arXiv subjects

Peter Schmelcher

Publications and source records attributed to Peter Schmelcher.

At least 127 records · Page 7Linked to original sources

arXiv2018

Driven power-law oscillator

We explore the nonlinear dynamics of a driven power law oscillator whose shape varies periodically in time covering a broad spectrum of anharmonicities. Combining weak and strong confinement of different geometry within a single driving period the phase space allows not only for regular and chaotic bounded motion but in particular also for an unbounded motion which exhibits an exponential net growth of the corresponding energies. Our computational study shows that phases of motion with energy gain and loss as well as approximate energy conservation alternate within a single period of the oscillator and can be assigned to the change of the underlying confinement geometry. We demonstrate how the crossover from a single- to a two-component phase space takes place with varying frequency and amplitude and analyze the corresponding volumes in phase space. In the high frequency regime an effective potential is derived that combines the different features of the driven power-law oscillator. Possible experimental realizations are discussed.

nlin.CD↗

arXiv2018

The BBGKY hierarchy for ultracold bosonic systems

We establish a theoretical framework for exploring the quantum dynamics of finite ultracold bosonic ensembles based on the Born-Bogoliubov-Green-Kirkwood-Yvon (BBGKY) hierarchy of equations of motion for few-particle reduced density matrices (RDMs). The theory applies to zero as well as low temperatures and is formulated in a highly efficient way by utilizing dynamically optimized single-particle basis states and representing the RDMs in terms of permanents with respect to those. An energy, RDM compatibility and symmetry conserving closure approximation is developed on the basis of a recursively formulated cluster expansion for these finite systems. In order to enforce necessary representability conditions, two novel, minimal-invasive and energy-conserving correction algorithms are proposed, involving the dynamical purification of the solution of the truncated BBGKY hierarchy and the correction of the equations of motion themselves, respectively. For gaining conceptual insights, the impact of two-particle correlations on the dynamical quantum depletion is studied analytically. We apply this theoretical framework to both a tunneling and an interaction-quench scenario. Due to our efficient formulation of the theory, we can reach truncation orders as large as twelve and thereby systematically study the impact of the truncation order on the results. While the short-time dynamics is found to be excellently described with controllable accuracy, significant deviations occur on a longer time-scale in sufficiently far off-equilibrium situations. Theses deviations are accompanied by exponential-like instabilities leading to unphysical results. The phenomenology of these instabilities is investigated in detail and we show that the minimal-invasive correction algorithm of the equation of motion can indeed stabilize the BBGKY hierarchy truncated at the second order.

quant-ph↗

arXiv2018

Quantum point spread function for imaging trapped few-body systems with a quantum gas microscope

Quantum gas microscopes, which image the atomic occupations in an optical lattice, have opened a new avenue to the exploration of many-body lattice systems. Imaging trapped systems after freezing the density distribution by ramping up a pinning lattice leads, however, to a distortion of the original density distribution, especially when its structures are on the scale of the pinning lattice spacing. We show that this dynamics can be described by a filter, which we call in analogy to classical optics a quantum point spread function. Using a machine learning approach, we demonstrate via several experimentally relevant setups that a suitable deconvolution allows for the reconstruction of the original density distribution. These findings are both of fundamental interest for the theory of imaging and of immediate importance for current quantum gas experiments.

cond-mat.quant-gas↗

arXiv2018

Correlation induced localization of lattice trapped bosons coupled to a Bose-Einstein condensate

We investigate the ground state properties of a lattice trapped bosonic system coupled to a Lieb-Liniger type gas. Our main goal is the description and in depth exploration and analysis of the two-species many-body quantum system including all relevant correlations beyond the standard mean-field approach. To achieve this, we use the Multi-Configuration Time-Dependent Hartree method for Mixtures (ML-MCTDHX). Increasing the lattice depth and the interspecies interaction strength, the wave function undergoes a transition from an uncorrelated to a highly correlated state, which manifests itself in the localization of the lattice atoms in the latter regime. For small interspecies couplings, we identify the process responsible for this cross-over in a single-particle-like picture. Moreover, we give a full characterization of the wave function's structure in both regimes, using Bloch and Wannier states of the lowest band, and we find an order parameter, which can be exploited as a corresponding experimental signature. To deepen the understanding, we use an effective Hamiltonian approach, which introduces an induced interaction and is valid for small interspecies interaction. We finally compare the ansatz of the effective Hamiltonian with the results of the ML-MCTDHX simulations.

