arXiv subjects

W. P. Schleich

Publications and source records attributed to W. P. Schleich.

At least 37 records · Page 2Linked to original sources

arXiv2009

Efimov states in atom-molecular collisions

We analyse scattering of a heavy atom off a weakly bound molecule comprising an identical heavy and a light atom in the Born-Oppenheimer approximation. We focus on the situation where the heavy atoms are bosons, which was realized in several experiments. The elastic and inelastic cross sections for the atom-molecular scattering exhibit a series of resonances corresponding to three-body Efimov states. Resonances in elastic collisions are accessible experimentally through thermalization rates, and thus constitute an alternative way of observing Efimov states.

quant-ph↗

arXiv2009

Commuting Heisenberg operators as the quantum response problem: Time-normal averages in the truncated Wigner representation

The applicability of the so-called truncated Wigner approximation (-W) is extended to multitime averages of Heisenberg field operators. This task splits naturally in two. Firstly, what class of multitime averages the -W approximates, and, secondly, how to proceed if the average in question does not belong to this class. To answer the first question we develop an (in principle, exact) path-integral approach in phase-space based on the symmetric (Weyl) ordering of creation and annihilation operators. These techniques calculate a new class of averages which we call time-symmetric. The -W equations emerge as an approximation within this path-integral techniques. We then show that the answer to the second question is associated with response properties of the system. In fact, for two-time averages Kubo's renowned formula relating the linear response function to two-time commutators suffices. The -W is trivially generalised to the response properties of the system allowing one to calculate approximate time-normally ordered two-time correlation functions with surprising ease. The techniques we develop are demonstrated for the Bose-Hubbard model.

cond-mat.stat-mech↗

arXiv2009

Rotation in relativity and the propagation of light

We compare and contrast the different points of view of rotation in general relativity, put forward by Mach, Thirring and Lense, and Goedel. Our analysis relies on two tools: (i) the Sagnac effect which allows us to measure rotations of a coordinate system or induced by the curvature of spacetime, and (ii) computer visualizations which bring out the alien features of the Goedel Universe. In order to keep the paper self-contained, we summarize in several appendices crucial ingredients of the mathematical tools used in general relativity. In this way, our lecture notes should be accessible to researchers familiar with the basic elements of tensor calculus and general relativity.

gr-qc↗

arXiv2008

Theory of fractional vortex escape in a 0-kappa long Josephson junction

We consider a fractional Josephson vortex in an infinitely long 0-kappa Josephson junction. A uniform bias current applied to the junction exerts a Lorentz force acting on a vortex. When the bias current becomes equal to the critical (or depinning) current, the Lorentz force tears away an integer fluxon and the junction switches to the resistive state. In the presence of thermal and quantum fluctuations this escape process takes place with finite probability already at subcritical values of the bias current. We analyze the escape of a fractional vortex by mapping the Josephson phase dynamics to the dynamics of a single particle in a metastable potential and derive the effective parameters of this potential. This allows us to predict the behavior of the escape rate as a function of the topological charge of the vortex.

cond-mat.supr-con↗

arXiv2008

Quantum tunneling of a single semifluxon in a 0-pi Josephson junction

We consider a symmetric 0-pi Josephson junction of length $L$, which classically can be in one of two degenerate ground states up or down, corresponding to supercurrents circulating clockwise or counterclockwise around the 0-pi boundary. When the length $L$ of the junction becomes smaller than the Josephson penetration depth $λ_J$, the system can switch from one state to the other due to thermal fluctuations or quantum tunneling. We map this problem to the dynamics of a single particle in a periodic double well potential and estimate parameters for which macroscopic quantum coherence may be observed. We conclude that this system is not very promising to build a qubit because (a) it requires very low temperatures to reach the quantum regime, (b) its tiny flux is hard to read out and (c) it is very sensitive to the asymmetries between the 0 and pi parts of the junction.

cond-mat.supr-con↗

arXiv2008

The granularity of weakly occupied bosonic fields beyond the local density approximation

We examine ground state correlations for repulsive, quasi one-dimensional bosons in a harmonic trap. In particular, we focus on the few particle limit N=2,3,4,..., where exact numerical solutions of the many particle Schroedinger equation are available employing the Multi-Configuration Time-dependent Hartree method. Our numerical results for the inhomogeneous system are modeled with the analytical solution of the homogeneous problem using the Bethe ansatz and the local density approximation. Tuning the interaction strength from the weakly correlated Gross-Pitaevskii- to the strongly correlated Tonks-Girardeau regime reveals finite particle number effects in the second order correlation function beyond the local density approximation.

