arXiv subjects

J. Stockhofe

Publications and source records attributed to J. Stockhofe.

At least 19 recordsLinked to original sources

arXiv2017

Electrostatic bending response of a charged helix

We explore the electrostatic bending response of a chain of charged particles confined on a finite helical filament. We analyze how the energy difference $ΔE$ between the bent and the unbent helical chain scales with the length of the helical segment and the radius of curvature and identify features that are not captured by the standard notion of the bending rigidity, normally used as a measure of bending tendency in the linear response regime. Using instead $ΔE$ to characterize the bending response of the helical chain we identify two regimes with qualitatively different bending behaviors for the ground state configuration: the regime of small and the regime of large radius-to-pitch ratio, respectively. Within the former regime, $ΔE$ changes smoothly with the variation of the system parameters. Of particular interest are its oscillations with the number of charged particles encountered for commensurate fillings which yield length-dependent oscillations in the preferred bending direction of the helical chain. We show that the origin of these oscillations is the non-uniformity of the charge distribution caused by the long-range character of the Coulomb interactions and the finite length of the helix. In the second regime of large values of the radius-to-pitch ratio, sudden changes in the ground state structure of the charges occur as the system parameters vary, leading to complex and discontinuous variations in the ground state bending response $ΔE$.

cond-mat.soft↗

arXiv2017

Stability and dynamics of dark-bright soliton bound states away from the integrable limit

The existence, stability, and dynamics of bound pairs of symbiotic matter waves in the form of dark-bright soliton pairs in two-component mixtures of atomic Bose-Einstein condensates is investigated. Motivated by the tunability of the atomic interactions in recent experiments, we explore in detail the impact that changes in the interaction strengths have on these bound pairs by considering significant deviations from the Manakov (integrable) limit. It is found that dark-bright soliton pairs exist as stable configurations in a wide parametric window spanning both the miscible and the immiscible regime of interactions. Outside this parameter interval two unstable regions are identified and are associated with a supercritical and a subcritical pitchfork bifurcation, respectively. Dynamical manifestation of these instabilities gives rise to a redistribution of the bright density between the dark solitons, and also to symmetry-broken stationary states that are mass imbalanced (asymmetric) with respect to their bright soliton counterpart. The long-time dynamics of both the stable and the unstable balanced and imbalanced dark-bright soliton pairs is analyzed.

cond-mat.quant-gas↗

arXiv2016

Dark-bright soliton interactions beyond the integrable limit

In this work we present a systematic theoretical analysis regarding dark-bright solitons and their interactions, motivated by recent advances in atomic two-component repulsively interacting Bose-Einstein condensates. In particular, we study analytically via a two-soliton ansatz adopted within a variational formulation the interaction between two dark-bright solitons in a homogeneous environment beyond the integrable regime, by considering general inter/intra-atomic interaction coefficients. We retrieve the possibility of a fixed point in the case where the bright solitons are out of phase. As the inter-component interaction is increased, we also identify an exponential instability of the two-soliton state, associated with a subcritical pitchfork bifurcation. The latter gives rise to an asymmetric partition of the bright soliton mass and dynamically leads to spontaneous splitting of the bound pair. In the case of the in-phase bright solitons, we explain via parsing the analytical approximations and monitoring the direct dynamics why no such pair is identified, despite its prediction by the variational analysis.

cond-mat.quant-gas↗

arXiv2016

Pinned-to-sliding transition and structural crossovers for helically confined charges

We explore the non-equilibrium dissipative dynamics of a system of identical charged particles trapped on a closed helix. The particles are subject to an external force accelerating them along the underlying structure. The effective interactions between the charges induce a coupling of the center-of-mass to the relative motion which in turn gives rise to a pinned-to-sliding transition with increasing magnitude of the external force. In the sliding regime we observe an Ohmic behaviour signified by a constant mobility. Within the same regime a structural transition of the helical particle chain takes place with increasing the helix radius leading to a global change of the crystalline arrangement. The resulting crystal is characterized by the existence of multiple defects whose number increases with the helix radius.

cond-mat.soft↗

arXiv2016

Local equilibria and state transfer of charged classical particles on a helix in an electric field

