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arXiv:0807.0233 · Physical Review B

Hidden vortex lattices in a thermally paired superfluid

E. K. Dahl, Egor S. Babaev, Asle Sudbø

Published Oct 15, 2008• 17 citations
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Abstract

We study the evolution of rotational response of a statistical mechanical model of two-component superfluid with a nondissipative drag interaction as the system undergoes a transition into a paired superfluid phase at finite temperature. The transition manifests itself in a change of (i) vortex-lattice symmetry and (ii) nature of the vortex state. Instead of a vortex lattice, the system forms a highly disordered tangle which constantly undergoes merger and reconnecting processes involving different types of vortices with a ``hidden'' breakdown of translation symmetry.

DOI
10.1103/physrevb.78.144510

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We study the evolution of rotational response of a statistical mechanical model of two-component superfluid with a nondissipative drag interaction as the system undergoes a transition into a paired superfluid phase at finite temperature. The transition manifests itself in a change of (i) vortex-lattice symmetry and (ii) nature of the vortex state. Instead of a vortex lattice, the system forms a highly disordered tangle which constantly undergoes merger and reconnecting processes involving different types of vortices with a ``hidden'' breakdown of translation symmetry.
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 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.
In a single-component superfluid under rotation a broken symmetry in the order parameter space results in a broken translational symmetry in real space: a vortex lattice. If translational symmetry is restored, the phase of the order parameter disorders and thus the broken symmetry in the order parameter space is also restored. We show that for Bose-Einstein condensate mixtures in optical lattices with negative dissipationless drag, a new situation arises. This state is a modulated vortex liquid which breaks translational symmetry in the direction transverse to the rotation vector.
We investigate the dynamics of vortex formation and the structure of vortex lattices in a Bose-Einstein condensate confined within a rotating double-well (DW) potential. The dynamical process is a formation process of ``ghost'' vortices, ``hidden'' vortices, and ``visible'' vortices. The critical rotation frequency for the creation of visible vortex is indicated by a sudden jump in the angular momentum evolution and an inflexion in the energy evolution. Different visible vortex structures can be formed by ruling the rotation frequency. In particular, structural change of visible vortex patterns can be achieved by regulating the anisotropy parameter of the DW potential. This feature allows to flexibly control the distribution of angular momentum in macroscopic quantum systems and study the interplay among rotation, interparticle interaction and external potential in superfluids.
We study a superfluid in a rotating anharmonic trap and explicate a rigorous proof of a transition from a vortex lattice to a giant vortex state as the rotation is increased beyond a limiting speed determined by the interaction strength. The transition is characterized by the disappearance of the vortices from the annulus where the bulk of the superfluid is concentrated due to centrifugal forces while a macroscopic phase circulation remains. The analysis is carried out within two-dimensional Gross-Pitaevskii theory at large coupling constant and reveals significant differences between ``soft'' anharmonic traps (like a quartic plus quadratic trapping potential) and traps with a fixed boundary: in the latter case the transition takes place in a parameter regime where the size of vortices is very small relative to the width of the annulus, whereas in soft traps the vortex lattice persists until the width of the annulus becomes comparable to the vortex cores. Moreover, the density profile in the annulus where the bulk is concentrated is, in the soft case, approximately Gaussian with long tails and not of the Thomas-Fermi type like in a trap with a fixed boundary.
We investigate the structure of vortex states in rotating two-component Bose-Einstein condensates with equal intracomponent but varying intercomponent-coupling constants. A phase diagram in the intercomponent-coupling versus rotation-frequency plane reveals rich equilibrium structures of vortex states. As the ratio of intercomponent to intracomponent couplings increases, the interlocked vortex lattices undergo phase transitions from triangular to square, to double-core lattices, and eventually develop interwoven "serpentine" vortex sheets with each component made up of chains of singly quantized vortices.