Dynamical Stability of Gap Soliton of One-Dimensional Condensate in Optical Lattices with Strong Interatomic Interaction

By developing the multiple scales method, we analytically study the dynamics properties of gap soliton of Bose- Einstein condensate in optical lattices. It is shown that the gap soliton will appear at Brillouin zone edge of linear band spectrum of the condensates when the interatomic interaction strength is larger than the lattice depth. Moreover, the density of gap soliton starts to be relatively small, while it increases with time and becomes stable.     

Quantum reflection of bright matter-wave solitons

We propose the use of bright matter-wave solitons formed from Bose-Einstein condensates with attractive interactions to probe and study quantum reflection from a solid surface at normal incidence. We demonstrate that the presence of attractive interatomic interactions leads to a number of advantages for the study of quantum reflection. The absence of dispersion as the soliton propagates allows precise control of the velocity normal to the surface and for much lower velocities to be achieved. Numerical modelling shows that the robust, self-trapped nature of bright solitons leads to a clean reflection from the surface, limiting the disruption of the density profile and permitting accurate measurements of the reflection probability.     

Quantum wave equations and non-radiating electromagnetic sources

A connection between classical non-radiating sources and free-particle wave equations in quantum mechanics is rigorously made. It is proven that free-particle wave equations for all spins have currents which can be defined and which are non-radiating electromagnetic sources. It is also proven that and the advanced and retarded fields are exactly equal for these sources. Implications of these results are discussed.     

Quantum anticentrifugal force for wormhole geometry

We show the existence of an anticentrifugal force in a wormhole geometry in R³. This counterintuitive force was shown to exist in a flat R² space. The role the geometry plays in the appearance of this force is discussed.     

Bose–Einstein condensates in magnetic waveguides

In this article, we describe an experimental system for generating Bose–Einstein condensates and controlling the shape and motion of a condensate by using miniaturised magnetic potentials. In particular, we describe the magnetic trap setup, the vacuum system, the use of dispenser sources for loading a high number of atoms into the magneto-optical trap, the magnetic transfer of atoms into the microtrap, and the experimental cycle for generating Bose–Einstein condensates. We present first results on outcoupling of condensates into a magnetic waveguide and discuss influences of the trap surface on the ultra-cold ensembles. Received: 21 August 2002 / Revised version: 10 December 2002 / Published online: 26 February 2003 RID="*" ID="*"Corresponding author. Fax: +49-7071/295-829, E-mail: fortagh@pit.uni-tuebingen.de     

Oscillatory motion in confined potential systems with dissipation in the context of the Schrödinger-Langevin-Kostin equation

The quantum dissipative motion of wave packets in confined systems with polynomial potentials is numerically investigated in the context of the Schrödinger-Langevin-Kostin equation. Oscillatory patterns are studied in detail and they confirm the validity of the correspondence principle. The transition to the stationary state is also discussed.     

Micromanipulation of neutral atoms with nanofabricated structures

A large variety of trapping and guiding potentials can be designed by bringing cold atoms close to charged or current carrying material objects. We describe the basic principles of constructing microscopic traps and guides and how to load atoms into them. The simplicity and versatility of these methods will allow for miniaturization and integration of atom optical elements into matter-wave quantum circuits on Atom Chips. These could form the basis for robust and widespread applications in atom optics, ranging from fundamental studies in mesoscopic physics to possibly quantum information systems. Received: 20 December 1999 / Revised version: 7 March 2000 / Published online: 5 April 2000     

Strong causality from weak via continuous monitoring

Repeated unbiased measurements cause a continual application of the weak causality principle, leading to an apparent arrow of time for continuously-monitored quantum systems.     

One-Dimensional Two-Component Bosons with Attractive Interaction

The Bethe-ansatz method is used to solve one-dimensional two-component bosons with a δ-function potential considering the negative coupling constant part. With the string hypothesis of Minoru Takahashi, the features of the ground state and low-lying excited states of this model are discussed explicitly by analytical and numerical methods. Especially for a N = 2 system, the two bosons being pairs is obvious, and the ground state which is independent of the coupling constant should be ferromagnetic.     

Modulational Instability of （1 ＋ 1）-Dimensional Bose-Einstein Condensate with Three-Body Interatomic Interaction

The modulational instability of Bose-Einstein condensate with three-body interatomic interaction and external harmonic trapping potential is investigated. Both of our analytical and numerical results show that the external potential will either cause the excitation of modulationally unstable modes or restrain the modulationally unstable modes from growing.     

