arXiv subjects

Peter Schmelcher

Publications and source records attributed to Peter Schmelcher.

At least 73 records · Page 4Linked to original sources

arXiv2022

Vibronic interactions in trilobite and butterfly Rydberg molecules

Ultralong-range Rydberg molecules provide an exciting testbed for molecular physics at exaggerated scales. In the so-called trilobite and butterfly Rydberg molecules, the Born-Oppenheimer approximation can fail due to strong non-adiabatic couplings arising from the combination of radial oscillations and rapid energy variations in the adiabatic potential energy curves. We utilize an accurate coupled-channel treatment of the vibronic system to observe the breakdown of Born-Oppenheimer physics, such as non-adiabatic trapping and decay of molecular states found near pronounced avoided crossings in the adiabatic potential curves. Even for vibrational states localized far away from avoided crossings, a single channel model is quantitatively sufficient only after including the diagonal non-adiabatic corrections to the Born-Oppenheimer potentials. Our results indicate the importance of including non-adiabatic physics in the description of ultralong-range Rydberg molecules and in the interpretation of measured vibronic spectra.

physics.atom-ph↗

arXiv2022

Magnetic monopole induced polarons in atomic superlattices

Magnetic monopoles have been realized as emergent quasiparticles in both condensed matter and ultracold atomic platforms, with growing interests in the coupling effects between the monopole and different magnetic quasiparticles. In this work, interaction effects between monopoles and magnons are investigated for an atomic pseudospin chain. We reveal that the monopole can excite a virtual magnon cloud in the paramagnetic chain, thereby giving rise to a new type of polaron, the monopole-cored polaron (McP). The McP is composed of the monopole as the impurity core and the virtual magnon excitation as the dressing cloud. The magnon dressing facilitates the Dirac string excitation and impacts the monopole hopping. This induces an anti-trapping effect of the McP, which refers to the fact that the dressing enhances the mobility of the McP, in contrast to the self-trapping of the common polarons. Moreover, heterogeneous bipolarons are shown to exist under the simultaneous doping of a north and a south monopole. The heterogeneous bipolaron possesses an inner degree of freedom composed of two identical impurities. Our investigation sheds light on the understanding of how the coupling between the impurity core and the dressing cloud can engineer the property of the polaron

quant-ph↗

arXiv2022

Interaction-controlled impurity transport in trapped mixtures of ultracold bosons

We explore the dynamical transport of an impurity between different embedding majority species which are spatially separated in a double well. The transfer and storage of the impurity is triggered by dynamically changing the interaction strengths between the impurity and the two majority species. We find a simple but efficient protocol consisting of linear ramps of majority-impurity interactions at designated times to pin or unpin the impurity. Our study of this highly imbalanced few-body triple mixture is conducted with the multi-layer multi-configuration time-dependent Hartree method for atomic mixtures which accounts for all interaction-induced correlations. We analyze the dynamics in terms of single-particle densities, entanglement growth and provide an effective potential description involving mean-fields of the interacting components. The majority components remain self-trapped in their individual wells at all times, which is a crucial element for the effectiveness of our protocol. During storage times each component performs low-amplitude dipole oscillations in a single well. Unexpectedly, the inter-species correlations possess a stabilizing impact on the transport and storage properties of the impurity particle.

cond-mat.quant-gas↗

arXiv2022

Characterizing a transition from limited to unlimited diffusion in energy for a time-dependent billiard

We explore Fermi acceleration in a driven oval billiard which shows unlimited to limited diffusion in energy when passing from the free to the dissipative case. We provide evidence for a second-order phase transition taking place while detuning the corresponding restitution coefficient from one responsible for the degree of dissipation. A corresponding order parameter is suggested, and its susceptibility is shown to diverge at the transition point. We also discuss the underlying symmetry breaking and the elementary excitation of the controlled diffusion process.

nlin.CD↗

arXiv2022

Dynamical formation of two-fold fragmented many-body state induced by an impurity in a double-well

We unravel the correlated quantum quench dynamics of a single impurity immersed in a bosonic environment confined in an one-dimensional double-well potential. A particular emphasis is placed on the structure of the time-evolved many-body wave function by relying on a Schmidt decomposition whose coefficients directly quantify the number of configurations that are macroscopically populated. For a non-interacting bosonic bath and weak postquench impurity-bath interactions, we observe the dynamical formation of a two-fold fragmented many-body state which is related to intra-band excitation processes of the impurity and manifests as a two-body phase separation (clustering) between the two species for repulsive (attractive) interactions. Increasing the postquench impurity-bath coupling strength leads to the destruction of the two-fold fragmentation since the impurity undergoes additional inter-band excitation dynamics. By contrast, a weakly interacting bath suppresses excitations of the bath particles and consequently the system attains a weakly fragmented many-body state. Our results explicate the interplay of intra- and inter-band impurity excitations for the dynamical generation of fragmented many-body states in multi-well traps and for designing specific entangled impurity states.