cond-mat.quant-gas↗

arXiv2018

Energy transfer mechanisms in a dipole chain: From energy equipartition to the formation of breathers

We study the energy transfer in a classical dipole chain of $N$ interacting rigid rotating dipoles. The underlying high--dimensional potential energy landscape is analyzed in particular by determining the equilibrium points and their stability in the common plane of rotation. Starting from the minimal energy configuration, the response of the chain to excitation of a single dipole is investigated. Using both the linearized and the exact Hamiltonian of the dipole chain, we detect an approximate excitation energy threshold between a weakly and a strongly nonlinear dynamics. In the weakly nonlinear regime, the chain approaches in the course of time the expected energy equipartition among the dipoles. For excitations of higher energy, strongly localized excitations appear whose trajectories in time are either periodic or irregular, relating to the well-known discrete or chaotic breathers, respectively. The phenomenon of spontaneous formation of domains of opposite polarization and phase locking is found to commonly accompany the time evolution of the chaotic breathers. Finally, the sensitivity of the dipole chain dynamics to the initial conditions is studied as a function of the initial excitation energy by computing a fast chaos indicator. The results of this study confirm the aforementioned approximate threshold value for the initial excitation energy, below which the dynamics of the dipole chain is regular and above which it is chaotic.

nlin.CD↗

arXiv2018

Dimensional coupling induced current reversal in two-dimensional driven lattices

We show that the direction of directed particle transport in a two dimensional ac-driven lattice can be dynamically reversed by changing the structure of the lattice in the direction perpendicular to the applied driving force. These structural changes introduce dimensional coupling effects, the strength of which governs the timescale of the current reversals. The underlying mechanism is based on the fact that dimensional coupling allows the particles to explore regions of phase space which are inaccessible otherwise. The experimental realization for cold atoms in ac-driven optical lattices is discussed.

cond-mat.quant-gas↗

arXiv2018

Spin-Interaction Effects for Ultralong-range Rydberg Molecules in a Magnetic Field

We investigate the fine and spin structure of ultralong-range Rydberg molecules exposed to a homogeneous magnetic field. Each molecule consists of a $^{87}$Rb Rydberg atom whose outer electron interacts via spin-dependent $s$- and p-wave scattering with a polarizable $^{87}$Rb ground state atom. Our model includes also the hyperfine structure of the ground state atom as well as spin-orbit couplings of the Rydberg and ground state atom. We focus on $d$-Rydberg states and principal quantum numbers $n$ in the vicinity of 40. The electronic structure and vibrational states are determined in the framework of the Born-Oppenheimer approximation for varying field strengths ranging from a few up to hundred Gauß. The results show that the interplay between the scattering interactions and the spin couplings gives rise to a large variety of molecular states in different spin configurations as well as in different spatial arrangements that can be tuned by the magnetic field. This includes relatively regularly shaped energy surfaces in a regime where the Zeeman splitting is large compared to the scattering interaction but small compared to the Rydberg fine structure, as well as more complex structures for both, weaker and stronger fields. We quantify the impact of spin couplings by comparing the extended theory to a spin-independent model.

physics.atom-ph↗

arXiv2018

Edge Modes of Scattering Chains with Aperiodic Order

We study the scattering resonances of one-dimensional deterministic aperiodic chains of electric dipoles using the vectorial Green's matrix method, which accounts for both short- and long-range electromagnetic interactions in open scattering systems. We discover the existence of edge-localized scattering states within fractal energy gaps with characteristic topological band structures. Notably, we report and characterize edge-localized modes in the classical wave analogues of the Su-Schrieffer-Heeger (SHH) dimer model, quasiperiodic Harper and Fibonacci crystals, as well as in more complex Thue-Morse aperiodic systems. Our study demonstrates that topological edge-modes with characteristic power-law envelope appear in open aperiodic systems and coexist with traditional exponentially localized ones. Our results extend the concept of topological states to the scattering resonances of complex open systems with aperiodic order, thus providing an important step towards the predictive design of topological optical metamaterials and devices beyond tightbinding models.

