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- ItemAccurate projective two-band description of topological superfluidity in spin-orbit-coupled Fermi gases(SciPost Foundation, 2018-08-01) Brand J; Toikka L; Zülicke U
Show more The interplay of spin-orbit coupling and Zeeman splitting in ultracold Fermi gases gives rise to a topological superfluid phase in two spatial dimensions that can host exotic Majorana excitations. Theoretical models have so far been based on a four-band Bogoliubov-de Gennes formalism for the combined spin-1/2 and particle-hole degrees of freedom. Here we present a simpler, yet accurate, two-band description based on a well-controlled projection technique that provides a new platform for exploring analogies with chiral p-wave superfluidity and detailed future studies of spatially non-uniform situations.Show more - ItemAndreev bound states at boundaries of polarized 2D Fermi superfluids with s-wave pairing and spin-orbit coupling(SciPost, 2023-05-16) Thompson K; Brand J; Zuelicke U
Show more A topological superfluid phase characterized by an emergent chiral-p-wave pair potential is expected to form in a two-dimensional Fermi superfluid subject to s-wave pairing, spin-orbit coupling and a large-enough Zeeman splitting. Andreev bound states appear at phase boundaries, including Majorana zero modes whose existence is assured by the bulk-boundary correspondence principle. Here we study the physical properties of these subgap-energy bound states at step-like interfaces using the spin-resolved Bogoliubov–de Gennes mean-field formalism and assuming small spin-orbit coupling. Extending a recently developed spin-projection technique based on Feshbach partitioning [SciPost Phys. 5, 016 (2018)] combined with the Andreev approximation allows us to obtain remarkably simple analytical expressions for the bound-state energies as well as the majority and minority spin components of their wave functions. Besides the vacuum boundary, where a majority-spin Majorana excitation is encountered, we also consider the boundary between the topological and a nontopological superfluid phase that can appear in a coexistence scenario due to the first-order topological phase transition predicted for this system. At this superfluid-superfluid interface, we find a localized chiral Majorana mode hosted by the minority-spin sector. Our theory further predicts majority-spin subgap-energy bound states similar to those found at a Josephson junction between same-chirality p-wave superfluids. Their presence affects the Majorana mode due to a coupling of minority and majority spin sectors only in the small energy range where their spectra overlap. Our results may inform experimental efforts aimed at realizing and characterizing unconventional Majorana quasiparticles.Show more - ItemEliminating the wave-function singularity for ultracold atoms by a similarity transformation(American Physical Society, 2020-11-20) Jeszenszki P; Ebling U; Luo H; Alavi A; Brand J
Show more A hyperbolic singularity in the wave function of δ-wave interacting atoms is the root problem for any accurate numerical simulation. Here, we apply the transcorrelated method, whereby the wave-function singularity is explicitly described by a two-body Jastrow factor, and then folded into the Hamiltonian via a similarity transformation. The resulting nonsingular eigenfunctions are approximated by stochastic Fock-space diagonalization with energy errors scaling with 1/Μ in the number M of single-particle basis functions. The performance of the transcorrelated method is demonstrated on the example of strongly correlated fermions with unitary interactions. The current method provides the most accurate ground-state energies so far for three and four fermions in a rectangular box with periodic boundary conditions.Show more - ItemMagnetic impurity in a one-dimensional few-fermion system(SciPost Foundation, 2023-01-24) Rammelmüller L; Huber D; Čufar M; Brand J; Hammer H-W; Volosniev AG
Show more We present a numerical analysis of spin- ½ fermions in a one-dimensional harmonic potential in the presence of a magnetic point-like impurity at the center of the trap. The model represents a few-body analogue of a magnetic impurity in the vicinity of an swave superconductor. Already for a few particles we find a ground-state level crossing between sectors with different fermion parities. We interpret this crossing as a few-body precursor of a quantum phase transition, which occurs when the impurity “breaks” a Cooper pair. This picture is further corroborated by analyzing density-density correlations in momentum space. Finally, we discuss how the system may be realized with existing cold-atoms platforms.Show more - ItemPolaron-Depleton Transition in the Yrast Excitations of a One-Dimensional Bose Gas with a Mobile Impurity(MDPI (Basel, Switzerland), 2022-03-01) Yang M; Čufar M; Pahl E; Brand J
