arXiv subjects

Joachim Brand

Publications and source records attributed to Joachim Brand.

At least 37 records · Page 2Linked to original sources

arXiv2019

Are smooth pseudopotentials a good choice for representing short-range interactions?

When seeking a numerical representation of a quantum-mechanical multiparticle problem it is tempting to replace a singular short-range interaction by a smooth finite-range pseudopotential. Finite basis set expansions, e.g.~in Fock space, are then guaranteed to converge exponentially. The need to faithfully represent the artificial length scale of the pseudopotential, however, places a costly burden on the basis set. Here we discuss scaling relations for the required size of the basis set and demonstrate the basis set convergence on the example of a two-dimensional system of few fermions with short-range $s$-wave interactions in a harmonic trapping potential. In particular we show that the number of harmonic-oscillator basis functions needed to reach a regime of exponential convergence for a Gaussian pseudopotential scales with the fourth power of the pseudopotential length scale, which can be improved to quadratic scaling when the basis functions are re-scaled appropriately. Numerical examples for three fermions with up to a few hundred single-particle basis functions are presented and implications for the feasibility of accurate numerical multi-particle simulations of interacting ultra-cold atom systems are discussed.

cond-mat.quant-gas↗

arXiv2018

Accelerating the convergence of exact diagonalization with the transcorrelated method: Quantum gas in one dimension with contact interactions

Exact diagonalization expansions of Bose or Fermi gases with contact interactions converge very slowly due to a non-analytic cusp in the wave function. Here we develop a transcorrelated approach where the cusp is treated exactly and folded into the many-body Hamiltonian with a similarity transformation that removes the leading order singularity. The resulting transcorrelated Hamiltonian is not hermitian but can be treated numerically with a standard projection approach. The smoothness of the wave function improves by at least one order and thus the convergence rate for the ground state energy improves. By numerical investigation of a one-dimensional gas of spin-$\frac{1}{2}$ fermions we find the error in the transcorrelated energy to scale as $M^{-3}$ with a single-particle basis of $M$ plane waves compared to $M^{-1}$ for the expansion of the original Hamiltonian and $M^{-2}$ using conventional lattice renormalization.

cond-mat.quant-gas↗

arXiv2018

Nonlinear standing waves in an array of coherently coupled Bose-Einstein condensates

Stationary solitary waves are studied in an array of $M$ linearly-coupled one-dimensional Bose-Einstein condensates (BECs) by means of the Gross-Pitaevskii equation. Solitary wave solutions with the character of overlapping dark solitons, Josephson vortex - antivortex arrays, and arrays of half-dark solitons are constructed for $M>2$ from known solutions for two coupled BECs. Additional solutions resembling vortex dipoles and rarefaction pulses are found numerically. Stability analysis of the solitary waves reveals that overlapping dark solitons can become unstable and susceptible to decay into arrays of Josephson vortices. The Josephson vortex arrays have mixed stability but for all parameters we find at least one stationary solitary wave configuration that is dynamically stable. The different families of nonlinear standing waves bifurcate from one another. In particular we demonstrate that Josephson-vortex arrays bifurcate from dark soliton solutions at instability thresholds. The stability thresholds for dark soliton and Josephson-vortex type solutions are provided, suggesting the feasibility of realization with optical lattice experiments.

cond-mat.quant-gas↗

arXiv2018

The $s$-wave scattering length of a Gaussian potential

We provide accurate expressions for the $s$-wave scattering length for a Gaussian potential well in one, two and three spatial dimensions. The Gaussian potential is widely used as a pseudopotential in the theoretical description of ultracold atomic gases, where the $s$-wave scattering length is a physically relevant parameter. We first describe a numerical procedure to compute the value of the $s$-wave scattering length from the parameters of the Gaussian but find that its accuracy is limited in the vicinity of singularities that result from the formation of new bound states. We then derive simple analytical expressions that capture the correct asymptotic behavior of the $s$-wave scattering length near the bound states. Expressions that are increasingly accurate in wide parameter regimes are found by a hierarchy of approximations that capture an increasing number of bound states. The small number of numerical coefficients that enter these expressions is determined from accurate numerical calculations. The approximate formulas combine the advantages of the numerical and approximate expressions, yielding an accurate and simple description from the weakly to the strongly interacting limit.

