We variationally determine the dynamics of bright soliton trains composed of harmonically trapped Bose-Einstein condensates with attractive interatomic interactions. In particular, we obtain the interaction potential between two solitons. We also discuss the formation of soliton trains due to the quantum mechanical phase fluctuations of a one-dimensional condensate.

The appearance of body-frame singularities in gauge potentials when three collective angles are separated by means of Wigner $D$-functions is a fundamental difficulty in the quantum $N$-body problem. We show that the use of the overcomplete basis of minimal multipolar harmonics allows these singularities to be avoided at the expense of increasing the dimension of the resulting system of coupled equations describing the internal motion of the system.

We have measured the index of refraction for sodium de Broglie waves in gases of Ar, Kr, Xe, and ${\mathrm{N}}_2$ over a wide range of sodium velocities. We observe glory oscillations—a velocity-dependent oscillation in the forward scattering amplitude. An atom interferometer was used to observe glory oscillations in the phase shift caused by the collision, which are larger than glory oscillations observed in the cross section. The glory oscillations depend sensitively on the shape of the interatomic potential, allowing us to discriminate among various predictions for these potentials, none of which completely agrees with our measurements.

We have measured the complete Wigner function $W$ of the vacuum and of a single-photon state for a field stored in a high-$Q$ cavity. This experiment implements the direct Lutterbach and Davidovich method [L. G. Lutterbach and L. Davidovich, Phys. Rev. Lett. 78, 2547 (1997)] and is based on the dispersive interaction of a single circular Rydberg atom with the cavity field. The nonclassical nature of the single-photon field is exhibited by a region of negative $W$ values. Extensions to other nonclassical cavity field states are discussed.

We study experimentally the line of a single quantized vortex in a rotating prolate Bose-Einstein condensate confined by a harmonic potential. In agreement with predictions, we find that the vortex line is in most cases curved at the ends. We monitor the vortex line leaving the condensate. Its length is measured as a function of time and temperature. For a low temperature, the survival time can be as large as 10 sec. The length of the line and its deviation from the center of the trap are related to the angular momentum per particle along the condensate axis.

We consider a mesoscopic measuring device whose conductance is sensitive to the state of a two-level system. The detector is described with the help of its scattering matrix. Its elements can be used to calculate the relaxation and decoherence times of the system, and determine the characteristic time for a reliable measurement. We derive conditions needed for an efficient ratio of decoherence and measurement times. To illustrate the theory we discuss the distribution function of the efficiency of an ensemble of open chaotic cavities.

We show that for one-dimensional fluids the thermal conductivity generically diverges with system size $L$ as $L^{1/3}$, as a result of momentum conservation. Our results are consistent with the largest-scale numerical studies of two-component hard-particle systems. We suggest explanations for the apparent disagreement with studies on Fermi-Pasta-Ulam chains.

Vortices were imprinted in a Bose-Einstein condensate using topological phases. Sodium condensates held in a Ioffe-Pritchard magnetic trap were transformed from a nonrotating state to one with quantized circulation by adiabatically inverting the magnetic bias field along the trap axis. Using surface wave spectroscopy, the axial angular momentum per particle of the vortex states was found to be consistent with $2\hslash$ or $4\hslash$, depending on the hyperfine state of the condensate.

We calculate the dependence of the Casimir force on the isotopic composition of the interacting objects. This dependence arises from the subtle influence of the nuclear masses on the electronic properties of the bodies. We discuss the relevance of these results to current experiments utilizing the isoelectronic effect to search at very short separations for new weak forces suggested by various unification theories.

We produce a quantum degenerate mixture composed by two Bose-Einstein condensates of different atomic species, ${}^{\mathrm{41}}\mathrm{K}$ and ${}^{\mathrm{87}}\mathrm{R}\mathrm{b}$. We study the dynamics of the superfluid system in an elongated magnetic trap, where off-axis collisions between the two interacting condensates induce scissorlike oscillations.

We consider the hydrodynamic modes for dense trapped ultracold gases, where the interparticle distance is comparable to the scattering length. We show that the experimental determination of the hydrodynamic mode frequencies allows one to obtain quite directly the equation of state of a dense gas. As an example, we investigate the case of two equal fermionic populations in different hyperfine states with attractive interaction.

