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

TL;DR

This work addresses the mean-field yrast spectrum of a two-component Bose gas on a ring under interaction asymmetry $ κ$, extending beyond the SU(2) symmetric case. By numerically solving the coupled Gross-Pitaevskii equations with an angular-momentum constraint, the authors map critical curves $x_B( gamma,k)$ for the emergence of plane-wave yrast states $(oldsymbol{ phi_0},oldsymbol{ phi_k})$ and construct phase diagrams that govern which fractional angular momenta $l=k x_B$ host nonanalyticities. A key result is the dichotomy in emergence mechanisms: for $ κ<0$ plane-wave yrast states arise via continuous soliton-to-plane-wave evolution, while for $ κ>0$ they appear through branch crossings, with a rich structure including a lobe where $(oldsymbol{ phi_0},oldsymbol{ phi_2})$ is yrast and asymptotes at $x_B=1/2$ and $x_B=1/3$. These findings illuminate how interaction asymmetry modulates persistent currents and the analytic structure of the yrast spectrum in asymmetric, two-component Bose gases, offering experimentally testable predictions. The analysis hinges on a self-consistent imaginary-time GP solver with a modulus-phase representation and a closed-form $ Omega$ expression that enforces the angular-momentum constraint, validated against the SU(2) benchmark.

Abstract

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 inter-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 inter-component interaction is stronger, plane-wave yrast states 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.

Figures (12)

• Figure 1: Illustration of the yrast spectrum for a single-component superfluid in a ring of radius $R$.
• Figure 2: The internal part of the mean-field yrast spectrum of an SU(2)-symmetric system, plotted in the fundamental range $0 < l \le 1/2$ for $\gamma = 100$. The circles mark the points at which the derivative of the spectrum is discontinuous and at which the corresponding yrast state is a plane-wave state.
• Figure 3: Critical curves for plane-wave yrast states $(\phi_0,\phi_k)$ with $k=2,3,4$ and the corresponding phase diagram for the SU(2)-symmetric system. Note that the $\gamma$ axis is plotted on a logarithmic scale.
• Figure 4: The internal part of the mean-field yrast spectrum of an asymmetric system with $\kappa = -0.1$, plotted in the fundamental range $0 < l \le 1/2$ for $\gamma = 20$. The circles indicate the locations at which the derivative of the spectrum is discontinuous.
• Figure 5: The internal part of the mean-field yrast spectrum of an asymmetric system with $\kappa = 1$, plotted in the fundamental range $0 < l \le 1/2$ for $\gamma = 20$. The circles mark the points at which the derivative of the spectrum is discontinuous and at which the corresponding yrast state is a plane-wave state.