cond-mat.quant-gas↗

arXiv2022

Formation and crossover of multiple helical dipole chains

We investigate the classical equilibrium properties and metamorphosis of the ground state of interacting dipoles with fixed locations on a helix. The dipoles are shown to align themselves along separate intertwined dipole chains forming single, double, and higher-order helical chains. The number of dipole chains, and their properties such as chirality and length scale on which the chains wind around each other, can be tuned by the geometrical parameters. We demonstrate that all possible configurations form a self-similar bifurcation diagram which can be linked to the Stern-Brocot tree and the underlying Farey sequence. We describe the mechanism responsible for this behavior and subsequently discuss corresponding implications and possible applications.

physics.class-ph↗

arXiv2022

Counterflow dynamics of two correlated impurities immersed in a bosonic gas

The counterflow dynamics of two correlated impurities in a double-well coupled to an one-dimensional bosonic medium is explored. We determine the ground state phase diagram of the system according to the impurity-medium entanglement and the impurities two-body correlations. Specifically, bound impurity structures reminiscent of bipolarons for strong attractive couplings as well as configurations with two clustered or separated impurities in the repulsive case are identified. The interval of existence of these phases depends strongly on the impurity-impurity interactions and external confinement of the medium. Accordingly the impurities dynamical response, triggered by suddenly ramping down the central potential barrier, is affected by the medium's trapping geometry. In particular, for a box-confined medium repulsive impurity-medium couplings lead, due to attractive induced interactions, to the localization of the impurities around the trap center. In contrast, for a harmonically trapped medium the impurities perform a periodic collision and expansion dynamics further interpreted in terms of a two-body effective model. Our findings elucidate the correlation aspects of the collisional physics of impurities which should be accessible in recent cold atom experiments.

cond-mat.quant-gas↗

arXiv2022

Interaction effects of pseudospin-based magnetic monopoles and kinks in a doped dipolar superlattice gas

Magnetic monopoles and kinks are topological excitations extensively investigated in quantum spin systems, but usually they are studied in different setups. We explore the conditions for the coexistence and the interaction effects of these quasiparticles in the pseudospin chain of the atomic dipolar superlattice gas. In this chain, the magnetic kink is the intrinsic quasiparticle, and the particle/hole defect takes over the role of the north/south magnetic monopole, exerting monopolar magnetic fields to neighboring spins. A confinement effect between the monopole and kink is revealed, which renormalizes the dispersion of the kink. The corresponding dynamical deconfinement process is observed and arises due to the kink-antikink annihilation. The rich interaction effects of the two quasiparticles could stimulate corresponding investigations in bulk spin systems.

cond-mat.quant-gas↗

arXiv2021

Intra- and interband excitations induced residue decay of the Bose polaron in a one-dimensional double-well

We investigate the polaronic properties of a single impurity immersed in a weakly interacting bosonic environment confined within a one-dimensional double-well potential using an exact diagonalization approach. We find that an increase of the impurity-bath coupling results in a vanishing residue, signifying the occurrence of the polaron orthogonality catastrophe. Asymptotic configurations of the systems' ground state wave function in the strongly interacting regime are obtained by means of a Schmidt decomposition, which in turn accounts for the observed orthogonality catastrophe of the polaron. We exemplify that depending on the repulsion of the Bose gas, three distinct residue behaviors appear with respect to the impurity-bath coupling. These residue regimes are characterized by two critical values of the bosonic repulsion and originate from the interplay between the intra- and the interband excitations of the impurity. Moreover, they can be clearly distinguished in the corresponding species reduced density matrices with the latter revealing a phase separation on either the one- or the two-body level. The impact of the interspecies mass-imbalance on the impurity's excitation processes is appreciated yielding an interaction shift of the residue regions. Our results explicate the interplay of intra- and interband excitation processes for the polaron generation in multiwell traps and for designing specific polaron entangled states motivating their exposure in current experiments.