We explore the effects of a homogeneous external electric field on the static properties and dynamical behavior of two charged particles confined to a helix. In contrast to the field-free setup which provides a separation of the center-of-mass and relative motion, the existence of an external force perpendicular to the helix axis couples the center-of-mass to the relative degree of freedom leading to equilibria with a localized center of mass. By tuning the external field various fixed points are created and/or annihilated through different bifurcation scenarios. We provide a detailed analysis of these bifurcations based on which we demonstrate a robust state transfer between essentially arbitrary equilibrium configurations of the two charges that can be induced by making the external force time-dependent.

physics.class-ph↗

arXiv2016

Modulational instability and localized breather modes in the discrete nonlinear Schrödinger equation with helicoidal hopping

We study a one-dimensional discrete nonlinear Schrödinger model with hopping to the first and a selected N-th neighbor, motivated by a helicoidal arrangement of lattice sites. We provide a detailed analysis of the modulational instability properties of this equation, identifying distinctive multi-stage instability cascades due to the helicoidal hopping term. Bistability is a characteristic feature of the intrinsically localized breather modes, and it is shown that information on the stability properties of weakly localized solutions can be inferred from the plane-wave modulational instability results. Based on this argument, we derive analytical estimates of the critical parameters at which the fundamental on-site breather branch of solutions turns unstable. In the limit of large N, these estimates predict the emergence of an effective threshold behavior, which can be viewed as the result of a dimensional crossover to a two-dimensional square lattice.

cond-mat.quant-gas↗

arXiv2015

Generating, dragging and releasing dark solitons in elongated Bose-Einstein condensates

We theoretically analyze quasi-one-dimensional Bose-Einstein condensates under the influence of a harmonic trap and a narrow potential defect that moves through the atomic cloud. Performing simulations on the mean field level, we explore a robust mechanism in which a single dark soliton is nucleated and immediately pinned by the moving defect, making it possible to drag it to a desired position and release it there. We argue on a perturbative level that a defect potential which is attractive to the atoms is suitable for holding and moving dark solitons. The soliton generation protocol is investigated over a wide range of model parameters and its success is systematically quantified by a suitable fidelity measure, demonstrating its robustness against parameter variations, but also the need for tight focusing of the defect potential. Holding the soliton at a stationary defect for long times may give rise to dynamical instabilities, whose origin we explore within a Bogoliubov-de Gennes linearization analysis. We show that iterating the generation process with multiple defects offers a perspective for initializing multiple soliton dynamics with freely chosen initial conditions.

cond-mat.quant-gas↗

arXiv2015

Dynamics of nonlinear excitations of helically confined charges

We explore the long-time dynamics of a system of identical charged particles trapped on a closed helix. This system has recently been found to exhibit an unconventional deformation of the linear spectrum when tuning the helix radius. Here we show that the same geometrical parameter can affect significantly also the dynamical behaviour of an initially broad excitation for long times. In particular, for small values of the radius, the excitation disperses into the whole crystal whereas within a specific narrow regime of larger radii the excitation self-focuses, assuming finally a localized form. Beyond this regime, the excitation defocuses and the dispersion gradually increases again. We analyze this geometrically controlled nonlinear behaviour using an effective discrete nonlinear Schrödinger model, which allows us among others to identify a number of breather-like excitations.

physics.class-ph↗

arXiv2015

Sub- and supercritical defect scattering in Schrödinger chains with higher-order hopping

We theoretically analyze a discrete Schrödinger chain with hopping to the first and second neighbors, as can be realized with zigzag arrangements of optical waveguides or lattice sites for cold atoms. Already at moderate values, the second-neighbor hopping has a strong impact on the band structure, leading to the emergence of a new extremum located inside the band, accompanied by a van Hove singularity in the density of states. The energy band is then divided into a subcritical regime with the usual unique correspondence between wave number and energy of the travelling waves, and a supercritical regime, in which waves of different wave number are degenerate in energy. We study the consequences of these features in a scattering setup, introducing a defect that locally breaks the translational invariance. The notion of a local probability current is generalized beyond the nearest-neighbor approximation and bound states with energies outside the band are discussed. At subcritical energies inside the band, an evanescent mode coexists with the travelling plane wave, giving rise to resonance phenomena in scattering. At weak coupling to the defect, we identify a prototypical Fano-Feshbach resonance of tunable shape and provide analytical expressions for its profile parameters. At supercritical energies, we observe coupling of the degenerate travelling waves, leading to an intricate wave packet fragmentation dynamics. The corresponding branching ratios are analyzed.