quant-ph↗

arXiv2018

Quasiparticles of widely tuneable inertial mass: The dispersion relation of atomic Josephson vortices and related solitary waves

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.

cond-mat.quant-gas↗

arXiv2017

Landau instability and mobility edges of the interacting one-dimensional Bose gas in weak random potentials

We study the frictional force exerted on the trapped, interacting 1D Bose gas under the influence of a moving random potential. Specifically we consider weak potentials generated by optical speckle patterns with finite correlation length. We show that repulsive interactions between bosons lead to a superfluid response and suppression of frictional force, which can inhibit the onset of Anderson localisation. We perform a quantitative analysis of the Landau instability based on the dynamic structure factor of the integrable Lieb-Liniger model and demonstrate the existence of effective mobility edges.

cond-mat.quant-gas↗

arXiv2017

Dark-soliton-like excitations in the Yang-Gaudin gas of attractively interacting fermions

Yrast states are the lowest energy states at given non-zero momentum and provide a natural extension of the concept of dark solitons to strongly-interacting one-dimensional quantum gases. Here we study the yrast states of the balanced spin-$\frac{1}{2}$ Fermi gas with attractive delta-function interactions in one dimension with the exactly solvable Yang-Gaudin model. The corresponding Bethe-ansatz equations are solved for finite particle number and in the thermodynamic limit. Properties corresponding to the soliton-like nature of the yrast excitations are calculated including the missing particle number, phase step, and inertial and physical masses. The inertial to physical mass ratio, which is related to the frequency of oscillations in a trapped gas, is found to be unity in the limits of strong and weak attraction and falls to $\approx 0.78$ in the crossover regime. This result is contrasted by one-dimensional mean field theory, which predicts a divergent mass ratio in the weakly attractive limit. By means of an exact mapping our results also predict the existence and properties of dark-soliton-like excitations in the super Tonks-Girardeau gas. The prospects for experimental observations are briefly discussed.

cond-mat.quant-gas↗

arXiv2017

Interaction blockade for bosons in an asymmetric double well

The interaction blockade phenomenon isolates the motion of a single quantum particle within a multi-particle system, in particular for coherent oscillations in and out of a region affected by the blockade mechanism. For identical quantum particles with Bose statistics, the presence of the other particles is still felt by a bosonic stimulation factor $\sqrt{N}$ that speeds up the coherent oscillations, where $N$ is the number of bosons. Here we propose an experiment to observe this enhancement factor with a small number of bosonic atoms. The proposed protocol realises an asymmetric double well potential with multiple optical tweezer laser beams. The ability to adjust bias independently of the coherent coupling between the wells allows the potential to be loaded with different particle numbers while maintaining the resonance condition needed for coherent oscillations. Numerical simulations with up to three bosons in a realistic potential generated by three optical tweezers predict that the relevant avoided level crossing can be probed and the expected bosonic enhancement factor observed.

cond-mat.quant-gas↗

arXiv2017

Hidden long-range order in a spin-orbit coupled two-dimensional Bose gas

A spin-orbit coupled two-dimensional (2D) Bose gas is shown to simultaneously possess quasi and true long-range order in the total and relative phase sectors, respectively. The total phase undergoes a Berenzinskii- Kosterlitz-Thouless transition to a low temperature phase with quasi long-range order, as expected for a two- dimensional quantum gas. Additionally, the relative phase undergoes an Ising-type transition building up true long-range order, which is induced by the anisotropic spin-orbit coupling. Based on the Bogoliubov approach, expressions for the total- and relative-phase fluctuations are derived analytically for the low temperature regime. Numerical simulations of the stochastic projected Gross-Pitaevskii equation (SPGPE) give a good agreement with the analytical predictions.

cond-mat.quant-gas↗

arXiv2016

The universe on a table top: engineering quantum decay of a relativistic scalar field from a metastable vacuum

