arXiv subjects
Publications and source records attributed to Wolfgang P. Schleich.
We show that the bound states in a three-body system display a Coulomb series with a Gaussian cut-off provided: (i) the system consists of a light particle and two heavy bosonic ones, (ii) the heavy-light short-range potential has a resonance in the $p$-wave scattering amplitude, and (iii) all three particles move in two space dimensions. For a decreasing mass ratio this quasi-Coulomb series merges into a pure Coulombic one.
We simultaneously measure the gravitationally-induced phase shift in two Raman-type matter-wave interferometers operated with laser-cooled ensembles of $^{87}$Rb and $^{39}$K atoms. Our measurement yields an Eötvös ratio of $η_{\text{Rb,K}}=(0.3\pm 5.4)\times 10^{-7}$. We briefly estimate possible bias effects and present strategies for future improvements.
We employ the Born-Oppenheimer approximation to find the effective potential in a three-body system consisting of a light particle and two heavy ones when the heavy-light short-range interaction potential has a resonance corresponding to a non-zero orbital angular momentum. In the case of an exact resonance in the p-wave scattering amplitude, the effective potential is attractive and long-range, namely it decreases as the third power of the inter-atomic distance. Moreover, we show that the range and power of the potential, as well as the number of bound states are determined by the mass ratio of the particles and the parameters of the heavy-light short-range potential.
The standard model of modern cosmology, which is based on the Friedmann-Lemaître-Robertson-Walker metric, allows the definition of an absolute time. However, there exist (cosmological) models consistent with the theory of general relativity for which such a definition cannot be given since they offer the possibility of time travel. The simplest of these models is the cosmological solution discovered by Kurt Gödel, which describes a homogeneous, rotating universe. Disregarding the paradoxes that come along with the abolishment of causality in such spacetimes, we are interested in the purely academical question how an observer would visually perceive the time travel of an object in Gödel's universe. For this purpose, we employ the technique of ray tracing, a standard tool in computer graphics, and visualize various scenarios to bring out the optical effects experienced by an observer located in this universe. In this way, we provide a new perspective on the space-time structure of Gödel's model.
We consider the scattering of an atom by a sequence of two near-resonant standing light waves each formed by two running waves with slightly different wave vectors. Due to opposite detunings of the two standing waves and within the rotating wave approximation, the adiabatic approximation applied to the atomic center-of-mass motion and a smooth turn-on and -off of the interaction, the dynamical phase cancels out and the final state of the atom differs from the initial one only by the sum of the two Berry phases accumulated in the two interaction regions. This phase depends on the position of the atom in a way such that the wave packet emerging from the scattering region will focus, which constitutes a novel method to observe the Berry phase without resorting to interferometric methods.
We propose a lens for atoms with reduced chromatic aberrations and calculate its focal length and spot size. In our scheme a two-level atom interacts with a near-resonant standing light wave formed by two running waves of slightly different wave vectors, and a far-detuned running wave propagating perpendicular to the standing wave. We show that within the Raman-Nath approximation and for an adiabatically slow atom-light interaction, the phase acquired by the atom is independent of the incident atomic velocity.
In recent years there has been an enormous progress in matter wave interferometry. The Colella- Overhauser-Werner (COW) type of neutron interferometer and the Kasevich-Chu (K-C) atom interferometer, are the prototype of such devices and the issue of whether they are sensitive to relativistic effects has recently aroused much controversy. We examine the question of to what extent the gravitational red shift, and the related twin paradox effect can be seen in both of these atom and neutron interferometers. We point out an asymmetry between the two types of devices. Because of this, the non-vanishing, non-relativistic residue of both effects can be seen in the neutron interferometer, while in the K-C interferometer the effects cancel out, leaving no residue, although they could be present in other types of atom interferometers. Also, the necessary shifting of the laser frequency (chirping) in the atom interferometer effectively changes the laboratory into a free-fall system, which could be exploited for other experiments.
Is it possible to trap a quantum particle in an open geometry? In this work we deal with the boundary value problem of the stationary Schroedinger (or Helmholtz) equation within a waveguide with straight segments and a rectangular bending. The problem can be reduced to a one dimensional matrix Schroedinger equation using two descriptions: oblique modes and conformal coordinates. We use a corner-corrected WKB formalism to find the energies of the one dimensional problem. It is shown that the presence of bound states is an effect due to the boundary alone, with no classical counterpart for this geometry. The conformal description proves to be simpler, as the coupling of transversal modes is not essential in this case.