cond-mat.quant-gas↗

arXiv2015

Positive and negative mass solitons in spin-orbit coupled Bose-Einstein condensates

We present a unified description of different types of matter-wave solitons that can emerge in quasi one-dimensional spin-orbit coupled (SOC) Bose-Einstein condensates (BECs). This description relies on the reduction of the original two-component Gross-Pitaevskii SOC-BEC model to a single nonlinear Schrödinger equation, via a multiscale expansion method. This way, we find approximate bright and dark soliton solutions, for attractive and repulsive interatomic interactions respectively, for different regimes of the SOC interactions. Beyond this, our approach also reveals "negative mass" regimes, where corresponding "negative mass" bright or dark solitons can exist for repulsive or attractive interactions, respectively. Such a unique opportunity stems from the structure of the excitation spectrum of the SOC-BEC. Numerical results are found to be in excellent agreement with our analytical predictions.

cond-mat.quant-gas↗

arXiv2014

Stability and Tunneling Dynamics of a Dark-Bright Soliton Pair in a Harmonic Trap

We consider a binary repulsive Bose-Einstein condensate in a harmonic trap in one spatial dimension and investigate particular solutions consisting of two dark-bright (DB) solitons. There are two different stationary solutions characterized by the phase difference in the bright component, in-phase and out-of-phase states. We show that above a critical particle number in the bright component, a symmetry breaking bifurcation of the pitchfork type occurs that leads to a new asymmetric solution whereas the parental branch, i.e., the out-of-phase state becomes unstable. These three different states support different small amplitude oscillations, characterized by an almost stationary density of the dark component and a tunneling of the bright component between the two dark solitons. Within a suitable effective double-well picture, these can be understood as the characteristic features of a Bosonic Josephson Junction (BJJ), and we show within a two-mode approach that all characteristic features of the BJJ phase space are recovered. For larger deviations from the stationary states, the simplifying double-well description breaks down due to the feedback of the bright component onto the dark one, causing the solitons to move. In this regime we observe intricate anharmonic and aperiodic dynamics, exhibiting remnants of the BJJ phase space.

cond-mat.quant-gas↗

arXiv2014

Bloch dynamics in lattices with long range hoppings

We study a discrete Schrödinger equation with arbitrary long range hopping terms under the influence of an external force. The impact of long range hoppings on the single particle Bloch dynamics in the lattice is investigated. A closed expression for the propagator is given, based on which we analyze the dynamics of initially Gaussian wave packets. Our findings capture the anharmonic oscillations recently observed in zigzag lattices and furthermore provide a detailed quantitative description of the crossover between center of mass Bloch oscillations for wide wave packets and left-right symmetric width oscillations for narrow single site excitations. The analytical results are shown to be in agreement with numerical simulations. A helix lattice setup for ultracold atoms is proposed where such hopping terms to far neighbors can be experimentally tuned to sizable values.

cond-mat.quant-gas↗

arXiv2014

Degeneracy and Inversion of Band Structure for Wigner Crystals on a Toroidal Helix

We explore the formation of Wigner crystals for charged particles on a toroidal helix. Focusing on certain commensurate cases we show that the ground state undergoes a pitchfork bifurcation from the totally symmetric polygonic to a zig-zag-like configuration with increasing radius of the helix. Remarkably, we find that for a specific value of the helix radius, below the bifurcation point, the vibrational frequency spectrum collapses to a single frequency. This allows for an essentially independent small-amplitude motion of the individual particles and consequently localized excitations can propagate in time without significant spreading. Increasing the radius beyond the degeneracy point, the band structure is inverted, with the out-of-phase oscillation mode becoming lower in frequency than the mode corresponding to the center of mass motion.

cond-mat.other↗

arXiv2014

Nonadiabatic couplings and gauge-theoretical structure of curved quantum waveguides

