We have observed the cold collision frequency shift of the $1S$- $2S$ transition in trapped spin-polarized atomic hydrogen. We find $\Delta {\nu }_{1S-2S}=-3.8\mathrm{}\pm 0.8\times {10}^{-10\mathrm{}}n\mathrm{Hz}{\mathrm{cm}}^3$, where $n$ is the sample density. From this we derive the $1S$- $2S$ $s$-wave triplet scattering length, $a_{1S-2S}=-1.4\mathrm{}\pm 0.3\mathrm{nm}$, which is in fair agreement with a recent calculation. The shift provides a valuable probe of the distribution of densities in a trapped sample.

We report observation of Bose-Einstein condensation (BEC) of a trapped, dilute gas of atomic hydrogen. The condensate and normal gas are studied by two-photon spectroscopy of the $1S$- $2S$ transition. Interactions among the atoms produce a shift of the resonance frequency proportional to density. The condensate is clearly distinguished by its large frequency shift. The peak condensate density is $4.8\pm 1.1\times {10}^{15}{\mathrm{cm}}^{-3\mathrm{}}$, corresponding to a condensate population of ${10}^9$ atoms. The BEC transition occurs at about $T=50\mathrm{}\mu \mathrm{K}$ and $n=1.8\mathrm{}\times {10}^{14}{\mathrm{cm}}^{-3\mathrm{}}$.

I discuss a simple numerical algorithm for direct evaluation of multiple Grassmann integrals. The approach is exact, suffers no fermion sign problems, and allows arbitrarily complicated interactions. Memory requirements grow exponentially with the interaction range and the transverse size of the system. Low dimensional systems with 1000 Grassmann variables can be evaluated on a workstation. The technique is illustrated with a spinless fermion hopping along a one dimensional chain.

Shallow water waves are studied using a nonlinear wave equation (W2) derived from Euler's equations by Whitham's method: W2 is the Korteweg–de Vries (KdV) equation plus higher-order correction terms. By projecting numerical simulations of W2 onto the soliton and radiation modes of the inverse scattering transform for the KdV equation we (i) generalize the soliton concept to higher order, (ii) provide a rigorous interpretation of a new soliton resonance effect, (iii) demonstrate that solitons and radiation undergo inelastic collisions, and (iv) find evidence for soliton creation and destruction.

A Franson-type test of Bell inequalities by photons 10.9 km apart is presented. Energy-time entangled photon pairs are measured using two-channel analyzers, leading to a violation of the inequalities by 16 standard deviations without subtracting accidental coincidences. Subtracting them, a two-photon interference visibility of $95.5\%$ is observed, demonstrating that distances up to 10 km have no significant effect on entanglement. This sets quantum cryptography with photon pairs as a practical competitor to the schemes based on weak pulses.

New physical insight into the correspondence between path integral concepts and the Schrödinger formulation is gained by the analysis of the effective classical potential, which is defined within the Feynman path integral formulation of statistical mechanics. This potential is related to the quasistatic response of the equilibrium system to an external force. These findings allow for a comprehensive formulation of dynamical approximations based on this potential.

The classical ground state of a $D$-dimensional many body system with two and three body interactions is studied as a function of the strength of the three body interaction. We prove exactly that beyond a critical strength of the three body interaction the classical ground state of the system is one in which all the particles are on a line. The positions of the particles in this string configuration are uniquely determined by the zeros of the Hermite polynomials.

We analyze the coherent formation of molecular Bose-Einstein condensate (BEC) from an atomic BEC, using a parametric field theory approach. We point out the transition between a quantum soliton regime, where atoms couple in a local way to a classical soliton domain, where a stable coupled-condensate soliton can form in three dimensions. This gives the possibility of an intense, stable atom-laser output.

Experiments with dielectric scatterers in a parallel-plate waveguide have verified for the first time the existence of proximity resonances in two dimensions. A numerical solution to the scattering problem supports the analysis of the experimental data.

To understand the physics of muscle contraction and molecular motor movement, we develop a model for nonequilibrium free energy transduction based on a diffusion in a periodic force field. It is shown that a nonconservative force is sufficient and necessary for a steady state with circular flux, but is not sufficient for a global unidirectional transport synonymous to motor protein movement. A vector potential for the flux is introduced for characterizing the circular flux and global transport. The model provides a natural distinction between the two types of muscle protein movement, namely the mechanical dominant “power-stroke” and the Brownian-motion dominant ratchet.

