Carlos Sa de Melo

Stability of Superfluid and Supersolid Phases of Dipolar Bosons in Optical Lattices

We perform a stability analysis of superfluid (SF) and supersolid (SS) phases of polarized dipolar bosons in two-dimensional optical lattices at high filling factors and zero temperature, and obtain the phase boundaries between SF, checkerboard SS (CSS), striped SS (SSS), and collapse. We show that the phase diagram can be explored through the application of an external field and the tuning of its direction with respect to the optical lattice plane. In particular, we find a transition between the CSS and SSS phases.

Dipolar bosons in triangular optical lattices: Quantum phase transitions and anomalous hysteresis

We study phase transitions and hysteresis in a system of dipolar bosons loaded into triangular optical lattices at zero temperature. We find that the quantum melting transition from supersolid to superfluid phase is first-order, in contrast with the previous report. We also find that due to strong quantum fluctuations the supersolid (or solid)-superfluid transition can exhibit an anomalous hysteretic behavior, in which the curve of density versus chemical potential does not form a standard loop structure. Furthermore, we show that the transition occurs unidirectionally along the anomalous hysteresis curve.

Effects of Spin-Orbit Coupling on the Berezinskii-Kosterlitz-Thouless Transition and the Vortex-Antivortex Structure in Two-Dimensional Fermi Gases

We investigate the Berezinskii-Kosterlitz-Thouless (BKT) transition in a 2D Fermi gas with spin-orbit coupling (SOC), as a function of the two-body binding energy and a perpendicular Zeeman field. By including a generic form of the SOC, as a function of Rashba and Dresselhaus terms, we study the evolution between the experimentally relevant equal Rashba-Dresselhaus (ERD) case and the Rashba-only (RO) case. We show that in the ERD case, at a fixed nonzero Zeeman field, the BKT transition temperature T(BKT) is increased by the presence of SOC for all values of the binding energy. We also find a significant increase in the value of the Clogston limit compared to the case without SOC. Furthermore, we demonstrate that the superfluid density tensor becomes anisotropic (except in the RO case), leading to an anisotropic phase-fluctuation action that describes elliptic vortices and antivortices, which become circular in the RO limit. This deformation constitutes an important experimental signature for superfluidity in a 2D Fermi gas with ERD SOC. Finally, we show that the anisotropic sound velocities exhibit anomalies at low temperatures, in the vicinity of quantum phase transitions between topologically distinct uniform superfluid phases.

First-order phase transition and anomalous hysteresis of Bose gases in optical lattices

We study the first-order quantum phase transitions of Bose gases in optical lattices. A special emphasis is placed on an anomalous hysteresis behavior, in which the phase transition occurs in a unidirectional way and a hysteresis loop does not form. We first revisit the hardcore Bose-Hubbard model with dipole-dipole interactions on a triangular lattice to analyze accurately the ground-state phase diagram and the hysteresis using the cluster mean-field theory combined with cluster-size scaling. Details of the anomalous hysteresis are presented. We next consider the two-component and spin-1 Bose-Hubbard models on a hypercubic lattice and show that the anomalous hysteresis can emerge in these systems as well. In particular, for the former model, we discuss the experimental feasibility of the first-order transitions and the associated hysteresis. We also explain an underlying mechanism of the anomalous hysteresis by means of the Ginzburg-Landau theory. From the given cases, we conclude that the anomalous hysteresis is a ubiquitous phenomenon of systems with a phase region of lobe shape that is surrounded by the first-order boundary.

Triplet versus singlet superconductivity in quasi-one-dimensional conductors

Quasi-one-dimensional organic conductors are highly unconventional materials, which exhibit a wide variety of phenomena, including spin density waves, quantum Hall effect, and superconductivity. In this paper, we review some experimental and theoretical developments concerning the superconducting state of these systems, where a particular emphasis is placed on the possibility of triplet superconductivity. This possibility is supported by various experiments including upper critical field, Knight shift and NMR relaxation time measurements on the Bechgaard salt bistetramethyltetraselenafulvalene hexafluorophosphate [(TMTSF)2PF6]. However, similar NMR results are still lacking for another compound (TMTSF)2ClO4 and other members of the Bechgaard salts family. Furthermore, the pairing mechanism and order parameter symmetry are not yet fully known. Therefore, we include a discussion of both triplet and singlet pairing states, and analyse briefly the possibility that the symmetries of the superconducting order parameters are different for various compounds. Finally, we also discuss some open questions regarding the superconducting state of these systems.

