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Bulletin of the American Physical Society

The A-B transition of superfluid $^{\mathrm{3}}$He under confinement

J. M. Parpia, Nikolay Zhelev, T. S. Abhilash, Eric N. Smith, Robert G. Bennett, L. V. Levitin, Xavier Rojas, J. Saunders

Published Mar 16, 2017• 0 citations
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The A-B transition of superfluid 3^{\mathrm{3}}3He under confinement
We investigate the single-site von Neumann entropy along a harmonically confined superfluid chain, as described by the one-dimensional fermionic Hubbard model with strongly attractive interactions. We find that by increasing the confinement (or equivalently the particle filling), the system undergoes a quantum phase transition from a superfluid (SF) to a non-trivial topological insulator (TI) phase, which is characterized by an insulating bulk surrounded by highly entangled superfluid edges. These highly entangled states are found to be robust against perturbations and topologically protected by the particle–hole symmetry, which is locally preserved. We also find a semi-quantitative agreement between entanglement and superconducting order parameter profiles, confirming that entanglement can be used as a topological marker and an order parameter in these systems. The charge gap not only confirms the SF–TI transition but also shows that this transition is mediated by a metallic intermediate regime within the bulk. Using the gap, we could depict a phase diagram for which the non-trivial topological insulator can be found in such harmonically confined attractive systems.
By using a well-established ``ab initio'' theoretical approach developed in the past to quantitatively study the superconductivity of condensed matter systems, based on the Kohn-Sham density functional theory, I study the superfluid properties and the BCS-BEC crossover of two parallel bi-dimensional layers of fermionic dipolar molecules, where the pairing mechanism leading to superfluidity is provided by the interlayer coupling between dipoles. The finite temperature superfluid properties of both the homogeneous system and one where the fermions in each layer are confined by a square optical lattice are studied at half filling conditions, and for different values of the strength of the confining optical potential. The T = 0 results for the homogeneous system are found to be in excellent agreement with diffusion Monte Carlo results. The superfluid transition temperature in the BCS region is found to increase, for a given interlayer coupling, with the strength of the confining optical potential. A transition occurs at sufficiently small interlayer distances, where the fermions becomes localized within the optical lattice sites in a square geometry with an increased effective lattice constant, forming a system of localized composite bosons. This transition should be signaled by a sudden drop in the superfluid fraction of the system.
The critical properties of the phase transition from a normal gas to a BEC (superfluid) of a harmonically confined Bose gas are analyzed using a proposed model for the equation of state of the underlying homogenous Bose fluid. The equation of state is given in terms of the homogenous particle density as a function of the chemical potential and temperature of the gas. On the normal side of the fluid it is assumed to be an ideal Bose gas while in the superfluid state we propose a function that, both, asymptotically reaches the Thomas-Fermi solution of a weakly interacting Bose gas at large densities and low temperatures and, at the transition, matches the critical properties of the ideal Bose gas. With this model we obtain the {\it global} thermodynamics of the harmonically confined gas which shows that, at the critical transition of the confined gas, the thermodynamic susceptibilities, such as the isothermal compressibility, do not diverge, in contrast to the behavior of the uniform gas. The singularity of the critical transition in the confined system appears now at the derivatives of the susceptibilities. We discuss how these properties can be experimentally tested.