Linden, Massar, and Popescu have recently given an optimization argument to show that a single two-qubit Werner state, or any other mixture of the maximally entangled Bell states, cannot be purified by local operations and classical communications. We generalize their result and give a simple explanation. In particular, we show that no purification scheme using local operations and classical communications can produce a pure singlet from any mixed state of two spin- $1/2$ particles. More generally, no such scheme can produce a maximally entangled state of any pair of finite-dimensional systems from a generic mixed state. We also show that the Werner states belong to a large class of states whose fidelity cannot be increased by such a scheme.

The new process of quantum injection into an optical parametric amplifier operating in entangled configuration is adopted to “amplify” into a large dimensionality spin- $\frac{1}{2}$ Hilbert space the quantum entanglement and superposition properties of the photon couples generated by parametric down-conversion. The structure of the Wigner function and of the field's correlation functions shows a decoherence-free multiphoton Schroedinger-cat behavior of the emitted field which is largely detectable against the squeezed-vacuum noise.

Continuous quantum measurement theory is used to construct a phenomenological description of the interaction of a quasiclassical variable $X$ with a quantum variable $x$, where the quasiclassical nature of $X$ is assumed to have come about as a result of decoherence. The state of the quantum subsystem evolves according to the stochastic nonlinear Schrödinger equation of a continuously measured system, and the classical system couples to a stochastic $c$ number $\overline{x}\left(t\right)$ representing the imprecisely measured value of $x$. The theory gives intuitively sensible results even when the quantum system starts out in a superposition of well-separated localized states.

We show that stochastic resonance (SR)-like phenomena in a nonlinear system can be described in terms of maximization of information-theoretic distance measures between probability distributions of the output variable or, equivalently, via a minimum probability of error in detection. This offers a new and unifying framework for SR-like phenomena in which the “resonance” becomes independent of the specific method used to measure it, the static or dynamic character of the nonlinear device in which it occurs, and the nature of the input signal. Our approach also provides fundamental limits of performance and yields an alternative set of design criteria for optimization of the information processing capabilities of nonlinear devices.

The influence of parametric noise on the spatiotemporal dynamics of a two-variable reaction-diffusion model, describing pattern formation in excitable media, is investigated. When a control parameter is perturbed by stochastic force with suitable intensity, noise induced pattern transition between “single” spiral wave and “double” spiral waves, which does not occur in the absence of noise, is observed. If this parameter also varies periodically in time around the bifurcation point, we find that the output signal-to-noise ratios show maxima with the variation of noise intensity, indicating the occurrence of spatiotemporal stochastic resonance.

A classically forbidden, transitory enhancement of the high positive momentum components of a quantum wave packet during its collision with a potential barrier is described. A quantity is defined to measure its importance; the universality of the effect is justified, and its main features are studied with the aid of an analytically solvable model. Its relation to other “anomalously high velocities” is also examined.

We introduce a parameter $p$ called partial survival in the persistence of stochastic processes and show that for smooth processes the persistence exponent $\theta \left(p\right)$ changes continuously with $p$, $\theta \left(0\right)$ being the usual persistence exponent. We compute $\theta \left(p\right)$ exactly for a one-dimensional deterministic coarsening model, and approximately for the diffusion equation. Finally we develop an exact, systematic series expansion for $\theta \left(p\right)$, in powers of $\epsilon =1-p$, for a general Gaussian process with finite density of zero crossings.

We show that systems with a first integral (i.e., a constant of motion) or a Lyapunov function can be written as “linear-gradient systems,” $\dot{x}=L\left(x\right)▽V\left(x\right)$, for an appropriate matrix function $L$, with a generalization to several integrals or Lyapunov functions. The discrete-time analog, $\Delta x/\Delta t=L\overline{▽}V$, where $\overline{▽}$ is a “discrete gradient,” preserves $V$ as an integral or Lyapunov function, respectively.

Using a moving coil watt balance, electric power measured in terms of the Josephson and quantum Hall effects is compared with mechanical power measured in terms of the meter, kilogram, and second. We find the Planck constant $h=6.626\mathrm{}06891\left(58\right)\times {10}^{-34\mathrm{}}\mathrm{J}\mathrm{s}$. The quoted standard uncertainty (1 standard deviation estimate) corresponds to $(8.7\times {10}^{-8\mathrm{}})h$. Comparing this measurement to an earlier measurement places an upper limit of $2\times {10}^{-8\mathrm{}}/\mathrm{yr}$ on the drift rate of the SI unit of mass, the kilogram.

We consider transitions in quantum networks analogous to those in the two-dimensional Ising model. We show that for a certain network configuration of active components the transition is between the quantum and the classical behavior of the network, and the critical amplification coincides with the fundamental quantum optical cloning limit.