Sound propagation has been studied in a magnetically trapped dilute Bose-Einstein condensate. Localized excitations were induced by suddenly modifying the trapping potential using the optical dipole force of a focused laser beam. The resulting propagation of sound was observed using a novel technique, rapid sequencing of nondestructive phase-contrast images. The speed of sound was determined as a function of density and found to be consistent with Bogoliubov theory. This method may generally be used to observe high-lying modes and perhaps second sound.

By using the method of orthogonal polynomials, we analyze the statistical properties of complex eigenvalues of random matrices describing a crossover from Hermitian matrices characterized by the Wigner-Dyson statistics of real eigenvalues to strongly non-Hermitian ones whose complex eigenvalues were studied by Ginibre. Two-point statistical measures [as, e.g., spectral form factor, number variance, and small distance behavior of the nearest neighbor distance distribution $p\left(s\right)$] are studied in more detail. In particular, we found that the latter function may exhibit unusual behavior $p\left(s\right)\propto s^{5/2}$ for some parameter values.

We have numerically determined the behavior of the magnetic susceptibility upon approach of the critical point in two-dimensional spin systems with an interaction range that was varied over nearly 2 orders of magnitude. The full crossover from classical to Ising-like critical behavior, spanning several decades in the reduced temperature, could be observed. Our results convincingly show that the effective susceptibility exponent ${\gamma }_{\mathrm{eff}}$ changes nonmonotonically from its classical to its Ising value when approaching the critical point in the ordered phase. In the disordered phase the behavior is monotonic. Furthermore, the hypothesis that the crossover function is universal is supported.

A variant of self-similar approximation theory is suggested, permitting an easy and accurate summation of divergent series consisting of only a few terms. The method is based on a power-law algebraic transformation, whose powers play the role of control functions governing the fastest convergence of the renormalized series. A striking relation between the theory of critical phenomena and optimal control theory is discovered: The critical indices are found to be directly related to limits of control functions at critical points. The method is applied to calculating the critical indices for several difficult problems. The results are in very good agreement with accurate numerical data.

We have used three-body recombination rates as a sensitive probe of the statistical correlations between atoms in Bose-Einstein condensates (BEC) and in ultracold noncondensed dilute atomic gases. We infer that density fluctuations are suppressed in the BEC samples. We measured the three-body recombination rate constants for condensates and cold noncondensates from number loss in the ${F=1,m}_f=-1\mathrm{}$ hyperfine state of ${}^{87}\mathrm{Rb}$. The ratio of these is $7.4\left(2.6\right)$ which agrees with the theoretical factor of $3!$ and demonstrates that condensate atoms are less bunched than noncondensate atoms.

Pairs of atoms have been prepared in an entangled state of the Einstein-Podolsky-Rosen (EPR) type. They were produced by the exchange of a single photon between the atoms in a high $Q$ cavity. The atoms, entangled in a superposition involving two different circular Rydberg states, were separated by a distance of the order of 1 cm. At variance with most previous EPR experiments, this one involves massive particles. It can be generalized to three or more atoms and opens the way to new tests of nonlocality in mesoscopic quantum systems.

We investigate quantum Brownian motion in adiabatically rocked ratchet systems. Above a crossover temperature $T_c$ tunneling events are rare, yet they already substantially enhance the classical particle current. Below $T_c$, quantum tunneling prevails and the classical predictions grossly underestimate the transport. Upon approaching $T=0\mathrm{}$ the quantum current exhibits a tunneling induced reversal, and tends to a finite limit.

We present a master equation governing the reduced density operator for a single trapped mode of a cold, dilute, weakly interacting Bose gas, and we obtain an operator fluctuation-dissipation relation in which the Ginzburg-Landau effective potential plays a physically transparent role. We also identify a decoherence effect that tends to preserve symmetry, even when the effective potential has a “Mexican hat” form.

Bialek, Callan, and Strong have recently given a solution of the problem of determining a continuous probability distribution from a finite set of experimental measurements by formulating it as a one-dimensional quantum field theory. This Letter gives a reparametrization invariant solution of the problem, obtained by coupling to gravity. The case of a large number of dimensions is also formulated geometrically, and solved, in terms of metrics of vanishing Weyl curvature.

