Phase Separation of a Fast Rotating Boson-Fermion Mixture in the Lowest-Landau-Level Regime

By minimizing the coupled mean-field energy functionals, we investigate the ground-state properties of a rotating atomic boson-fermion mixture in a two-dimensional parabolic trap. At high angular frequencies in the mean-field-lowest-Landau-level regime, quantized vortices enter the bosonic condensate, and a finite number of degenerate fermions form the maximum-density-droplet state. As the boson-fermion coupling constant increases, the maximum density droplet develops into a lower-density state associated with the phase separation, revealing characteristics of a Landau-level structure

Attractive ultracold bosons in a necklace optical potential

We study the ground state properties of the Bose-Hubbard model with attractive interactions on a M-site one-dimensional periodic -- necklace-like -- lattice, whose experimental realization in terms of ultracold atoms is promised by a recently proposed optical trapping scheme, as well as by the control over the atomic interactions and tunneling amplitudes granted by well-established optical techniques. We compare the properties of the quantum model to a semiclassical picture based on a number-conserving su(M) coherent state, which results into a set of modified discrete nonlinear Schroedinger equations. We show that, owing to the presence of a correction factor ensuing from number conservation, the ground-state solution to these equations provides a remarkably satisfactory description of its quantum counterpart not only -- as expected -- in the weak-interaction, superfluid regime, but even in the deeply quantum regime of large interactions and possibly small populations. In particular, we show that in this regime, the delocalized, Schroedinger-cat-like quantum ground state can be seen as a coherent quantum superposition of the localized, symmetry-breaking ground-state of the variational approach. We also show that, depending on the hopping to interaction ratio, three regimes can be recognized both in the semiclassical and quantum picture of the system.Comment: 11 pages, 7 figures; typos corrected and references added; to appear in Phys. Rev.

Effectively attractive Bose-Einstein condensates in a rotating toroidal trap

We examine an effectively attractive quasi-one-dimensional Bose-Einstein condensate of atoms confined in a rotating toroidal trap, as the magnitude of the coupling constant and the rotational frequency are varied. Using both a variational mean-field approach, as well as a diagonalization technique, we identify the phase diagram between a uniform and a localized state and we describe the system in the two phases.Comment: 4 pages, 4 ps figures, RevTe

Metastable Quantum Phase Transitions in a Periodic One-dimensional Bose Gas: Mean-Field and Bogoliubov Analyses

We generalize the concept of quantum phase transitions, which is conventionally defined for a ground state and usually applied in the thermodynamic limit, to one for \emph{metastable states} in \emph{finite size systems}. In particular, we treat the one-dimensional Bose gas on a ring in the presence of both interactions and rotation. To support our study, we bring to bear mean-field theory, i.e., the nonlinear Schr\"odinger equation, and linear perturbation or Bogoliubov-de Gennes theory. Both methods give a consistent result in the weakly interacting regime: there exist \emph{two topologically distinct quantum phases}. The first is the typical picture of superfluidity in a Bose-Einstein condensate on a ring: average angular momentum is quantized and the superflow is uniform. The second is new: one or more dark solitons appear as stationary states, breaking the symmetry, the average angular momentum becomes a continuous quantity, and the phase of the condensate can be continuously wound and unwound

Collective modes and the broken symmetry of a rotating attractive Bose gas in an anharmonic trap

We study the rotational properties of an attractively interacting Bose gas in a quadratic + quartic potential. The low-lying modes of both rotational ground state configurations, namely the vortex and the center of mass rotating states, are solved. The vortex excitation spectrum is positive for weak interactions but the lowest modes decrease rapidly to negative values when the interactions become stronger. The broken rotational symmetry involved in the center of mass rotating state induces the appearance of an extra zero-energy mode in the Bogoliubov spectrum. The excitations of the center of mass rotational state also demonstrate the coupling between the center of mass and relative motions.Comment: 4 pages, 3 eps figures (2 in color) v2: changes in Title, all figures, in text (especially in Sec III) and in Reference

Quantization with Action-Angle Coherent States

For a single degree of freedom confined mechanical system with given energy, we know that the motion is always periodic and action-angle variables are convenient choice as conjugate phase-space variables. We construct action-angle coherent states in view to provide a quantization scheme that yields precisely a given observed energy spectrum ${E_n}$ for such a system. This construction is based on a Bayesian approach: each family corresponds to a choice of probability distributions such that the classical energy averaged with respect to this probability distribution is precisely $E_n$ up to a constant shift. The formalism is viewed as a natural extension of the Bohr-Sommerfeld rule and an alternative to the canonical quantization. In particular, it also yields a satisfactory angle operator as a bounded self-adjoint operator

Reflection of a Lieb-Liniger wave packet from the hard-wall potential

Nonequilibrium dynamics of a Lieb-Liniger system in the presence of the hard-wall potential is studied. We demonstrate that a time-dependent wave function, which describes quantum dynamics of a Lieb-Liniger wave packet comprised of N particles, can be found by solving an $N$-dimensional Fourier transform; this follows from the symmetry properties of the many-body eigenstates in the presence of the hard-wall potential. The presented formalism is employed to numerically calculate reflection of a few-body wave packet from the hard wall for various interaction strengths and incident momenta.Comment: revised version, improved notation, Fig. 5 adde

Evolution of the macroscopically entangled states in optical lattices

We consider dynamics of boson condensates in finite optical lattices under a slow external perturbation which brings the system to the unstable equilibrium. It is shown that quantum fluctuations drive the condensate into the maximally entangled state. We argue that the truncated Wigner approximation being a natural generalization of the Gross-Pitaevskii classical equations of motion is adequate to correctly describe the time evolution including both collapse and revival of the condensate.Comment: 14 pages, 10 figures, Discussion of reversibility of entanglement is adde

Quantum corrections to the dynamics of interacting bosons: beyond the truncated Wigner approximation

We develop a consistent perturbation theory in quantum fluctuations around the classical evolution of a system of interacting bosons. The zero order approximation gives the classical Gross-Pitaevskii equations. In the next order we recover the truncated Wigner approximation, where the evolution is still classical but the initial conditions are distributed according to the Wigner transform of the initial density matrix. Further corrections can be characterized as quantum scattering events, which appear in the form of a nonlinear response of the observable to an infinitesimal displacement of the field along its classical evolution. At the end of the paper we give a few numerical examples to test the formalism.Comment: published versio

Angular Pseudomomentum Theory for the Generalized Nonlinear Schr\"{o}dinger Equation in Discrete Rotational Symmetry Media

We develop a complete mathematical theory for the symmetrical solutions of the generalized nonlinear Schr\"odinger equation based on the new concept of angular pseudomomentum. We consider the symmetric solitons of a generalized nonlinear Schr\"odinger equation with a nonlinearity depending on the modulus of the field. We provide a rigorous proof of a set of mathematical results justifying that these solitons can be classified according to the irreducible representations of a discrete group. Then we extend this theory to non-stationary solutions and study the relationship between angular momentum and pseudomomentum. We illustrate these theoretical results with numerical examples. Finally, we explore the possibilities of the generalization of the previous framework to the quantum limit.Comment: 18 pages; submitted to Physica