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arXiv:1710.11441 · New Journal of Physics

Excitation spectrum of a mixture of two Bose gases confined in a ring potential with interaction asymmetry

A Roussou, J Smyrnakis, M Magiropoulos, N K Efremidis, G M Kavoulakis, P Sandin, Magnus Ögren, M Gulliksson

Published Mar 9, 2018• 10 citations
arXivHTMLPDF

Abstract

We study the rotational properties of a two-component Bose–Einstein condensed gas of distinguishable atoms which are confined in a ring potential using both the mean-field approximation, as well as the method of diagonalization of the many-body Hamiltonian. We demonstrate that the angular momentum may be given to the system either via single-particle, or 'collective' excitation. Furthermore, despite the complexity of this problem, under rather typical conditions the dispersion relation takes a remarkably simple and regular form. Finally, we argue that under certain conditions the dispersion relation is determined via collective excitation. The corresponding many-body state, which, in addition to the interaction energy minimizes also the kinetic energy, is dictated by elementary number theory.

DOI
10.1088/1367-2630/aab599

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We study the rotational properties of a two-component Bose–Einstein condensed gas of distinguishable atoms which are confined in a ring potential using both the mean-field approximation, as well as the method of diagonalization of the many-body Hamiltonian. We demonstrate that the angular momentum may be given to the system either via single-particle, or 'collective' excitation. Furthermore, despite the complexity of this problem, under rather typical conditions the dispersion relation takes a remarkably simple and regular form. Finally, we argue that under certain conditions the dispersion relation is determined via collective excitation. The corresponding many-body state, which, in addition to the interaction energy minimizes also the kinetic energy, is dictated by elementary number theory.
A Bose-Einstein condensate is a type of gas consisting of one or more types of particles called bosons which are cooled to a temperature very close the absolute zero. Under these conditions the particles all start to occupy their lowest quantum state. Once in these states it is necessary to use quantum physics to describe the behaviour of the particles by the means of a wave function which describes the probability of finding the particles in different locations. In this thesis we will study a gas consisting of two components. The wave function satisfies the Schrödinger equation, which is a linear partial differential equation. The gas will be considered to be confined within a thin ring with a cross section small enough to treat it as one dimensional. By using the mean field approximation we're able to consider a much simpler model than the individual particle interaction and reduce the many-body problem to a one-body problem. However, the linear Schrödinger equation is replaced by the non-linear Schrödinger equation. We will also investigate the mean-field yrast spectrum, where these states are the ones with minimum energy for a given angular momentum. The existence of a minimum gives the possibility of having persistent currents as argued in previous research. In order to identify the yrast states, we first look for critical points of the energy under the constraints of total probability mass and angular momentum using a special Ansatz. We then try to determine if they are minimizers using analytic and numerical methods.
The Hamiltonian of an NNN-boson system confined on a ring with zero spin and repulsive interaction is diagonalized. The excitation of a pair of ppp-wave particles rotating reversely appears to be a basic mode. The fluctuation of many of these excited pairs provides a mechanism of oscillation; the states can be thereby classified as oscillation bands. The particle correlation is studied intuitively via the two-body densities. Bose clustering originating from the symmetrization of wave functions is found, which leads to the appearance of one-, two-, and three-cluster structures. The motion is divided into being collective and relative; this leads to the establishment of a relation between the very high vortex states and the low-lying states.
The mean-field yrast spectrum of an SU(2)-symmetric two-component Bose gas confined to a ring geometry is known to exhibit an intricate nonanalytic structure that is absent in single-component systems. In particular, due to the interplay between the species concentration and the atomic interactions, a sequence of plane-wave states can emerge as yrast states at fractional values of the angular momentum per particle. This behavior stands in sharp contrast to the single-component case, where plane-wave states occur only at integer angular momenta. In this paper, we investigate how the structure of the yrast spectrum in a two-component Bose gas is modified by interaction asymmetry. By numerically solving the coupled Gross-Pitaevskii equations for propagating soliton states, we compute the mean-field yrast spectrum and, in particular, determine the critical curves associated with the emergence of various plane-wave yrast states. We find that both the behavior of these critical curves and the mechanisms by which plane-wave yrast states arise depend sensitively on the relative strengths of the inter- and intra-component interactions. When the intra-component interaction is weaker, the plane-wave yrast states replace soliton states through a continuous evolution, as in the SU(2)-symmetric case, although the conditions for their existence become more restrictive. In contrast, when the intra-component interaction is stronger, plane-wave yrast states may emerge by overtaking soliton states via branch crossings, and their stability is significantly enhanced. Our results have important implications for the existence and stability of persistent currents in asymmetric, two-component Bose gases.
We study the rotational properties of a two-component Bose gas trapped in a rotating harmonic potential, effectively in two dimensions. We first consider a completely homogeneous interaction between particles, and assume the bosons to be in the lowest Landau level. We derive analytical expressions for some wave functions and energies at low angular momenta, and use these results together with exact numerical diagonalization results to test the applicability of composite fermion (CF) trial wave functions to the system. We find that a general procedure based on CF wave functions reproduces the exact ground states and many of the excited states for sufficiently low angular momenta, and give very good approximate results at angular momenta up to the two-component analogy of a single vortex. Additionally, we produce very simple CF states that have remarkably high overlaps with the lowest-lying states. Finally, we briefly discuss the case of inhomogeneous interactions, pointing out the difficulties arising from this generalization.