We analyze theoretically an experiment in which a trapped Bose-Einstein condensate is cut in half, and the parts are subsequently allowed to interfere. If the delay between cutting and atom detection is small, the interference pattern of the two halves of the condensate is the same in every experiment. However, for longer delays the spatial phase of the interference shows random fluctuations from one experiment to the other. This phase diffusion is characterized quantitatively.

Simultaneous solitary wave solutions for laser propagation in nonlinear parametric media with up to ( $3+1$) dimensions are proved to exist. The combination of the large dispersion of a Bragg grating and the strong nonlinearity of ${\chi }^{\left(2\right)}$ optical material results in stable behavior with short interaction distances and low power requirements. The solutions are obtained by using the effective mass approximation to reduce the coupled propagation equations to those describing a dispersive parametric nonlinear waveguide, and are verified by solving the complete set of coupled band-gap equations numerically.

An unambiguous microscopic description of the semion statistics is developed by analyzing Haldanes's counting formula for $g=1\mathrm{}/2$. The description thus obtained is shown to be completely consistent with the general principles of statistical mechanics—no negative probabilities appear anywhere. Extensions of these results to the statistics corresponding values of $g=1\mathrm{}/m$ are briefly discussed.

Effective field theories of two-dimensional lattice models of fluctuating loops are constructed by mapping them onto random surfaces whose large scale fluctuations are described by a Liouville field theory. This provides a geometrical view of conformal invariance in two-dimensional critical phenomena and a method for calculating critical properties of loop models exactly. As an application of the method, the conformal charge and critical exponents for two mutually excluding Hamiltonian walks on the square lattice are calculated.

The dynamics of a globally neutral system of diffusing Coulomb charges in two dimensions, driven by an applied electric field, is studied in a wide temperature range around the Berezinskiĭ-Kosterlitz-Thouless transition. I argue that the commonly accepted “free particle drift” mechanism of charge transport in this system is limited to relatively low particle densities. For higher densities, I propose a modified picture involving collective “partner transfer” between bound pairs. The new picture provides a natural explanation for recent experimental and numerical findings which deviate from standard theory. It also clarifies the origin of dynamical scaling in this context.

The macroscopic interference of two Bose condensates released from a double minimum potential has been demonstrated recently [M. R. Andrews et al., Science 275, 637 (1997)]. In this Letter we show the excellent agreement between those experiments and theoretical predictions based on the nonlinear Schrödinger equation. In addition, the transition from interference of coupled condensates, comparable with the Josephson effect in superconductors, to the interference of independent Bose condensates is studied.

A new class of identical particles which may exhibit both Bose and Fermi statistics with respective probabilities $p_b$ and $p_f$ is introduced. Such an uncertainty may be either an intrinsic property of a particle or can be viewed as an “experimental uncertainty.” Statistical equivalence of such particles and particles obeying parastatistics of infinite order is shown. Generalized statistical distributions are derived, and statistical and thermodynamical properties of an ideal gas of the particles are investigated. The physical nature of such particles and the implications of this investigation for the statistics of extremal black holes are discussed.

We report short-term memory formation in a nonlinear dynamical system with many degrees of freedom. The system “remembers” a sequence of impulses for a transient period, but it coarsens and eventually “forgets” nearly all of them. The memory duration increases as the number of degrees of freedom in the system increases. We demonstrate the existence of these transient memories in a laboratory experiment.

We investigate the thermodynamics of a Bose gas interacting with repulsive forces and confined in a harmonic trap. We show that the relevant parameters of the system (temperature, number $N$ of atoms, harmonic oscillator length, deformation of the trap, $s$-wave scattering length) fix its thermodynamic behavior in the large $N$ limit through two dimensionless scaling parameters. These are the reduced temperature $t=T/T_c^0$ and the ratio $\eta$ between the $T=0\mathrm{}$ value of the chemical potential, evaluated in the Thomas-Fermi limit, and the critical temperature $T_c^0$ of the noninteracting model. The scaling functions relative to the condensate fraction, energy, chemical potential, and moment of inertia are calculated within the Popov approximation.

We present a quantitative evaluation of the predictions of mean-field theory for describing a Bose-Einstein condensate in a magnetic trap by comparing directly with experimental observations. We study the release energy from ballistic expansion and the cloud density profile as a function of mean-field effects. Significant departure of the cloud shape from both the noninteracting limit and the strongly repulsive limit is observed for our parameters, consistent with theoretical prediction.