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arXiv:1309.1734 · Physical Review A

Mean-field yrast spectrum of a two-component Bose gas in ring geometry: Persistent currents at higher angular momentum

Zhigang Wu, E. Zaremba

Published Dec 26, 2013• 18 citations
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Abstract

We use analytic soliton solutions of a two-component Bose gas in the ring geometry to analyze the mean-field yrast spectrum of the system. We find that the spectrum exhibits a surprisingly rich structure as a result of an intricate interplay of interparticle interactions and population imbalance. We discuss the implication of these results in regard to the possibility of persistent currents at higher angular momenta.

DOI
10.1103/physreva.88.063640

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Structure of the mean-field yrast spectrum of a two-component Bose gas in a ring: role of interaction asymmetry

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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.

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Motivated by a recent experiment [Beattie, Moulder, Fletcher, and Hadzibabic, Phys. Rev. Lett. 110, 025301 (2013)], we study the superflow of atomic spinor Bose-Einstein condensates optically trapped in a ring-shaped geometry. Within a dissipative mean-field approach we simulate a two-component condensate in conditions adapted to the experiment. In qualitative agreement with the experimental findings, we observe stable superflow if the spin-population imbalance is above some well-defined threshold value. Below the stability threshold the persistent currents with higher-order circulation decay in quantized steps, and the vortex lines escape from the center of the ring through dynamically created ``weak links'' in the condensate annulus. These regions with reduced density of one spin component are filled by atoms of the other component. The vortices then leave the ring-shaped high-density region of the condensate and finally decay into elementary excitations.

arXiv:1309.3978•Physical Review A•Nov 27, 2013•32 citations
We use analytic soliton solutions of a two-component Bose gas in the ring geometry to analyze the mean-field yrast spectrum of the system. We find that the spectrum exhibits a surprisingly rich structure as a result of an intricate interplay of interparticle interactions and population imbalance. We discuss the implication of these results in regard to the possibility of persistent currents at higher angular momenta.
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 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.
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.
In this article we investigate the stability of quantized yrast states in a mixture of two distinguishable equal mass bosonic atoms confined in a ring. We focus in the study of energetic stability since the Bloch analysis and the Bogoliubov theory establishes that only energetically stable quantized yrast states are capable of sustain a persistent current. In the framework of the Bogoliubov theory we study the stability in two different cases chosen by physical considerations. In one case we analyze how the inter and intraspecies interaction strengths affect the stability of a selected quantized yrast state specified by the angular momentum per particle and the population imbalance. In the other case, for a fixed dynamics specified by given values of interaction strengths, we determine the stability of quantized yrast states as function of the angular momentum per particle and the population imbalance. We also examined the stability of the mixture in the rarefied limit and we found a critical value of the population imbalance which gives the size of the window of energetic stability and a critical value of angular momentum per particle which is an upper bound of the possible values of angular momentum per particle carried by energetically stable quantized yrast states.
Motivated by a recent experiment [Beattie, Moulder, Fletcher, and Hadzibabic, Phys. Rev. Lett. 110, 025301 (2013)], we study the superflow of atomic spinor Bose-Einstein condensates optically trapped in a ring-shaped geometry. Within a dissipative mean-field approach we simulate a two-component condensate in conditions adapted to the experiment. In qualitative agreement with the experimental findings, we observe stable superflow if the spin-population imbalance is above some well-defined threshold value. Below the stability threshold the persistent currents with higher-order circulation decay in quantized steps, and the vortex lines escape from the center of the ring through dynamically created ``weak links'' in the condensate annulus. These regions with reduced density of one spin component are filled by atoms of the other component. The vortices then leave the ring-shaped high-density region of the condensate and finally decay into elementary excitations.