Atomic physics: Atoms playing dress-up

The idea of using ultracold atoms to simulate the behaviour of electrons in new kinds of quantum systems — from topological insulators to exotic superfluids and superconductors — is a step closer to becoming a reality. See Letter p.83 Spin-orbit coupling describes the interaction between a quantum particles spin and its momentum, and is important for many areas of physics from spintronics to the quantum spin Hall effect and topological insulators. However, in systems of ultracold neutral atoms, there is no coupling between the spin and the centre-of-mass motion of the atom. Lin et al. use lasers to engineer such spin-orbit coupling in a neutral atomic Bose–Einstein condensate, the first time this has been achieved for any bosonic system. This should lead to the realization of topological insulators in fermionic neutral atom systems.

Quantum phase transitions and Berezinskii-Kosterlitz-Thouless temperature in a two-dimensional spin-orbit-coupled Fermi gas

We study the effect of spin-orbit coupling on both the zero-temperature and non-zero temperature behavior of a two-dimensional (2D) Fermi gas. We include a generic combination of Rashba and Dresselhaus terms into the system Hamiltonian, which allows us to study both the experimentally relevant equal-Rashba-Dresselhaus (ERD) limit and the Rashba-only (RO) limit. At zero temperature, we derive the phase diagram as a function of the two-body binding energy and Zeeman field. In the ERD case, this phase diagram reveals several topologically distinct uniform superfluid phases, classified according to the nodal structure of the quasiparticle excitation energies. Furthermore, we use a momentum dependent SU(2)-rotation to transform the system into a generalized helicity basis, revealing that spin-orbit coupling induces a triplet pairing component of the order parameter. At non-zero temperature, we study the Berezinskii-Kosterlitz-Thouless (BKT) phase transition by including phase fluctuations of the order parameter up to second order. We show that the superfluid density becomes anisotropic due to the presence of spin-orbit coupling (except in the RO case). This leads both to elliptic vortices and antivortices, and to anisotropic sound velocities. The latter prove to be sensitive to quantum phase transitions between topologically distinct phases. We show further that at a fixed non-zero Zeeman field, the BKT critical temperature is increased by the presence of ERD spin-orbit coupling. Subsequently, we demonstrate that the Clogston limit becomes infinite:

Exchange interactions in the Hubbard-Stratonovich transformation for the stability analysis of itinerant ferromagnetism

T_{\rm{BKT}}

Reentrant quantum phase transition in double-well optical lattices

remains non-zero at all finite values of the Zeeman field. We conclude by extending the quantum phase transition lines to non-zero temperature, using the nodal structure of the quasiparticle spectrum, thus connecting the BKT critical temperature with the zero-temperature results.

Disorder effects in the evolution from BCS to BEC superfluidity

Itinerant ferromagnetism, i.e. spontaneous polarization of non-localized particles, is expected to occur for strong repulsive interactions in a spin-1/2 Fermi system. However, this state has proven notoriously hard to find experimentally, both in ultracold gases and in solids. This raises questions about the stability of the itinerant ferromagnetic state itself. Here we develop a new approach to describe both the direct and exchange interactions for a general interaction potential in the path-integral formalism and we apply this method to itinerant ferromagnetism in three-dimensional ultracold Fermi gases. We show that the exchange interactions are lost in the Hubbard-Stratonovich transformation and we propose to explicitly include the exchange effects in a new modified interaction potential. In the saddle-point approximation, the effect of interactions can be taken into account using only three parameters. If the interactions become too strong, all saddle points become unstable to density fluctuations. This greatly restricts the area in the phase diagram where uniform itinerant ferromagnetism is expected to occur.