arXiv subjects

G. M. Kavoulakis

Publications and source records attributed to G. M. Kavoulakis.

At least 37 records · Page 2Linked to original sources

arXiv2017

Dimensional reduction in Bose-Einstein condensed clouds of atoms confined in tight potentials of any geometry and any interaction strength

Motivated by numerous experiments on Bose-Einstein condensed atoms which have been performed in tight trapping potentials of various geometries (elongated and/or toroidal/annular), we develop a general method which allows us to reduce the corresponding three-dimensional Gross-Pitaevskii equation for the order parameter into an effectively one-dimensional equation, taking into account the interactions (i.e., treating the width of the transverse profile variationally) and the curvature of the trapping potential. As an application of our model we consider atoms which rotate in a toroidal trapping potential. We evaluate the state of lowest energy for a fixed value of the angular momentum within various approximations of the effectively one-dimensional model and compare our results with the full solution of the three-dimensional problem, thus getting evidence for the accuracy of our model.

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arXiv2016

Rotating Bose-Einstein condensates with a finite number of atoms confined in a ring potential: Spontaneous symmetry breaking, beyond the mean-field approximation

Motivated by recent experiments on Bose-Einstein condensed atoms which rotate in annular/toroidal traps we study the effect of the finiteness of the atom number $N$ on the states of lowest energy for a fixed expectation value of the angular momentum, under periodic boundary conditions. To attack this problem, we develop a general strategy, considering a linear superposition of the eigenstates of the many-body Hamiltonian, with amplitudes that we extract from the mean field approximation. This many-body state breaks the symmetry of the Hamiltonian, it has the same energy to leading order in $N$ as the mean-field state and the corresponding eigenstate of the Hamiltonian, however it has a lower energy to subleading order in $N$ and thus it is energetically favorable.

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arXiv2016

Spin-orbit-coupled Bose-Einstein-condensed atoms confined in annular potentials

A spin-orbit-coupled Bose-Einstein-condensed cloud of atoms confined in an annular trapping potential shows a variety of phases that we investigate in the present study. Starting with the non-interacting problem, the homogeneous phase that is present in an untrapped system is replaced by a sinusoidal density variation in the limit of a very narrow annulus. In the case of an untrapped system there is another phase with a striped-like density distribution, and its counterpart is also found in the limit of a very narrow annulus. As the width of the annulus increases, this picture persists qualitatively. Depending on the relative strength between the inter- and the intra-components, interactions either favor the striped phase, or suppress it, in which case either a homogeneous, or a sinusoidal-like phase appears. Interactions also give rise to novel solutions with a nonzero circulation.

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arXiv2015

Mean-field yrast spectrum and persistent currents in a two-component Bose gas with interaction asymmetry

We analyze the mean-field yrast spectrum of a two-component Bose gas in the ring geometry with arbitrary interaction asymmetry. Of particular interest is the possibility that the yrast spectrum develops local minima at which persistent superfluid flow can occur. By analyzing the mean-field energy functional, we show that local minima can be found at plane-wave states and arise when the system parameters satisfy certain inequalities. We then go on to show that these plane-wave states can be yrast states even when the yrast spectrum no longer exhibits a local minimum. Finally, we obtain conditions which establish when the plane-wave states cease to be yrast states. Specific examples illustrating the roles played by the various interaction asymmetries are presented.

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arXiv2015

Hysteresis and metastability of Bose-Einstein condensed clouds of atoms confined in ring potentials

We consider a Bose-Einstein condensed cloud of atoms which rotate in a toroidal/annular potential. Assuming one-dimensional motion, we evaluate the critical frequencies associated with the effect of hysteresis and the critical coupling for stability of the persistent currents. We perform these calculations using both the mean-field approximation and the method of numerical diagonalization of the many-body Hamiltonian which includes corrections due to the finiteness of the atom number.

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arXiv2015

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.

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arXiv2014

Persistent currents in a two-component Bose-Einstein condensate confined in a ring potential

We present variational and numerical solutions for the problem of stability of persistent currents in a two-component Bose-Einstein condensate of distinguishable atoms which rotate in a ring potential. We consider the general class of solutions of constant density in the two components separately, thus providing an alternative approach of the solution of the same problem given recently by Zhigang Wu and Eugene Zaremba [Phys. Rev. A {\bf 88}, 063640 (2013)]. Our approach provides a physically transparent solution of this delicate problem. Finally, we give a unified and simple picture of the lowest-energy state of the system for large values of the coupling.