cond-mat.quant-gas↗

arXiv2021

Polarons and their induced interactions in highly imbalanced triple mixtures

We unravel the polaronic properties of impurities immersed in a correlated trapped one-dimensional (1D) Bose-Bose mixture. This setup allows for the impurities to couple either attractively or repulsively to a specific host, thus offering a highly flexible platform for steering the emergent polaronic properties. Specifically, the polaronic residue peak and strength of induced interactions can be controlled by varying the coupling of the impurities to the individual bosonic components. In particular, it is possible to maintain the quasiparticle character for larger interaction strengths as compared to the case of impurities immersed in a single bosonic species. We explicate a hierarchy of the polaron binding energies in terms of the impurity-medium interactions, thereby elucidating the identification of the polaronic resonances in recent experimental radiofrequency schemes. For strong attractive impurity-medium couplings bipolaron formation is captured. Our findings pave the way for continuously changing the quasiparticle character, under the impact of trap effects, while exposing the role of correlations in triple mixture settings.

cond-mat.quant-gas↗

arXiv2021

Chaos and thermalization in a classical chain of dipoles

We explore the connection between chaos, thermalization and ergodicity in a linear chain of $N$ interacting dipoles. Starting from the ground state, and considering chains of different numbers of dipoles, we introduce single site excitations with energy $ΔK$. The time evolution of the chaoticy of the system and the energy localization along the chain is analyzed by computing, up to very long times, the statistical average of the finite time Lyapunov exponent $λ(t)$ and of the participation ratio $Π(t)$. For small $ΔK$, the evolution of $λ(t)$ and $Π(t)$ indicates that the system becomes chaotic at roughly the same time as $Π(t)$ reaches a steady state. For the largest values of $ΔK$, the system becomes chaotic at an extremely early stage in comparison with the energy relaxation times. We find that this fact is due to the presence of chaotic breathers that keep the system far from equipartition and ergodicity. Finally, we show that the asymptotic values attained by the participation ratio $Π(t)$ fairly corresponds to thermal equilibrium.

nlin.CD↗

arXiv2021

Breathing dynamics of the Bose polaron in a species-selective harmonic trap

We perform an extensive numerical study on the breathing dynamics of a few-body Bose polaron setup in a one-dimensional species-selective harmonic trap. The dynamics is triggered by a quench of the impurity trap. The excitation of the background majority atoms is mediated via the majority-impurity interaction. The breathing spectrum is obtained for different numbers of majority particles, several values of the majority-component interaction strengths and trap ratios. It is further compared to the breathing spectrum of a particle-balanced few-body Bose-Bose mixture. In particular, for equal post-quench traps the employed protocol allows to couple states of different center-of-mass parity in contrast to species-symmetric trap quenches. Among the participating eigenstates we identify one having odd center-of-mass parity and even global parity. The breathing frequency induced by this state is a monotonically decreasing function of the coupling parameter. Importantly, in order to be observable it requires the entanglement between the species to be taken into account. We demonstrate this by comparing the numerically exact results obtained by means of the Multi-Layer Multi-Configuration Time-Dependent Hartree Method for Mixtures to the ones of a species mean-field ansatz. The entanglement-sensitive breathing frequency persists also for unequal post-quench traps where the center-of-mass cannot be decoupled. Finally, we analyze the impact of parity symmetry on the breathing dynamics by initializing a state of odd global parity. We evidence a striking resemblance to the ground state breathing dynamics.

cond-mat.quant-gas↗

arXiv2021

On symmetries of a matrix and its isospectral reduction

The analysis of diagonalizable matrices in terms of their so-called isospectral reduction represents a versatile approach to the underlying eigenvalue problem. Starting from a symmetry of the isospectral reduction, we show in the present work that it is possible to construct a corresponding symmetry of the original matrix.

math.GM↗

arXiv2021

External field-induced dynamics of a charged particle on a closed helix

We investigate the dynamics of a charged particle confined to move on a toroidal helix while being driven by an external time-dependent electric field. The underlying phase space is analyzed for linearly and circularly polarized fields. For small driving amplitudes and a linearly polarized field, we find a split-up of the chaotic part of the phase space which prevents the particle from inverting its direction of motion. This allows for a non-zero average velocity of chaotic trajectories without breaking the well-known symmetries commonly responsible for directed transport. Within our chosen normalized units, the resulting average transport velocity is constant and does not change significantly with the driving amplitude. A very similar effect is found in case of the circularly polarized field and low driving amplitudes. Furthermore, when driving with a circularly polarized field, we unravel a second mechanism of the split-up of the chaotic phase space region for very large driving amplitudes. There exists a wide range of parameter values for which trajectories may travel between the two chaotic regions by crossing a permeable cantorus. The limitations of these phenomena, as well as their implication on manipulating directed transport in helical geometries are discussed.

nlin.CD↗

arXiv2021

Many-body collisional dynamics of impurities injected into a double-well trapped Bose-Einstein condensate