physics.optics↗

arXiv2017

Generating scalable entanglement of ultracold bosons in superlattices through resonant shaking

Based on a one-dimensional double-well superlattice with a unit filling of ultracold atoms per site, we propose a scheme to generate scalable entangled states in the superlattice through resonant lattice shakings. Our scheme utilizes periodic lattice modulations to entangle two atoms in each unit cell with respect to their orbital degree of freedom, and the complete atomic system in the superlattice becomes a cluster of bipartite entangled atom pairs. To demonstrate this we perform $ab \ initio$ quantum dynamical simulations using the Multi-Layer Multi-Configuration Time-Dependent Hartree Method for Bosons, which accounts for all correlations among the atoms. The proposed clusters of bipartite entanglements manifest as an essential resource for various quantum applications, such as measurement based quantum computation. The lattice shaking scheme to generate this cluster possesses advantages such as a high scalability, fast processing speed, rich controllability on the target entangled states, and accessibility with current experimental techniques.

cond-mat.quant-gas↗

arXiv2017

The BBGKY hierarchy for ultracold bosonic systems: II. Applications

In this work, which is based on our previously derived theoretical framework [1], we apply the truncated Born-Bogoliubov-Green-Kirkwood-Yvon (BBGKY) hierarchy for ultracold bosonic systems with a fixed number of particles to two out-of-equilibrium scenarios, namely tunneling in a double-well potential and an interaction quench in a harmonic trap. The efficient formulation of the theory provided in [1] allows for going to large truncation orders such that the impact of the truncation order on the accuracy of the results can be systematically explored. While the short-time dynamics is found to be excellently described with controllable accuracy, significant deviations occur on a longer time-scale for a sufficiently strong interaction quench or the tunneling scenario. Theses deviations are accompanied by exponential-like instabilities leading to unphysical results. The phenomenology of these instabilities is investigated in detail and we show that the minimal-invasive correction algorithm of the equation of motion as proposed in [1] can indeed stabilize the BBGKY hierarchy truncated at the second order.

quant-ph↗

arXiv2017

Simultaneous control of multi-species particle transport and segregation in driven lattices

We provide a generic scheme to separate the particles of a mixture by their physical properties like mass, friction or size. The scheme employs a periodically shaken two dimensional dissipative lattice and hinges on a simultaneous transport of particles in species-specific directions. This selective transport is achieved by controlling the late-time nonlinear particle dynamics, via the attractors embedded in the phase space and their bifurcations. To illustrate the spectrum of possible applications of the scheme, we exemplarily demonstrate the separation of polydisperse colloids and mixtures of cold thermal alkali atoms in optical lattices.

nlin.CD↗

arXiv2017

Electronic structure of ultralong-range Rydberg pentaatomic molecules with two polar diatomic molecules

We explore the electronic structure of ultralong-range pentaatomic Rydberg molecules from a merger of a Rydberg atom and two ground state heteronuclear diatomic molecules. Our focus is on the interaction of Rb($23s$) and Rb($n=20$, $l\ge 3$) Rydberg states with ground and rotationally excited KRb diatomic polar molecules. For symmetric and asymmetric configurations of the pentaatomic Rydberg molecule, we investigate the metamorphosis of the Born-Oppenheimer potential curves, essential for the binding of the molecule, with varying distance from the Rydberg core and analyze the alignment and orientation of the polar diatomic molecules.

quant-ph↗

arXiv2017

Spectral properties and breathing dynamics of a few-body Bose-Bose mixture in a 1D harmonic trap

We investigate a few-body mixture of two bosonic components, each consisting of two particles confined in a quasi one-dimensional harmonic trap. By means of exact diagonalization with a correlated basis approach we obtain the low-energy spectrum and eigenstates for the whole range of repulsive intra- and inter-component interaction strengths. We analyse the eigenvalues as a function of the inter-component coupling, covering hereby all the limiting regimes, and characterize the behaviour in-between these regimes by exploiting the symmetries of the Hamiltonian. Provided with this knowledge we study the breathing dynamics in the linear-response regime by slightly quenching the trap frequency symmetrically for both components. Depending on the choice of interactions strengths, we identify 1 to 3 monopole modes besides the breathing mode of the center of mass coordinate. For the uncoupled mixture each monopole mode corresponds to the breathing oscillation of a specific relative coordinate. Increasing the inter-component coupling first leads to multi-mode oscillations in each relative coordinate, which turn into single-mode oscillations of the same frequency in the composite-fermionization regime.