Geometry,commutation relations and the quantum fictitious force

We express the commutation relation between the operators of the momentum and the radial unit vectors in D dimensions in differential and integral form. We connect this commutator with the quantum fictitious potential emerging in the radial Schr?dinger equation of an s-wave. Received: 6 August 2002 / Revised version: 30 October 2002 / Published online: 26 February 2003 RID="*" ID="*"Corresponding author. Fax: +49-731/502-3086, E-mail: markus.cirone@physik.uni-ulm.de     

Quantum Effects of Many Atoms in Spinor Bose-Einstein Condensates

We have studied the evolutions of the population transfer, tunnelling current and antibunching effects between spin-（＋1） and spin-（-1） in the case of the strong laser pulses. It is found that the population transfer and tunnelling current exhibit periodical oscillation. For the same Rabi frequency, the larger the atom number, the longer the oscillation period is. For the spin-（-1） component, when the atomic numbers are N=4 and 10, the antibunching effect can appear. For different atomic numbers, the appearing regions are very different. For spin component ＋1, the antibunching effect can always appear for different atomic numbers.     

Quantum tomograms from intermediate entangled states

We show that for quantum tomography there exist two mutually conjugating intermediate coordinate-momentum entangled states |η₁,η_2〉λ,ν and |?₁,?_2〉σ,τ. The Radon transforms of the Wigner operators are just the pure-state density matrices and , respectively. As a result, the tomogram of quantum states is the module-square of their wave function in these representations. A new convenient formalism of quantum tomogram is thus established.     

Build-up of coherence between initially-independent subsystems: The case of Bose-Einstein condensates

When initially-independent subsystems are made to contact, coherence can develop due to interaction between them. We exemplify and demonstrate this paradigm through several scenarios of two initially-independent Bose-Einstein condensates which are allowed to collide. The build-up of coherence depends strongly on time, interaction strength and other parameters of each condensate. Implications are discussed.     

A neutral atom and a wire: towards mesoscopic atom optics

A large variety of trapping and guiding potentials can be designed by bringing cold atoms close to charged or current-carrying material objects. Using a current-carrying wire we demonstrate how to build guides and traps for neutral atoms and using a charged wire we study a 1/r ² singularity. The simplicity and versatility of the principles demonstrated in our experiments will allow for miniaturization and integration of atom optical elements into matter-wave quantum circuits. Received: 13 December 1998 / Revised version: 8 July 1999 / Published online: 8 September 1999     

Quantum and classical divide: the gravitational case

We study the transition between quantum and classical behaviour of particles in a gravitational quantum well. We analyze how an increase in the particles mass turns the energy spectrum into a continuous one, from an experimental point of view. We also discuss the way these effects could be tested by conducting experiments with atoms and fullerene-type molecules.     

Quantum reflection

Recent experimental and theoretical results concerning the sticking coefficient at ultralow energy are described. The need for an accurate treatment of long range forces, including retardation, is emphasized. The system involving H atoms incident on liquid helium provides the first clear evidence of quantum reflection. New results are reported for the sticking of D atoms incident on helium. The energy upper bound for the regime of quantum reflection for alkali atoms is found to be extremely low, but ultimately achievable.     

Photodetachment of a Negative Hydrogen Molecular Ion near an Interface

Photodetachment of a negative hydrogen molecular ion near an interface is studied by using the two-centre model and the closed orbit theory. The calculation results show that the photodetachment cross section is related to the distance between the two centres in the H₂^- and different molecular ion-interface distances. The comparison between the cross section of H₂^- near an interface with the section of Hˉ shows that at the equilibrium distance of two centres and at low photon energy, the photodetachment cross section of H₂^- is about twice the cross section of Hˉ, which shows that the interference of the two nuclei is very strong; when the distance between the two centres is large, the section of H₂^- is almost the same as the cross section of Hˉ near one interface, which indicates that the interference effect of the two centres anishes.     

Quantum particles from coarse grained classical probabilities in phase space

Quantum particles can be obtained from a classical probability distribution in phase space by a suitable coarse graining, whereby simultaneous classical information about position and momentum can be lost. For a suitable time evolution of the classical probabilities and choice of observables all features of a quantum particle in a potential follow from classical statistics. This includes interference, tunneling and the uncertainty relation.     

Van der Waals interactions and Photoelectric Effect in Noncommutative Quantum Mechanics

We calculate the long-range Van der Waals force and the photoelectric cross section in a noncommutative setup. It is argued that non-commutativity effects could not be discerned for the Van der Waals interactions. The result for the photoelectric effect shows deviation from the usual commutative one, which in principle can be used to put bounds on the space-space non-commutativity parameter.