We unravel the many-body dynamics of a harmonically trapped impurity colliding with a bosonic medium confined in a double-well upon quenching the initially displaced harmonic trap to the center of the double-well. We reveal that the emerging correlation dynamics crucially depends on the impurity-medium interaction strength allowing for a classification into different dynamical response regimes. For strong attractive impurity-medium couplings the impurity is bound to the bosonic bath, while for intermediate attractions it undergoes an effective tunneling. In the case of weak attractive or repulsive couplings the impurity penetrates the bosonic bath and performs a dissipative oscillatory motion. Further increasing the impurity-bath repulsion results in the pinning of the impurity between the density peaks of the bosonic medium, a phenomenon that is associated with a strong impurity-medium entanglement. For strong repulsions the impurity is totally reflected by the bosonic medium. To unravel the underlying microscopic excitation processes accompanying the dynamics we employ an effective potential picture. We extend our results to the case of two bosonic impurities and demonstrate the existence of a qualitatively similar impurity dynamics.

cond-mat.quant-gas↗

arXiv2021

Bosonic Quantum Dynamics Following Colliding Potential Wells

We employ the multi-configuration time-dependent Hartree method for bosons (MCTDHB) in order to investigate the correlated non-equilibrium quantum dynamics of two bosons confined in two colliding and uniformly accelerated Gaussian wells. As the wells approach each other an effective, transient double-well structure is formed. This induces a transient and oscillatory over-barrier transport. We monitor both the amplitude of the intra-well dipole mode in the course of the dynamics as well as the final distribution of the particles between the two wells. For fast collisions we observe an emission process which we attribute to two distinct mechanisms. Energy transfer processes lead to an untrapped fraction of bosons and a resonant enhancement of the deconfinement for certain kinematic configurations can be observed. Despite the comparatively weak interaction strengths employed in this work, we identify strong inter-particle correlations by analyzing the corresponding Von Neumann entropy.

quant-ph↗

arXiv2021

Cospectrality preserving graph modifications and eigenvector properties via walk equivalence of vertices

Originating from spectral graph theory, cospectrality is a powerful generalization of exchange symmetry and can be applied to all real-valued symmetric matrices. Two vertices of an undirected graph with real edge weights are cospectral iff the underlying weighted adjacency matrix $M$ fulfills $[M^k]_{u,u} = [M^k]_{v,v}$ for all non-negative integer $k$, and as a result any eigenvector $ϕ$ of $M$ has (or, in the presence of degeneracies, can be chosen to have) definite parity on $u$ and $v$. We here show that the powers of a matrix with cospectral vertices induce further local relations on its eigenvectors, and also can be used to design cospectrality preserving modifications. To this end, we introduce the concept of \emph{walk equivalence} of cospectral vertices with respect to \emph{walk multiplets} which are special vertex subsets of a graph. Walk multiplets allow for systematic and flexible modifications of a graph with a given cospectral pair while preserving this cospectrality. The set of modifications includes the addition and removal of both vertices and edges, such that the underlying topology of the graph can be altered. In particular, we prove that any new vertex connected to a walk multiplet by suitable connection weights becomes a so-called unrestricted substitution point (USP), meaning that any arbitrary graph may be connected to it without breaking cospectrality. Also, suitable interconnections between walk multiplets within a graph are shown to preserve the associated cospectrality. Importantly, we demonstrate that the walk equivalence of cospectral vertices $u,v$ imposes a local structure on every eigenvector $ϕ$ obeying $ϕ_{u} = \pm ϕ_{v} \ne 0$ (in the case of degeneracies, a specific choice of the eigenvector basis is needed). Our work paves the way for flexibly exploiting hidden structural symmetries in the design of generic complex network-like systems.

math.CO↗

arXiv2021

Spectral Properties of Confining Superexponential Potentials

We explore the spectral properties and behaviour of confining superexponential potentials. Several prototypes of these highly nonlinear potentials are analyzed in terms of the eigenvalues and eigenstates of the underlying stationary Schrödinger equation up to several hundreds of excited states. A generalization of the superexponential self-interacting oscillator shows a scaling behaviour of the spacing of the eigenvalues which turns into an alternating behaviour for the power law modified oscillator. Superexponential potentials with an oscillating power show a very rich spectral structure with varying amplitudes and wave vectors. In the parity symmetric case doublets of near degenerate energy eigenvalues emerge in the spectrum. The corresponding eigenstates are strongly localized in the outer wells of the potential and occur as even-odd pairs which are interspersed into the spectrum of delocalized states. We provide an outlook on future perspectives including the possibility to use these features for applications in e.g. cold atom physics.

quant-ph↗