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Register a new userQuantum Phases of Attractive Matter Waves in a Toroidal Trap
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Investigating the quantum phase transition in a ring from a uniform attractive Bose-Einstein condensate to a localized bright soliton we find that the soliton undergoes transverse collapse at a critical interaction strength, which depends on the ring dimensions. In addition, we predict the existence of other soliton configurations with many peaks, showing that they have a limited stability domain. Finally, we show that the phase diagram displays several new features when the toroidal trap is set in rotation.
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We investigate the thermodynamic properties of a Bose-Einstein condensate with negative scattering length confined in a toroidal trapping potential. By numerically solving the coupled Gross-Pitaevskii and Bogoliubov-de Gennes equations, we study the phase transition from the uniform state to the symmetry-breaking state characterized by a bright-soliton condensate and a localized thermal cloud. In the localized regime three states with a finite condensate fraction are present: the thermodynamically stable localized state, a metastable localized state and also a metastable uniform state. Remarkably, the presence of the stable localized state strongly increases the critical temperature of Bose-Einstein condensation.
The dynamics of quantum vortices in a two-dimensional annular condensate are considered by numerically simulating the Gross-Pitaevskii equation. Families of solitary wave sequences are reported, both without and with a persistent flow, for various values of interaction strength. It is shown that in the toroidal geometry the dispersion curve of solutions is much richer than in the cases of a semi-infinite channel or uniform condensate studied previously. In particular, the toroidal condensate is found to have states of single vortices at the same position and circulation that move with different velocities. The stability of the solitary wave sequences for the annular condensate without a persistent flow are also investigated by numerically evolving the solutions in time. In addition, the interaction of vortex-vortex pairs and vortex-antivortex pairs is considered and it is demonstrated that the collisions are either elastic or inelastic depending on the magnitude of the angular velocity. The similarities and differences between numerically simulating the Gross-Pitaevskii equation and using a point vortex model for these collisions are elucidated.
We have observed the persistent flow of Bose-condensed atoms in a toroidal trap. The flow persists without decay for up to 10 s, limited only by experimental factors such as drift and trap lifetime. The quantized rotation was initiated by transferring one unit, $hbar$, of the orbital angular momentum from Laguerre-Gaussian photons to each atom. Stable flow was only possible when the trap was multiply-connected, and was observed with a BEC fraction as small as 15%. We also created flow with two units of angular momentum, and observed its splitting into two singly-charged vortices when the trap geometry was changed from multiply- to simply-connected.
The ground state of $^4$He confined in a system with the topology of a cylinder can display properties of a solid, superfluid and liquid crystal. This phase, which we call compactified supersolid (CSS), originates from wrapping the basal planes of the bulk hcp solid into concentric cylindrical shells, with several central shells exhibiting superfluidity along the axial direction. Its main feature is the presence of a topological defect which can be viewed as a disclination with Frank index $n=1$ observed in liquid crystals, and which, in addition, has a superfluid core. The CSS as well as its transition to an insulating compactified solid with a very wide hysteresis loop are found by ab initio Monte Carlo simulations. A simple analytical model captures qualitatively correctly the main property of the CSS -- a gradual decrease of the superfluid response with increasing pressure.
We introduce the concepts of a symmetry-protected sign problem and symmetry-protected magic to study the complexity of symmetry-protected topological (SPT) phases of matter. In particular, we say a state has a symmetry-protected sign problem or symmetry-protected magic, if finite-depth quantum circuits composed of symmetric gates are unable to transform the state into a non-negative real wave function or stabilizer state, respectively. We prove that states belonging to certain SPT phases have these properties, as a result of their anomalous symmetry action at a boundary. For example, we find that one-dimensional $mathbb{Z}_2 times mathbb{Z}_2$ SPT states (e.g. cluster state) have a symmetry-protected sign problem, and two-dimensional $mathbb{Z}_2$ SPT states (e.g. Levin-Gu state) have both a symmetry-protected sign problem and symmetry-protected magic. We also comment on the relation of a symmetry-protected sign problem to the computational wire property of one-dimensional SPT states and speculate about the greater implications of our results for measurement-based quantum computing.
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