Atom interferometry represents a quantum leap in the technology for the ultra-precise monitoring of accelerations and rotations and, therefore, for all the science that relies on the latter quantities. These sensors evolved from a new kind of optics based on matter-waves rather than light-waves and might result in an advancement of the fundamental detection limits by several orders of magnitude. Matter-wave optics is still a young, but rapidly progressing science. The Space Atom Interferometer project (SAI), funded by the European Space Agency, in a multi-pronged approach aims to investigate both experimentally and theoretically the various aspects of placing atom interferometers in space: the equipment needs, the realistically expected performance limits and potential scientific applications in a micro-gravity environment considering all aspects of quantum, relativistic and metrological sciences. A drop-tower compatible prototype of a single-axis atom interferometry accelerometer is under construction. At the same time the team is studying new schemes, e.g. based on degenerate quantum gases as source for the interferometer. A drop-tower compatible atom interferometry acceleration sensor prototype has been designed, and the manufacturing of its subsystems has been started. A compact modular laser system for cooling and trapping rubidium atoms has been assembled. A compact Raman laser module, featuring outstandingly low phase noise, has been realized. Possible schemes to implement coherent atomic sources in the atom interferometer have been experimentally demonstrated.
We report on the successful operation of an analogue computer designed to factor numbers. Our device relies solely on the interference of classical light and brings together the field of ultrashort laser pulses with number theory. Indeed, the frequency component of the electric field corresponding to a sequence of appropriately shaped femtosecond pulses is determined by a Gauss sum which allows us to find the factors of a number.
We consider a two-photon transition in a specific ladder system driven by a chirped laser pulse. In the weak field limit, we find that the excited state probability amplitude arises due to interference of multiple quantum paths which are weighted by quadratic phase factors. The excited state population has the form of a Gauss sum which plays a prominent role in number theory.
We study the mechanical effects of light on an atom trapped in a harmonic potential when an atomic dipole transition is driven by a laser and it is strongly coupled to a mode of an optical resonator. We investigate the cooling dynamics in the bad cavity limit, focussing on the case in which the effective transition linewidth is smaller than the trap frequency, hence when sideband cooling could be implemented. We show that quantum correlations between the mechanical actions of laser and cavity field can lead to an enhancement of the cooling efficiency with respect to sideband cooling. Such interference effects are found when the resonator losses prevail over spontaneous decay and over the rates of the coherent processes characterizing the dynamics.
We propose a scheme that allows to coherently extract cold atoms from a reservoir in a deterministic way. The transfer is achieved by means of radiation pulses coupling two atomic states which are object to different trapping conditions. A particular realization is proposed, where one state has zero magnetic moment and is confined by a dipole trap, whereas the other state with non-vanishing magnetic moment is confined by a steep microtrap potential. We show that in this setup a predetermined number of atoms can be transferred from a reservoir, a Bose-Einstein condensate, into the collective quantum state of the steep trap with high efficiency in the parameter regime of present experiments.
We draw attention to various aspects of number theory emerging in the time evolution of elementary quantum systems with quadratic phases. Such model systems can be realized in actual experiments. Our analysis paves the way to a new, promising and effective method to factorize numbers.
We connect three phenomena of wave packet dynamics: Talbot images, revivals of a particle in a box and fractional revivals. The physical origin of these effects is deeply rooted in phase factors which are quadratic in the quantum number. We show that the characteristic structures in the time evolution of these systems allow us to factorize large integers.
We consider a general central-field system in D dimensions and show that the division of the kinetic energy into radial and angular parts proceeds differently in the wavefunction picture and the Weyl-Wigner phase-space picture. Thus, the radial and angular kinetic energies are different quantities in the two pictures, containing different physical information, but the relation between them is well defined. We discuss this relation and illustrate its nature by examples referring to a free particle and to a ground-state hydrogen atom.
Quantum carpets are generic spacetime patterns formed in the probability distributions P(x,t) of one-dimensional quantum particles, first discovered in 1995. For the case of an infinite square well potential, these patterns are shown to have a detailed quantitative explanation in terms of a travelling-wave decomposition of P(x,t). Each wave directly yields the time-averaged structure of P(x,t) along the (quantised)spacetime direction in which the wave propagates. The decomposition leads to new predictions of locations, widths depths and shapes of carpet structures, and results are also applicable to light diffracted by a periodic grating and to the quantum rotator. A simple connection between the waves and the Wigner function of the initial state of the particle is demonstrated, and some results for more general potentials are given.
We propose to measure the quantum state of a single mode of the radiation field in a cavity---the signal field---by coupling it via a quantum-non-demolition Hamiltonian to a meter field in a highly squeezed state. We show that quantum state tomography on the meter field using balanced homodyne detection provides full information about the signal state. We discuss the influence of measurement of the meter on the signal field.