The quantum decay of a relativistic scalar field from a metastable state ("false vacuum decay") is a fundamental idea in quantum field theory and cosmology. This occurs via local formation of bubbles of true vacuum with their subsequent rapid expansion. It can be considered as a relativistic analog of a first-order phase transition in condensed matter. Here we expand upon our recent proposal [EPL 110, 56001 (2015)] for an experimental test of false vacuum decay using an ultra-cold spinor Bose gas. A false vacuum for the relative phase of two spin components, serving as the unstable scalar field, is generated by means of a modulated linear coupling of the spin components. We analyze the system theoretically using the functional integral approach and show that various microscopic degrees of freedom in the system, albeit leading to dissipation in the relative phase sector, will not hamper the observation of the false vacuum decay in the laboratory. This is well supported by numerical simulations demonstrating the spontaneous formation of true vacuum bubbles on millisecond time-scales in two-component $^{7}$Li or $^{41}$K bosonic condensates in one-dimensional traps of $\sim100\,μ\mathrm{m}$ size.

cond-mat.quant-gas↗

arXiv2016

Comment on: `Single-shot simulations of dynamic quantum many-body systems' [arXiv:1501.03224]

In their recent paper [Nature Physics 15, 451 (2006)], Sakmann and Kasevich study the formation of fringe patterns in ultra-cold Bose gases and claim: `Here, we show how single shots can be simulated from numerical solutions of the time-dependent many-body Schrödinger equation.' It would be remarkable if they had solved this exponentially complex equation. Instead they solve nonlinear equations with the aim to approximate the solution of the Schrödinger equation. The authors proceed to criticize phase-space approaches to simulating quantum dynamics and claim the impossibility of interpreting single trajectories of the truncated Wigner (tW) method as single-shot experimental outcomes. Here we aim to provide relevant context and elaborate why we disagree with the authors' claims.

cond-mat.quant-gas↗

arXiv2016

Center-of-mass motion as a sensitive convergence test for variational multi-mode quantum dynamics

Multi-mode expansions in computational quantum dynamics promise convergence toward exact results upon increasing the number of modes. Convergence is difficult to ascertain in practice due to the unfavourable scaling of required resources for many-particle problems and therefore a simplified criterion based on a threshold value for the least occupied mode function is often used. Here we show how the separable quantum motion of the center of mass can be used to sensitively detect unconverged numerical multi-particle dynamics in harmonic potentials. Based on an experimentally relevant example of attractively interacting bosons in one dimension, we demonstrate that the simplified convergence criterion fails to assure qualitatively correct results. Furthermore, the numerical evidence for the creation of two-hump fragmented bright soliton-like states presented by Streltsov \emph{et al.} [PRL 100, 130401 (2008)] is shown to be inconsistent with exact results. Implications for our understanding of dynamical fragmentation in attractive boson systems are briefly discussed.

quant-ph↗

arXiv2015

Motion of an Impurity in a Bose-Einstein Condensate with Weyl Spin-Orbit Coupling: Non-collinear Drag Force and Anisotropic Critical Velocity

We consider the motion of a point-like impurity through a three-dimensional two-component Bose-Einstein condensate subject to Weyl spin-orbit coupling. Using linear-response theory, we calculate the drag force felt by the impurity and the associated anisotropic critical velocity from the spectrum of elementary excitations. The drag force is shown to be generally not collinear with the velocity of the impurity. This unusual behavior is a consequence of condensation into a finite-momentum state due to the spin-orbit coupling.

cond-mat.quant-gas↗

arXiv2015

Stability and dispersion relations of three-dimensional solitary waves in trapped Bose-Einstein condensates

