The survival probability $P(c,t)$ of a random walk of $t$ steps with static traps at concentration $c$ is studied in two and three dimensions by an efficient Monte Carlo method based on a mapping onto a polymer model. On the basis of the theoretical work of Donsker and Varadhan [Commun. Pure Appl. Math. 28, 525 (1975); 32, 721 (1979)] and of Rosenstock [J. Math. Phys. (N.Y.) 11, 487 (1970)] one expects a data collapse for $-\ln \left[P\right(c,t\left)\right]/\ln \left(t\right)$ plotted vs $\sqrt{\lambda t}/\ln \left(t\right)$ [with $\lambda =-\ln (1-c)$], in two dimensions, and for ${-t}^{-1/3\mathrm{}}\ln \left[P\right(c,t\left)\right]$ vs $t^{2/3}\lambda$ in three dimensions. These predictions are well supported by the Monte Carlo results.

We have performed time-domain interferometry experiments with matter waves trapped in a harmonic potential above and below the Bose-Einstein phase transition, by means of the method of separated oscillating fields, with a variable time delay $T$. We observe the oscillations of the population between two internal Zeeman states versus the delay $T$ to be rapidly depleted both below and slightly above Bose-Einstein condensation. We give a quantitative explanation in terms of the phase evolution due to the entanglement between the internal and external degrees of freedom.

We present one-dimensional local potentials with an absolute reflection at a given energy value which can be above barriers. The corresponding energy dependence of a reflection coefficient exhibits resonance behavior. The inversion technique provides the potentials with specified widths of reflection resonances, their number and positions. The multichannel systems (exact models) with a complete reflection are also given.

We report on the measurement of the temporal coherence of an atom laser beam extracted from a ${}^{87}\mathrm{Rb}$ Bose-Einstein condensate. Reflecting the beam from a potential barrier creates a standing matter wave structure. From the contrast of this interference pattern, observed by magnetic resonance imaging, we have deduced an energy width of the atom laser beam which is Fourier limited by the duration of output coupling. This gives an upper limit for temporal phase fluctuations in the Bose-Einstein condensate.

Bose-Einstein condensates of rubidium atoms are stored in a two-dimensional periodic dipole force potential, formed by a pair of standing wave laser fields. The resulting potential consists of a lattice of tightly confining tubes, each filled with a 1D quantum gas. Tunnel coupling between neighboring tubes is controlled by the intensity of the laser fields. By observing the interference pattern of atoms released from more than 3000 individual lattice tubes, the phase coherence of the coupled quantum gases is studied. The lifetime of the condensate in the lattice and the dependence of the interference pattern on the lattice configuration are investigated.

The occurrence of phase fluctuations due to thermal excitations in Bose-Einstein condensates (BECs) is studied for a variety of temperatures and trap geometries. We observe the statistical nature of the appearance of phase fluctuations and characterize the dependence of their average value on temperature, number of particles, and the trapping potential. We find pronounced phase fluctuations for condensates in very elongated traps in a broad temperature range. The results are of great importance for the realization of BEC in quasi-1D geometries, for matter wave interferometry with BECs, as well as for coherence properties of guided atom laser beams.

An effective field theory for the three-body system with large two-body scattering length $a$ is applied to three-body recombination into deep bound states in a Bose gas. The recombination constant $\alpha$ is calculated to first order in the short-distance interactions that allow the recombination. For $a<\mathrm{}0\mathrm{}$, the dimensionless combination $m\alpha /\left(ħa^4\right)$ is a periodic function of $\ln |a|$ that exhibits resonances at values of $a$ that differ by multiplicative factors of 22.7. This dramatic behavior should be observable near a Feshbach resonance when $a$ becomes large and negative.

We theoretically examine photoassociation of a nonideal Bose-Einstein condensate, focusing on evidence for a macroscopic superposition of atoms and molecules. This problem raises an interest because, rather than two states of a given object, an atom-molecule system is a seemingly impossible macroscopic superposition of different objects. Nevertheless, photoassociation enables coherent intraparticle conversion, and we thereby propose a viable scheme for creating a superposition of a macroscopic number of atoms with a macroscopic number of molecules.

We introduce a time-dependent projected Gross-Pitaevskii equation to describe a partially condensed homogeneous Bose gas, and find that this equation will evolve randomized initial wave functions to equilibrium. We compare our numerical data to the predictions of a gapless, second order theory of Bose-Einstein condensation [S. A. Morgan, J. Phys. B 33, 3847 (2000)], and find that we can determine a temperature when the theory is valid. As the Gross-Pitaevskii equation is nonperturbative, we expect that it can describe the correct thermal behavior of a Bose gas as long as all relevant modes are highly occupied. Our method could be applied to other boson fields.