cond-mat.other↗

arXiv2008

Semifluxons in Superconductivity and Cold Atomic Gases

Josephson junctions and junction arrays are well studied devices in superconductivity. With external magnetic fields one can modulate the phase in a long junction and create traveling, solitonic waves of magnetic flux, called fluxons. Today, it is also possible to device two different types of junctions: depending on the sign of the critical current density, they are called 0- or pi-junction. In turn, a 0-pi junction is formed by joining two of such junctions. As a result, one obtains a pinned Josephson vortex of fractional magnetic flux, at the 0-pi boundary. Here, we analyze this arrangement of superconducting junctions in the context of an atomic bosonic quantum gas, where two-state atoms in a double well trap are coupled in an analogous fashion. There, an all-optical 0-pi Josephson junction is created by the phase of a complex valued Rabi-frequency and we a derive a discrete four-mode model for this situation, which qualitatively resembles a semifluxon.

cond-mat.mes-hall↗

arXiv2007

Exploring the growth of correlations in a quasi one-dimensional trapped Bose gas

Phase correlations, density fluctuations and three-body loss rates are relevant for many experiments in quasi one-dimensional geometries. Extended mean-field theory is used to evaluate correlation functions up to third order for a quasi one-dimensional trapped Bose gas at zero and finite temperature. At zero temperature and in the homogeneous limit, we also study the transition from the weakly correlated Gross-Pitaevskii regime to the strongly correlated Tonks-Girardeau regime analytically. We compare our results with the exact Lieb-Liniger solution for the homogeneous case and find good agreement up to the cross-over regime.

cond-mat.mes-hall↗

arXiv2007

Gauss sum factorization with cold atoms

We report the first implementation of a Gauss sum factorization algorithm by an internal state Ramsey interferometer using cold atoms. A sequence of appropriately designed light pulses interacts with an ensemble of cold rubidium atoms. The final population in the involved atomic levels determines a Gauss sum. With this technique we factor the number N=263193.

quant-ph↗

arXiv2007

Resonant Feshbach scattering of fermions in one-dimensional optical lattices

We consider Feshbach scattering of fermions in a one-dimensional optical lattice. By formulating the scattering theory in the crystal momentum basis, one can exploit the lattice symmetry and factorize the scattering problem in terms of center-of-mass and relative momentum in the reduced Brillouin zone scheme. Within a single band approximation, we can tune the position of a Feshbach resonance with the center-of-mass momentum due to the non-parabolic form of the energy band.

physics.atm-clus↗

arXiv2007

Time Asymmetry in Quantum Physics - II. Experimental Demonstration Using a Single Ion

Quantum physics involves an ensemble of quantum systems, usually one thinks of a large ensemble of identical quantum systems at one single time. In single ion experiments one has a single quantum system at an ensemble of different times. This provides the means of demonstrating the beginning of time of a semigroup evolution for a decaying state.

quant-ph↗

arXiv2006

Dropping cold quantum gases on Earth over long times and large distances

We describe the non-relativistic time evolution of an ultra-cold degenerate quantum gas (bosons/fermions) falling in Earth's gravity during long times (10 sec) and over large distances (100 m). This models a drop tower experiment that is currently performed by the QUANTUS collaboration at ZARM (Bremen, Germany). Starting from the classical mechanics of the drop capsule and a single particle trapped within, we develop the quantum field theoretical description for this experimental situation in an inertial frame, the corotating frame of the Earth, as well as the comoving frame of the drop capsule. Suitable transformations eliminate non-inertial forces, provided all external potentials (trap, gravity) can be approximated with a second order Taylor expansion around the instantaneous trap center. This is an excellent assumption and the harmonic potential theorem applies. As an application, we study the quantum dynamics of a cigar-shaped Bose-Einstein condensate in the Gross-Pitaevskii mean-field approximation. Due to the instantaneous transformation to the rest-frame of the superfluid wave packet, the long-distance drop (100m) can be studied easily on a numerical grid.

cond-mat.other↗

arXiv2006

Quantum Dynamics of Atomic Coherence in a Spin-1 Condensate: Mean-Field versus Many-Body Simulation