We analyse the dynamical properties of three-dimensional solitary waves in cylindrically trapped Bose-Einstein condensates. Families of solitary waves bifurcate from the planar dark soliton and include the solitonic vortex, the vortex ring and more complex structures of intersecting vortex-line known collectively as Chladni solitons. The particle-like dynamics of these guided solitary waves provides potentially profitable features for their implementation in atomtronic circuits, and play a key role in the generation of metastable loop currents. Based on the time-dependent Gross-Pitaevskii equation we calculate the dispersion relations of moving solitary waves and their modes of dynamical instability. The dispersion relations reveal a complex crossing and bifurcation scenario. For stationary structures we find that for $μ/\hbarω_\perp > 2.65$ the solitonic vortex is the only stable solitary wave. More complex Chladni solitons still have weaker instabilities than planar dark solitons and may be seen as transient structures in experiments. Fully time-dependent simulations illustrate typical decay scenarios, which may result in the generation of multiple separated solitonic vortices.

cond-mat.quant-gas↗

arXiv2015

Traveling Majorana solitons in a one-dimensional spin-orbit coupled Fermi superfluid

We investigate traveling solitons of a one-dimensional spin-orbit coupled Fermi superfluid in both topologically trivial and non-trivial regimes by solving the static and time-dependent Bogoliubov-de Gennes equations. We find a critical velocity $v_{h}$ for traveling solitons that is much smaller than the value predicted using the Landau criterion due to the presence of spin-orbit coupling, which strongly upshifts the energy level of the soliton-induced Andreev bound states towards the quasi-particle scattering continuum. Above $v_{h}$, our time-dependent simulations in harmonic traps indicate that traveling solitons decay by radiating sound waves. In the topological phase, we predict the existence of peculiar Majorana solitons, which host two Majorana fermions and feature a phase jump of $π$ across the soliton, irrespective of the velocity of travel. These unusual properties of Majorana solitons may open an alternative way to manipulate Majorana fermions for fault-tolerant topological quantum computations.

cond-mat.quant-gas↗

arXiv2015

Multicriticality, Metastability, and Roton Feature in Bose-Einstein Condensates with Three-Dimensional Spin-Orbit Coupling

We theoretically study homogeneously trapped atomic Bose-Einstein condensates where all three momentum components couple to a pseudo-spin-$1/2$ degree of freedom. Tuning the anisotropies of spin-orbit coupling and the spin-dependent interactions is shown to provide access to a rich phase diagram with a tetracritical point, first-order phase transitions, and multiple metastable phases of stripe and plane-wave character. The elementary excitation spectrum of the axial plane-wave phase features an anisotropic roton feature and can be used to probe the phase diagram. In addition to providing a versatile laboratory for studying fundamental concepts in statistical physics, the emergence of metastable phases creates new opportunities for observing false-vacuum decay and bubble nucleation in ultra-cold-atom experiments.

cond-mat.quant-gas↗

arXiv2015

Oscillons in coupled Bose-Einstein condensates

Long-lived, spatially localized, and temporally oscillating nonlinear excitations are predicted by numerical simulation of coupled Gross-Pitaevskii equations. These oscillons closely resemble the time-periodic breather solutions of the sine-Gordon equation but decay slowly by radiating Bogoliubov phonons. Their time-dependent profile is closely matched with solutions of the sine-Gordon equation, which emerges as an effective field theory for the relative phase of two linearly coupled Bose fields in the weak-coupling limit. For strong coupling the long-lived oscillons persist and involve both relative and total phase fields. The oscillons decay via Bogoliubov phonon radiation that is increasingly suppressed for decreasing oscillon amplitude. Possibilities for creating oscillons are addressed in atomic gas experiments by collision of oppositely charged Bose-Josephson vortices and direct phase imprinting.

cond-mat.quant-gas↗

arXiv2013

Quantum simulations of the early universe

A procedure is described whereby a linearly coupled spinor Bose condensate can be used as a physically accessible quantum simulator of the early universe. In particular, an experiment to generate an analog of an unstable vacuum in a relativistic scalar field theory is proposed. This is related to quantum theories of the inflationary phase of the early universe. There is an unstable vacuum sector whose dynamics correspond to the quantum sine-Gordon equations in one, two or three space dimensions. Numerical simulations of the expected behavior are reported using a truncated Wigner phase-space method, giving evidence for the dynamical formation of complex spatial clusters. Preliminary results showing the dependence on coupling strength, condensate size and dimensionality are obtained.

cond-mat.quant-gas↗