys. Rev.
Quantum dynamics of a model for two Josephson-coupled Bose--Einstein condensates
In this work we investigate the quantum dynamics of a model for two
single-mode Bose--Einstein condensates which are coupled via Josephson
tunneling. Using direct numerical diagonalisation of the Hamiltonian, we
compute the time evolution of the expectation value for the relative particle
number across a wide range of couplings. Our analysis shows that the system
exhibits rich and complex behaviours varying between harmonic and non-harmonic
oscillations, particularly around the threshold coupling between the
delocalised and self-trapping phases. We show that these behaviours are
dependent on both the initial state of the system as well as regime of the
coupling. In addition, a study of the dynamics for the variance of the relative
particle number expectation and the entanglement for different initial states
is presented in detail.Comment: 15 pages, 8 eps figures, accepted in J. Phys.
The extended Heine-Stieltjes polynomials associated with a special LMG model
New polynomials associated with a special Lipkin-Meshkov-Glick (LMG) model
corresponding to the standard two-site Bose-Hubbard model are derived based on
the Stieltjes correspondence. It is shown that there is a one-to-one
correspondence between zeros of this new polynomial and solutions of the Bethe
ansatz equations for the LMG model.A one-dimensional classical electrostatic
analogue corresponding to the special LMG model is established according to
Stieltjes early work. It shows that any possible configuration of equilibrium
positions of the charges in the electrostatic problem corresponds uniquely to
one set of roots of the Bethe ansatz equations for the LMG model, and the
number of possible configurations of equilibrium positions of the charges
equals exactly to the number of energy levels in the LMG model. Some relations
of sums of powers and inverse powers of zeros of the new polynomials related to
the eigenenergies of the LMG model are derived.Comment: 11 pages, LaTe
On quantum group symmetry and Bethe ansatz for the asymmetric twin spin chain with integrable boundary
Motivated by a study of the crossing symmetry of the `gemini' representation
of the affine Hecke algebra we give a construction for crossing tensor space
representations of ordinary Hecke algebras. These representations build
solutions to the Yang--Baxter equation satisfying the crossing condition (that
is, integrable quantum spin chains). We show that every crossing representation
of the Temperley--Lieb algebra appears in this construction, and in particular
that this construction builds new representations. We extend these to new
representations of the blob algebra, which build new solutions to the Boundary
Yang--Baxter equation (i.e. open spin chains with integrable boundary
conditions).
We prove that the open spin chain Hamiltonian derived from Sklyanin's
commuting transfer matrix using such a solution can always be expressed as the
representation of an element of the blob algebra, and determine this element.
We determine the representation theory (irreducible content) of the new
representations and hence show that all such Hamiltonians have the same
spectrum up to multiplicity, for any given value of the algebraic boundary
parameter. (A corollary is that our models have the same spectrum as the open
XXZ chain with nondiagonal boundary -- despite differing from this model in
having reference states.) Using this multiplicity data, and other ideas, we
investigate the underlying quantum group symmetry of the new Hamiltonians. We
derive the form of the spectrum and the Bethe ansatz equations.Comment: 43 pages, multiple figure
Exactly solvable models for triatomic-molecular Bose-Einstein Condensates
We construct a family of triatomic models for heteronuclear and homonuclear
molecular Bose-Einstein condensates. We show that these new generalized models
are exactly solvable through the algebraic Bethe ansatz method and derive their
corresponding Bethe ansatz equations and energies.Comment: 11 page
Hecke algebraic approach to the reflection equation for spin chains
We use the structural similarity of certain Coxeter Artin Systems to the
Yang--Baxter and Reflection Equations to convert representations of these
systems into new solutions of the Reflection Equation. We construct certain
Bethe ansatz states for these solutions, using a parameterisation suggested by
abstract representation theory.Comment: 27 pages, multiple figures, late