We investigate the quantum mechanics of a single particle constrained to move along an arbitrary smooth reference curve by a confinement that is allowed to vary along the waveguide. The Schrödinger equation is evaluated in the adapted coordinate frame and a transverse mode decomposition is performed, taking into account both curvature and torsion effects and the possibility of a cross-section potential that changes along the curve in an arbitrary way. We discuss the adiabatic structure of the problem, and examine nonadiabatic couplings that arise due to the curved geometry, the varying transverse profile and their interplay. The exact multi-mode matrix Hamiltonian is taken as the natural starting point for few-mode approximations. Such approximate equations are provided, and it is worked out how these recover known results for twisting waveguides and can be applied to other types of waveguide designs. The quantum waveguide Hamiltonian is recast into a form that clearly illustrates how it generalizes the Born-Oppenheimer Hamiltonian encountered in molecular physics. In analogy to the latter, we explore the local gauge structure inherent to the quantum waveguide problem and suggest the usefulness of diabatic states, giving an explicit construction of the adiabatic-to-diabatic basis transformation.

quant-ph↗

arXiv2013

Classical scattering of charged particles confined on an inhomogeneous helix

We explore the effects arising due to the coupling of the center of mass and relative motion of two charged particles confined on an inhomogeneous helix with a locally modified radius. It is first proven that a separation of the center of mass and the relative motion is provided if and only if the confining manifold represents a homogeneous helix. In this case bound states of repulsively Coulomb interacting particles occur. For an inhomogeneous helix, the coupling of the center of mass and relative motion induces an energy transfer between the collective and relative motion, leading to dissociation of initially bound states in a scattering process. Due to the time reversal symmetry, a binding of the particles out of the scattering continuum is thus equally possible. We identify the regimes of dissociation for different initial conditions and provide an analysis of the underlying phase space via Poincaré surfaces of section. Bound states inside the inhomogeneity as well as resonant states are identified.

physics.class-ph↗

arXiv2013

Matter-wave dark solitons and their excitation spectra in spin-orbit coupled Bose-Einstein condensates

We present three types of dark solitons in quasi-one-dimensional spin-orbit coupled repulsive Bose-Einstein condensates. Among these families, two are always stable, while the third one is only stable sufficiently close to the linear regime. The solitons' excitation spectra reveal the potential existence of a second anomalous mode. While the first such mode describes the soliton oscillatory motion in a parabolic trap, the second, when present, reflects the double well structure of the underlying single-particle spectrum. This novel mode results in moving density stripes in the vicinity of the soliton core, or in an out-of-phase oscillation of the constituent components, with little effect on the nearly stationary striped total density of the composite soliton.

cond-mat.quant-gas↗

arXiv2012

Vortex-Bright Soliton Dipoles: Bifurcations, Symmetry Breaking and Soliton Tunneling in a Vortex-Induced Double Well

The emergence of vortex-bright soliton dipoles in two-component Bose-Einstein condensates through bifurcations from suitable eigenstates of the underlying linear system is examined. These dipoles can have their bright solitary structures be in phase (symmetric) or out of phase (anti-symmetric). The dynamical robustness of each of these two possibilities is considered and the out-of-phase case is found to exhibit an intriguing symmetry-breaking instability that can in turn lead to tunneling of the bright wavefunction between the two vortex "wells". We interpret this phenomenon by virtue of a vortex-induced double well system, whose spontaneous symmetry breaking leads to asymmetric vortex-bright dipoles, in addition to the symmetric and anti-symmetric ones. The theoretical prediction of these states is corroborated by detailed numerical computations.

cond-mat.quant-gas↗

arXiv2012

Existence, stability and nonlinear dynamics of vortices and vortex clusters in anisotropic Bose-Einstein condensates

We study vortex excitations in one-component Bose-Einstein condensates, with a special emphasis on the role of anisotropic confinement for the existence, stability and dynamical properties of vortices and particularly few-vortex clusters. Symmetry breaking features are pervasive within this system even in its isotropic installment, where cascades of symmetry breaking bifurcations give rise to the multi-vortex clusters, but also within the anisotropic realm which naturally breaks the rotational symmetry of the multi-vortex states. Our first main tool for analyzing the system consists of a weakly nonlinear (bifurcation) approach which starts from the linear states of the problem and examines their continuation and bifurcation into novel symmetry-broken configurations in the nonlinear case. This is first done in the isotropic limit and the modifications introduced by the anisotropy are subsequently presented. The second main tool concerns the highly nonlinear regime where the vortices can be considered as individual topologically charged "particles" which precess within the parabolic trap and interact with each other, similarly to fluid vortices. The conclusions stemming from both the bifurcation and the interacting particle picture are corroborated by numerical computations which are also used to bridge the gap between these two opposite-end regimes.

cond-mat.quant-gas↗