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arXiv2014

Bose-Einstein Condensation of Excitons in Cu$_2$O: Progress Over Thirty Years

Experiments on Bose-Einstein condensation (BEC) of excitons in the semiconductor Cu$_2$O started over thirty years ago, as one of the first serious attempts at exciton BEC. Early claims were based on spectroscopic signatures and transport data which have since been reinterpreted, in large part because the Auger recombination process for excitons was not well understood. Understanding of the Auger process has also advanced, and recent experiments have made significant progress toward exciton BEC. We review the history of experiments on exciton BEC in Cu$_2$O, the Auger recombination process, and the prospects for observing exciton BEC in this system in the near future.

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arXiv2013

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.

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arXiv2013

Phase diagram of a rapidly-rotating two-component Bose gas

We derive analytically the phase diagram of a two-component Bose gas confined in an anharmonic potential, which becomes exact and universal in the limit of weak interactions and small anharmonicity of the trapping potential. The transitions between the different phases, which consist of vortex states of single and multiple quantization, are all continuous because of the addition of the second component.

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arXiv2012

Solitary-wave solutions in binary mixtures of Bose-Einstein condensates under periodic boundary conditions

We derive solitary-wave solutions within the mean-field approximation in quasi-one-dimensional binary mixtures of Bose-Einstein condensates under periodic boundary conditions, for the case of an effective repulsive interatomic interaction. The particular gray-bright solutions that give the global energy minima are determined. Their characteristics and the associated dispersion relation are derived. In the case of weak coupling, we diagonalize the Hamiltonian analytically to obtain the full excitation spectrum of "quantum" solitary-wave solutions.

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arXiv2012

Rotational properties of non-dipolar and dipolar Bose-Einstein condensates confined in annular potentials

We investigate the rotational response of both non-dipolar and dipolar Bose-Einstein condensates confined in an annular potential. For the non-dipolar case we identify certain critical rotational frequencies associated with the formation of vortices. For the dipolar case, assuming that the dipoles are aligned along some arbitrary and tunable direction, we study the same problem as a function of the orientation angle of the dipole moment of the atoms.

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arXiv2012

Excitation spectrum of a two-component Bose-Einstein condensate in a ring potential

A mixture of two distinguishable Bose-Einstein condensates confined in a ring potential has numerous interesting properties under rotational and solitary-wave excitation. The lowest-energy states for a fixed angular momentum coincide with a family of solitary-wave solutions. In the limit of weak interactions, exact diagonalization of the many-body Hamiltonian is possible and permits evaluation of the complete excitation spectrum of the system.

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arXiv2012

Condensates of p-wave pairs are exact solutions for rotating two-component Bose gases

We derive exact analytical results for the wave functions and energies of harmonically trapped two-component Bose-Einstein condensates with weakly repulsive interactions under rotation. The isospin symmetric wave functions are universal and do not depend on the matrix elements of the two-body interaction. The comparison with the results from numerical diagonalization shows that the ground state and low-lying excitations consists of condensates of p-wave pairs for repulsive contact interactions, Coulomb interactions, and the repulsive interactions between aligned dipoles.

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arXiv2011

Persistent currents in dipolar Bose-Einstein condensates confined in annular potentials

We consider a dipolar Bose-Einstein condensate confined in an annular potential, with all the dipoles being aligned along some arbitrary direction. In addition to the dipole-dipole interaction, we also assume a zero-range hard-core potential. We investigate the stability of the system against collapse, as well as the stability of persistent currents as a function of the orientation of the dipoles and of the strength of the hard-core interaction.

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arXiv2011

Rotational properties of dipolar Bose-Einstein condensates confined in anisotropic harmonic potentials

We study the rotational properties of a dipolar Bose-Einstein condensate confined in a quasi-two- dimensional anisotropic trap, for an arbitrary orientation of the dipoles with respect to their plane of motion. Within the mean-field approximation we find that the lowest-energy state of the system depends strongly on the relative strength between the dipolar and the contact interactions, as well as on the size and the orientation of the dipoles, and the size and the orientation of the deformation of the trapping potential.

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arXiv2011

Solitary waves and yrast states in Bose-Einstein condensed gases of atoms

Considering a Bose-Einstein condensed gas confined in one dimension with periodic boundary conditions, we demonstrate that, very generally, solitary-wave and rotational excitations coincide. This exact equivalence allows us to establish connections between a number of effects that are present in these two problems, many of which have been studied using the mean-field approximation.

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arXiv2010

Persistent currents in Bose gases confined in annular traps

We examine the problem of stability of persistent currents in a mixture of two Bose gases trapped in an annular potential. We evaluate the critical coupling for metastability in the transition from quasi-one to two-dimensional motion. We also evaluate the critical coupling for metastability in a mixture of two species as function of the population imbalance. The stability of the currents is shown to be sensitive to the deviation from one-dimensional motion.

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