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arXiv:1503.05583

Immiscibile two-component Bose Einstein condensates beyond mean-field approximation: phase transitions and rotational response

Peder Notto Galteland, Egor S. Babaev, Asle Sudbø

Published Mar 18, 2015• 1 citation
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Abstract

We consider a two-component immiscible Bose-Einstein condensate with dominating intra-species repulsive density-density interactions. In the ground-state phase of such a system only one condensates is present. This can be viewed as a spontaneous breakdown of $\mathbb{Z}_2$ symmetry. We study the phase diagram of the system at finite temperature beyond mean-field approximation. In the absence of rotation, we show that the system undergoes a first order phase transition from this ground state to a miscible two-component normal fluid as temperature is increased. In the presence of rotation, the system features a competition between vortex-vortex interaction and short range density-density interactions. This leads to a rotation-driven "mixing" phase transition in a spatially inhomogeneous state with additional broken $\mathrm{U}(1)$ symmetry. Thermal fluctuations in this state lead to nematic two-component sheets of vortex liquids. At sufficiently strong inter-component interaction, we find that the superfluid and $\mathbb{Z}_2$ phase transitions split. This results in the formation of an intermediate state which breaks only $\mathbb{Z}_2$ symmetry. It represents two phase separated normal fluids with density imbalance.