We consider systems whose steady states exhibit a nonequilibrium phase transition from an active state to one—among an infinite number—absorbing state, as some control parameter is varied across a threshold value. The pair contact process, stochastic fixed-energy sandpiles, activated random walks, and many other cellular automata or reaction-diffusion processes are covered by our analysis. We argue that the upper-critical dimension below which anomalous fluctuation driven scaling appears is $d_c=6$, in contrast to a widespread belief. We provide the exponents governing the critical behavior close to or at the transition point to first order in an $\epsilon =6-d$ expansion.

An attractive Bose-Einstein condensate with a vortex splits into two pieces via the quadrupole dynamical instability, which arises at a weaker strength of interaction than the monopole and the dipole instabilities. The split pieces subsequently unite to restore the original vortex or collapse.

We propose a quantum device that can approximate any projective measurement on a qubit—a quantum “multimeter.” The desired measurement basis is selected by the quantum state of a “program register.” Two different kinds of programs are considered and in both cases the device is optimized with respect to maximal average fidelity (assuming uniform distribution of measurement bases). Quantum multimeters exhibiting the covariance property are introduced and an optimal covariant multimeter with a single-qubit program register is found. Possible experimental realization of the simplest proposed device is presented.

We have analyzed kinetic roughening in Fe-Cr superlattices by energy-filtered transmission electron microscopy. The direct access to individual interfaces provides both static and dynamic roughness exponents. We find an anomalous non-self-affine scaling of the interface roughness with a time dependent local roughness at short length scales. While the deposition conditions affect strongly the long-range dynamics, the anomalous short-range exponent remains unchanged. The different short- and long-range dynamics outline the importance of long-range interactions in kinetic roughening.

Systematic inaccuracy is inherent in any computational estimate of a nonlinear average, due to the availability of only a finite number of data values, $N$. Free energy differences $\Delta F$ between two states or systems are critically important examples of such averages. Previous work has demonstrated, empirically, that the “finite-sampling error” can be very large—many times $k_{B}T$—in $\Delta F$ estimates for simple molecular systems. Here we present a theoretical description of the inaccuracy, including the exact solution of a sample problem, the precise asymptotic behavior in terms of $1/N$ for large $N$, the identification of a universal law, and numerical illustrations. The theory relies on corrections to the central and other limit theorems.

Recent Feshbach-resonance experiments with ${}^{\mathrm{85}}\mathrm{R}\mathrm{b}$ Bose-Einstein condensates have led to a host of unexplained results: dramatic losses of condensate atoms for an across-resonance sweep of the magnetic field, a collapsing condensate with a burst of atoms emanating from the remnant condensate, increased losses for decreasing interaction times, and coherent oscillations between remnant and burst atoms. Using a simple yet realistic mean-field model, we find that rogue dissociation, molecular dissociation to noncondensate atom pairs, is strongly implicated as the physical mechanism responsible for these observations.

In a recent experiment, a Feshbach scattering resonance was exploited to observe Ramsey fringes in a ${}^{\mathrm{85}}\mathrm{R}\mathrm{b}$ Bose-Einstein condensate. The oscillation frequency corresponded to the binding energy of the molecular state. We show that the observations are remarkably consistent with predictions of a resonance field theory in which the fringes arise from oscillations between atoms and molecules.

We consider the amount of work which can be extracted from a heat bath using a bipartite state $\rho$ shared by two parties. In general it is less then the amount of work extractable when one party is in possession of the entire state. We derive bounds for this “work deficit” and calculate it explicitly for a number of different cases. In particuar, for pure states the work deficit is exactly equal to the distillable entanglement of the state. A form of complementarity exists between physical work which can be extracted and distillable entanglement. The work deficit is a good measure of the quantum correlations in a state and provides a new paradigm for understanding quantum nonlocality.

We present large scale simulations for a one-dimensional chain of hard-point particles with alternating masses and correct several claims in recent literature based on much smaller simulations. We find heat conductivities $\kappa$ to diverge with the number $N$ of particles. These depended strongly on the mass ratio, and extrapolations to $N\to \infty$, and $t\to \infty$, are difficult due to very large finite-size and finite-time corrections. Nevertheless, our data seem compatible with a universal power law $\kappa \sim N^{\alpha }$ with $\alpha \approx 0.33$ suggesting a relation to the Kardar-Parisi-Zhang model. We finally discuss why the system leads nevertheless to energy dissipation and entropy production, in spite of not being chaotic in the usual sense.