We show that high-temperature expansions provide a basis for the novel approach to efficient Monte Carlo simulations. “Worm” algorithms utilize the idea of updating closed-path configurations (produced by high-temperature expansions) through the motion of end points of a disconnected path. An amazing result is that local, Metropolis-type schemes using this approach appear to have dynamical critical exponents close to zero (i.e., their efficiency is comparable to the best cluster methods) as proved by finite-size scaling of the autocorrelation time for various universality classes.

We demonstrate that structures made of light can be used to coherently control the motion of complex molecules. In particular, we show diffraction of the fullerenes ${\mathrm{C}}_{60}$ and ${\mathrm{C}}_{70}$ at a thin grating based on a standing light wave. We prove experimentally that the principles of this effect, well known from atom optics, can be successfully extended to massive and large molecules which are internally in a thermodynamic mixed state and which do not exhibit narrow optical resonances. Our results will be important for the observation of quantum interference with even larger and more complex objects.

We report the creation of an entangled multiphoton quantum superposition by quantum injection of entangled 2-photon states into a parity selective parametric amplifier. The information preserving property of the state transformation suggests for these macrostates the name of large qubits. They are ideal objects for investigating the emergence of the classical world in complex quantum systems and have relevant new applications in quantum information.

A symbolic language allowing one to solve statistical problems for the systems with non-Abelian braidlike topology in $2+1$ dimensions is developed. The approach is based on the similarity between a growing braid and a “heap of colored pieces.” As an application, the problem of a vortex glass transition in high- $T_c$ superconductors is reexamined on a microscopic level.

We consider the steady state of an open system in which there is a flux of matter between two reservoirs at different chemical potentials. For a large system of size $N$, the probability of any macroscopic density profile $\rho \left(x\right)$ is $\exp [-NF(\{\rho \}\left)\right]$; $F$ thus generalizes to nonequilibrium systems the notion of free energy density for equilibrium systems. Our exact expression for $F$ is a nonlocal functional of $\rho$, which yields the macroscopically long range correlations in the nonequilibrium steady state previously predicted by fluctuating hydrodynamics and observed experimentally.

We show that an ensemble of spinor Bose-Einstein condensates confined in a one-dimensional optical lattice can undergo a ferromagnetic phase transition and spontaneous magnetization arises due to the magnetic dipole-dipole interaction. This phenomenon is analogous to ferromagnetism in solid state physics, but occurs with bosons instead of fermions.

In this paper we study a gaseous Bose-Einstein condensate and show the following: (i) A minimum value of the interaction is needed for the existence of stable persistent currents. (ii) Vorticity is not a fundamental invariant of the system, as there exists a conservative mechanism which can destroy a vortex and change its sign. (iii) This mechanism is suppressed by strong interactions.

Classical periodic orbits associated with the nonadiabatic dynamics of a spin-boson-type problem are introduced. To facilitate a classical description of spin states, the formulation employs an exact mapping of the discrete quantum variables onto continuous degrees of freedom. Adopting a one-dimensional spin-boson model, the shortest periodic orbits of the problem are identified and used to analyze the nonadiabatic quantum dynamics. The possibility of directly observing these vibronic periodic orbits in femtosecond time-resolved experiments is discussed.

The transverse coherence of x rays was measured with an intensity interferometer using a $120-\mu \mathrm{eV}$-bandwidth monochromator operating at 14.41 keV. By analyzing the transverse coherence profiles, a vertical source profile of a 25-m long undulator of SPring-8, as well as the coherence degradation by a phase object in the beam path, were quantitatively characterized.

We have loaded Bose-Einstein condensates into one-dimensional, off-resonant optical lattices and accelerated them by chirping the frequency difference between the two lattice beams. For small values of the lattice well depth, Bloch oscillations were observed. Reducing the potential depth further, Landau-Zener tunneling out of the lowest lattice band, leading to a breakdown of the oscillations, was also studied and used as a probe for the effective potential resulting from mean-field interactions as predicted by Choi and Niu [Phys. Rev. Lett. 82, 2022 (1999)]. The effective potential was measured for various condensate densities and trap geometries, yielding good qualitative agreement with theoretical calculations.

The structure and dynamics of the domain walls separating segregated condensates in trapped mixtures of repulsive Bose-Einstein condensates are studied. Our work reveals that, under fairly general conditions, these domain walls behave as independent dynamical entities, which allows us to identify them as constituting a novel class of multicomponent solitons in Bose-Einstein condensates.