cond-mat.quant-gas↗

arXiv2017

Dynamical ion transfer between coupled Coulomb crystals in a double well potential

We investigate the non-equilibrium dynamics of coupled Coulomb crystals of different sizes trapped in a double well potential. The dynamics is induced by an instantaneous quench of the potential barrier separating the two crystals. Due to the intra- and inter-crystal Coulomb interactions and the asymmetric population of the potential wells we observe a complex reordering of ions within the two crystals as well as ion transfer processes from one well to the other. The study and analysis of the latter processes constitutes the main focus of this work. In particular we examine the dependence of the observed ion transfers on the quench amplitude performing an analysis for different crystalline configurations ranging from one-dimensional ion chains via two-dimensional zig-zag chains and ring structures to three-dimensional spherical structures. Such an analysis provides us with the means to extract the general principles governing the ion transfer dynamics and we gain some insight on the structural disorder caused by the quench of the barrier height.

physics.atom-ph↗

arXiv2017

Dipolar confinement-induced molecular states in harmonic waveguides

The bound states of two identical dipoles in a harmonic waveguide are investigated. In the regime of weak dipole-dipole interactions, the local frame transformation (LFT) method is applied to determine the spectrum of dipolar confinement-induced bound states analytically. The accuracy of the LFT approach is discussed by comparing the analytical results with the numerical ones based on a solution of the close-coupling equations. It is found that close to the threshold energy in the waveguide, the LFT method needs to include more partial wave states to obtain accurate bound state energies. As the binding energy increases, the LFT method using a single partial wave state becomes more accurate. We also compare the bound states in waveguides and in free space. For the bosonic case, the s-wave dominated bound state looks like a free-space state when its energy is below a certain value. For the fermionic case, the p-wave dominated bound state energies in waveguides and in free-space coincide even close to zero energy.

physics.atm-clus↗

arXiv2017

Highly excited electronic image states of metallic nanorings

We study electronic image states around a metallic nanoring and show that the interplay between the attractive polarization force and a repulsive centrifugal force gives rise to Rydberg-like image states trapped several nanometers away from the surface. The nanoring is modeled as a perfectly conducting isolated torus whose electrostatic image potential is derived analytically. The image states are computed via a two-dimensional finite-difference scheme as solutions of the effective Schrödinger equation describing the outer electron subject to this image potential. These findings demonstrate not only the existence of detached image states around nanorings but allow us also to provide general criteria on the ring geometry, i.e. the aspect ratio of the torus, that need to be fulfilled in order to support such states.

cond-mat.mes-hall↗

arXiv2017

Generalized continuity equations from two-field Schrödinger Lagrangians

A variational scheme for the derivation of generalized, symmetry-induced continuity equations for Hermitian and non-Hermitian quantum mechanical systems is developed. We introduce a Lagrangian which involves two complex wave fields and whose global invariance under dilation and phase variations leads to a mixed continuity equation for the two fields. In combination with discrete spatial symmetries of the underlying Hamiltonian, the mixed continuity equation is shown to produce bilocal conservation laws for a single field. This leads to generalized conserved charges for vanishing boundary currents, and to divergenceless bilocal currents for stationary states. The formalism reproduces the bilocal continuity equation obtained in the special case of $\mathcal{PT}$ symmetric quantum mechanics and paraxial optics.

quant-ph↗

arXiv2016

Non-Local Currents and the Structure of Eigenstates in Planar Discrete Systems with Local Symmetries

Local symmetries are spatial symmetries present in a subdomain of a complex system. By using and extending a framework of so-called non-local currents that has been established recently, we show that one can gain knowledge about the structure of eigenstates in locally symmetric setups through a Kirchhoff-type law for the non-local currents. The framework is applicable to all discrete planar Schrödinger setups, including those with non-uniform connectivity. Conditions for spatially constant non-local currents are derived and we explore two types of locally symmetric subsystems in detail, closed-loops and one-dimensional open ended chains. We find these systems to support locally similar or even locally symmetric eigenstates.

quant-ph↗