Show more We present exact numerical data for the lowest-energy momentum eigenstates (yrast states) of a repulsive spin impurity in a one-dimensional Bose gas using full configuration interaction quantum Monte Carlo (FCIQMC). As a stochastic extension of exact diagonalization, it is well suited for the study of yrast states of a lattice-renormalized model for a quantum gas. Yrast states carry valuable information about the dynamic properties of slow-moving mobile impurities immersed in a many-body system. Based on the energies and the first and second-order correlation functions of yrast states, we identify different dynamical regimes and the transitions between them: The polaron regime, where the impurity’s motion is affected by the Bose gas through a renormalized effective mass; a regime of a gray soliton that is weakly correlated with a stationary impurity, and the depleton regime, where the impurity occupies a dark or gray soliton. Extracting the depleton effective mass reveals a super heavy regime where the magnitude of the (negative) depleton mass exceeds the mass of the finite Bose gas.Show more - ItemQuasiparticles of widely tuneable inertial mass: The dispersion relation of atomic Josephson vortices and related solitary waves(SciPost Foundation, 2018-03-01) Shamailov SS; Brand J
Show more Superconducting Josephson vortices have direct analogues in ultracold-atom physics as solitary-wave excitations of two-component superfluid Bose gases with linear coupling. Here we numerically extend the zero-velocity Josephson vortex solutions of the coupled Gross-Pitaevskii equations to non-zero velocities, thus obtaining the full dispersion relation. The inertial mass of the Josephson vortex obtained from the dispersion relation depends on the strength of linear coupling and has a simple pole divergence at a critical value where it changes sign while assuming large absolute values. Additional low-velocity quasiparticles with negative inertial mass emerge at finite momentum that are reminiscent of a dark soliton in one component with counter-flow in the other. In the limit of small linear coupling we compare the Josephson vortex solutions to sine-Gordon solitons and show that the correspondence between them is asymptotic, but significant differences appear at finite values of the coupling constant. Finally, for unequal and non-zero self- and cross-component nonlinearities, we find a new solitary-wave excitation branch. In its presence, both dark solitons and Josephson vortices are dynamically stable while the new excitations are unstable.Show more - ItemSignatures of the BCS-BEC crossover in the yrast spectra of Fermi quantum rings(American Physical Society, 2021-05) Ebling U; Alavi A; Brand J
Show more We study properties of the lowest energy states at nonzero total momentum (yrast states) of the Hubbard model for spin-½ fermions in the quantum ring configuration with attractive on-site interaction at low density. In the one-dimensional (1D) case we solve the Hubbard model using the Bethe ansatz, while for the crossover into the 2D regime we use the Full-Configuration-Interaction Quantum Monte Carlo method to obtain the yrast states for the spin-balanced Fermi system. We show how the yrast excitation spectrum changes from the 1D to the 2D regime and how pairing affects the yrast spectra. We also find signatures of fragmented condensation for certain yrast states usually associated with dark solitons.Show more - ItemTriplet character of 2D-fermion dimers arising from s-wave attraction via spin-orbit coupling and Zeeman splitting(SciPost Foundation, 2022-05-19) Ebling U; Zulicke U; Brand J
Show more We theoretically study spin-1=2 fermions confined to two spatial dimensions and experiencing isotropic short-range attraction in the presence of both spin-orbit coupling and Zeeman spin splitting - a prototypical system for developing topological superfluidity in the many-body sector. Exact solutions for two-particle bound states are found to have a triplet contribution that dominates over the singlet part in an extended region of parameter space where the combined Zeeman- and center-of-mass-motion-induced spin-splitting energy is large. The triplet character of dimers is purest in the regime of weak s-wave interaction strength. Center-of-mass momentum is one of the parameters determining the existence of bound states, which we map out for both two- and onedimensional types of spin-orbit coupling. Distinctive features emerging in the orbital part of the bound-state wave function, including but not limited to its p-wave character, provide observable signatures of unconventional pairing.Show more