DOI
10.48550/arxiv.1503.05583

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We consider a two-component immiscible Bose-Einstein condensate with dominating intra-species repulsive density-density interactions. In the ground-state phase of such a system only one condensates is present. This can be viewed as a spontaneous breakdown of Z2\mathbb{Z}_2Z2​ symmetry. We study the phase diagram of the system at finite temperature beyond mean-field approximation. In the absence of rotation, we show that the system undergoes a first order phase transition from this ground state to a miscible two-component normal fluid as temperature is increased. In the presence of rotation, the system features a competition between vortex-vortex interaction and short range density-density interactions. This leads to a rotation-driven "mixing" phase transition in a spatially inhomogeneous state with additional broken U(1)\mathrm{U}(1)U(1) symmetry. Thermal fluctuations in this state lead to nematic two-component sheets of vortex liquids. At sufficiently strong inter-component interaction, we find that the superfluid and Z2\mathbb{Z}_2Z2​ phase transitions split. This results in the formation of an intermediate state which breaks only Z2\mathbb{Z}_2Z2​ symmetry. It represents two phase separated normal fluids with density imbalance.
We consider a two-component interacting bosonic condensate with dominating intra-species repulsive density–density interactions. We study the phase diagram of the system at finite temperature with rotation, using large-scale Monte Carlo simulations of a two-component Ginzburg–Landau model of the system. In the presence of rotation, the system features a competition between long-range vortex–vortex interactions and short-range density–density interactions. This leads to a rotation-driven 'mixing' phase transition in a spatially inhomogeneous state with a broken symmetry. Thermal fluctuations in this state lead to nematic two-component sheets of vortex liquids. At sufficiently strong inter-component interaction, we find that the superfluid and phase transitions split. This results in the formation of an intermediate state which breaks only symmetry. It represents two phase separated normal fluids with a difference in their densities.
Thermal fluctuations and melting transitions for rotating single-component superfluids have been intensively studied and are well understood. In contrast, the thermal effects on vortex states for two-component superfluids with density-density interaction, which have a much richer variety of vortex ground states, have been much less studied. Here, we investigate the thermal effects on vortex matter in superfluids with $\mathrm{U}(1)\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)$ broken symmetries and intercomponent density-density interactions, as well as the case with a larger SU(2)\mathrm{SU}(2)SU(2) broken symmetry obtainable from the $[\mathrm{U}(1)\ifmmode\times\else\texttimes\fi{}\mathrm{U}(1)]$-symmetric case by tuning scattering lengths. In the former case we find that, in addition to first-order melting transitions, the system exhibits thermally driven phase transitions between square and hexagonal lattices. Our main result, however, concerns the case where the condensate exhibits SU(2)\mathrm{SU}(2)SU(2) symmetry, and where vortices are not topological. At finite temperature, the system exhibits effects which do not have a counterpart in single-component systems. Namely, it has a state where thermally averaged quantities show no regular vortex lattice, yet the system retains superfluid coherence along the axis of rotation. In such a state, the thermal fluctuations result in transitions between different (nearly) degenerate vortex states without undergoing a melting transition. Our results apply to multicomponent Bose-Einstein condensates, and we suggest how to detect some of these unusual effects experimentally in such systems.
We investigate vortex states of immiscible two-component Bose-Einstein condensates under rotation through numerical simulations of the coupled Gross-Pitaevskii equations. For strong intercomponent repulsion, the two components undergo phase separation to form several density domains of the same component. In the presence of the rotation, the nucleated vortices are aligned between the domains to make up winding chains of singly quantized vortices, a vortex sheet, instead of periodic vortex lattices. The vortices of one component are located at the region of the density domains of the other component, which results in the serpentine domain structure. The sheet configuration is stable as long as the imbalance of the intracomponent parameter is small. We employ a planar sheet model to estimate the distance between neighboring sheets, determined by the competition between the surface tension of the domain wall and the kinetic energy of the superflow via quantized vortices. By comparing the several length scales in this system, the phase diagram of the vortex state is obtained.
Abstract We present a systematic investigation of symmetries and ground state phase transitions in two-dimensional Bose–Einstein condensates with rotational and spin–orbit couplings confined within one-dimensional optical lattices. For lattice phases φ = π 2 , the vortex arrangement exhibits mirror symmetry about the y-axis, and the density distribution in momentum space maintains mirror symmetry about the k x -axis. For φ = 0, in contrast, the system exhibits spontaneous symmetry breaking, leading to ground state degeneracy. The optical lattice divides the condensate into distinct units. With a fixed spin–orbit coupling strength, the two-component condensates in different units successively undergo immiscible to miscible transitions as the rotational angular frequency increases. For φ = 0, in particular, the unit of condensate located in the center of the external potential consistently remains in the phase separation.
Abstract We revisit the structure of the phase diagram of the two-component mean-field Bose mixture at finite temperatures, considering both the cases of attractive and repulsive interspecies interactions. In particular, we analyze the evolution of the phase diagram upon driving the system towards collapse and point out its distinctive features in this limit. We provide analytical insights into the global structure of the phase diagram and the properties of the phase transitions between the normal phase and the phases involving Bose–Einstein condensates. Inter alia we analytically demonstrate that for sufficiently weak interspecies interactions a 12 the system generically exhibits a line of quadruple points but has no triple nor tricritical points in the phase diagram spanned by the chemical potentials µ 1, µ 2 and temperature T. In contrast, for sufficiently large, positive values of a 12, the system displays both triple and tricritical points but no quadruple points. As pointed out in recent studies, in addition to the phase transitions involving condensation, the mixture may be driven through a liquid–gas type transition, and we clarify the conditions for its occurrence. We finally discuss the impact of interaction- and mass-imbalance on the phase diagram of the mixture.
The miscibility of quantum liquids is an interesting topic in many-body physics, which has been intensively investigated in 3He-4He superfluids and the mixtures of ultracold atoms. In the context of dual species Bose-Einstein condensates, the mean-field description has been well established, according to which, the miscibility condition is density independent and determined only by the ratio of inter- and intra-species interaction strength. Recently, Nadion and Petrov proposed that [ Phys. Rev. Lett. 126 115301 ], in the vicinity of the mixing-demixing threshold, quantum fluctuations play an important role to affect the equilibrium stability, and as a result, the partially miscible state emerges. This new phase of quantum matter opens up new perspectives to explore the beyond mean-field effect in ultracold atomic gases. In this work, according to the equation of state taking the Lee-Huang-Yang correction into consideration, we investigate the ground state phase diagram of repulsive binary Bose mixtures in the interacting regime suffering a weak mean-field instability. Under the thermodynamic balance conditions, the phase boundaries between the immiscible state, partially miscible state and the homogenous state are determined. For the equal-mass case, these phase transitions only take place on condition that intra-species interactions are in an asymmetric form. In terms of interaction parameters, we explicitly derive analytical expressions of the phase boundaries, which are appropriate to describe the transitions in sufficiently dilute atomic gases. At the quantum critical point, where the partially miscible state terminates, the susceptibility tensor of the density response exhibits a divergent behavior. For the unequal-mass case, the beyond-mean-field equation of state cannot be written in a compact form, thus the determination of the phase boundaries is more involved. By expanding the Lee-Huang-Yang energy expression to the terms linear in the concentration of the minority species, we analytically obtain the threshold density for the partially miscible transition. We also propose a discriminant function, from which the configuration of the partially miscible state can be identified for the given mass ratio and interaction strength. Applications of these theoretical results to experimental systems, such as sodium, potassium, and rubidium gases, are presented.