We analyse and numerically simulate the full many-body quantum dynamics of a spin-1 condensate in the single spatial mode approximation. Initially, the condensate is in a ``ferromagnetic'' state with all spins aligned along the $y$ axis and the magnetic field pointing along the z axis. In the course of evolution the spinor condensate undergoes a characteristic change of symmetry, which in a real experiment could be a signature of spin-mixing many-body interactions. The results of our simulations are conveniently visualised within the picture of irreducible tensor operators.

cond-mat.other↗

arXiv2005

Collective Feshbach scattering of a superfluid droplet from a mesoscopic two-component Bose-Einstein condensate

We examine the collective scattering of a superfluid droplet impinging on a mesoscopic Bose-Einstein condensate (BEC) as a target. The BEC consists of an atomic gas with two internal electronic states, each of which is trapped by a finite-depth external potential. An off-resonant optical laser field provides a localized coupling between the BEC components in the trapping region. This mesoscopic scenario matches the microscopic setup for Feshbach scattering of two particles, when a bound state of one sub-manifold is embedded in the scattering continuum of the other sub-manifold. Within the mean-field picture, we obtain resonant scattering phase shifts from a linear response theory in agreement with an exact numerical solution of the real time scattering process and simple analytical approximations thereof. We find an energy-dependent transmission coefficient that is controllable via the optical field between 0 and 100%.

cond-mat.mes-hall↗

arXiv2005

Observation of Nonspreading Wave Packets in an Imaginary Potential

We propose and experimentally demonstrate a method to prepare a nonspreading atomic wave packet. Our technique relies on a spatially modulated absorption constantly chiseling away from an initially broad de Broglie wave. The resulting contraction is balanced by dispersion due to Heisenberg's uncertainty principle. This quantum evolution results in the formation of a nonspreading wave packet of Gaussian form with a spatially quadratic phase. Experimentally, we confirm these predictions by observing the evolution of the momentum distribution. Moreover, by employing interferometric techniques, we measure the predicted quadratic phase across the wave packet. Nonspreading wave packets of this kind also exist in two space dimensions and we can control their amplitude and phase using optical elements.

quant-ph↗

arXiv2005

Quantum tunneling of semifluxons

We consider a system of two semifluxons of opposite polarity in a 0-pi-0 long Josephson junction, which classically can be in one of two degenerate states: up-down or down-up. When the distance $a$ between the 0-pi boundaries (semifluxon's centers) is a bit larger than the crossover distance $a_c$, the system can switch from one state to the other due to thermal fluctuations or quantum tunneling. We map this problem to the dynamics of a single particle in a double well potential and estimate parameters for which quantum effects emerge. We also determine the classical-to-quantum crossover temperature as well as the tunneling rate (energy level splitting) between the states up-down and down-up.

cond-mat.supr-con↗

arXiv2004

Sagnac Effect of Goedel's Universe

We present exact expressions for the Sagnac effect of Goedel's Universe. For this purpose we first derive a formula for the Sagnac time delay along a circular path in the presence of an arbitrary stationary metric in cylindrical coordinates. We then apply this result to Goedel's metric for two different experimental situations: First, the light source and the detector are at rest relative to the matter generating the gravitational field. In this case we find an expression that is formally equivalent to the familiar nonrelativistic Sagnac time delay. Second, the light source and the detector are rotating relative to the matter. Here we show that for a special rotation rate of the detector the Sagnac time delay vanishes. Finally we propose a formulation of the Sagnac time delay in terms of invariant physical quantities. We show that this result is very close to the analogous formula of the Sagnac time delay of a rotating coordinate system in Minkowski spacetime.

gr-qc↗

arXiv2004

How to STIRAP a vortex

We examine a scheme for the optical creation of a superfluid vortex in a trapped Bose-Einstein condensate (BEC), using the stimulated Raman adiabatic passage (STIRAP) technique. By exposing an oblate, axis-symmetric condensate to two co-propagating laser pulses, one can transfer external angular momentum from the light field to the matter wave, if one of the beams is the fundamental Gaussian mode and the other is a Gauss-Laguerre mode of angular momentum $1\hbar$. We demonstrate the complete transfer efficiency by numerical integration of the multi-component Gross-Pitaevskii equation and explain the results with an intuitive and accurate approximation within the Thomas-Fermi limit. In addition, we discuss residual excitations (breathing modes) which occur in the two-dimensional regime and present the Bogoliubov excitation spectrum.

cond-mat.soft↗