We present the experimental observation of polarization entanglement for three spatially separated photons. Such states of more than two entangled particles, known as Greenberger-Horne-Zeilinger (GHZ) states, play a crucial role in fundamental tests of quantum mechanics versus local realism and in many quantum information and quantum computation schemes. Our experimental arrangement is such that we start with two pairs of entangled photons and register the photons in a way that any information as to which pair each photon belongs to is erased. After detecting a trigger photon, the registered events at the detectors for the remaining three photons exhibit the desired GHZ correlations.

We investigate the spectrum and coherence of an atomic beam slowly coupled out of an atomic trap which contains a partially condensed Bose gas at a finite temperature. The spectrum contains a coherent fraction emerging from the condensate and a thermal fraction emerging from the thermal excitations in the trap. We show the existence of a remarkable process involving the simultaneous creation of an output atom and an elementary excitation (quasiparticle) inside the trap. This process, which can serve as a probe to pair correlations in the condensate, can become dominant for a suitable choice of the coupling parameters.

We have observed Bragg diffraction of a Bose-Einstein condensate of sodium atoms by a moving, periodic, optical potential. The coherent process of Bragg diffraction produced a splitting of the condensate with unidirectional momentum transfer. Using the momentum selectivity of the Bragg process, we separated a condensate component with a momentum width narrower than that of the original condensate. By repeatedly pulsing the optical potential while the atoms were trapped, we observed the trajectory of the split atomic wave packets in the confining magnetic potential.

The occupation number of a magnetically trapped Bose-Einstein condensate is limited for atoms with attractive interactions. It has been predicted that, as this limit is approached, the condensate will collapse by a collective process. The measured spread in condensate number for samples of ${}^7\mathrm{Li}$ atoms undergoing thermal equilibration is consistent with the occurrence of such collapses.

We consider in two dimensions (2D) the most general star-shaped copolymer, mixing random walks (RW) or self-avoiding walks (SAW) with specific mutual avoidance interactions thereof. Its exact conformal scaling dimensions in the plane are derived from an algebraic structure existing on a random lattice (2D quantum gravity). The multifractal dimensions $\tau \left(n\right)$ of the harmonic measure of a 2D RW or SAW are conformal dimensions of certain star copolymers. The exact associated $f\left(\alpha \right)$ are identical for a RW or a SAW in 2D. These are the first examples of conformal multifractality.

An order of magnitude sensitivity gain is described for using quasar spectra to investigate possible time or space variation in the fine structure constant $\alpha$. Applied to a sample of 30 absorption systems, spanning redshifts $0.5<z<\mathrm{}1.6\mathrm{}$, we derive limits on variations in $\alpha$ over a wide range of epochs. For the whole sample, $\Delta \alpha /\alpha =(-1.1\mathrm{}\pm 0.4)\times {10}^{-5\mathrm{}}$. This deviation is dominated by measurements at $z>\mathrm{}1\mathrm{}$, where $\Delta \alpha /\alpha =(-1.9\mathrm{}\pm 0.5)\times {10}^{-5\mathrm{}}$. For $z<\mathrm{}1\mathrm{}$, $\Delta \alpha /\alpha =(-0.2\mathrm{}\pm 0.4)\times {10}^{-5\mathrm{}}$. While this is consistent with a time-varying $\alpha$, further work is required to explore possible systematic errors in the data, although careful searches have so far revealed none.

High-redshift absorption systems detected in the optical spectra of quasars provide a powerful tool for constraining possible spatial and temporal variations of physical “constants” in the Universe. It is demonstrated that high sensitivity to the variation of the fine structure constant $\alpha$ can be obtained from a comparison of the spectra of heavy and light atoms. We have performed calculations for Mg I, Mg II, Cr II, and Fe II for which accurate quasar and laboratory spectra are available. Some possibilities for observing enhanced effects in variations of the fundamental constants in laboratory measurements are also discussed.

The experimental evidence of stochastic resonance in the polarized emission of vertical cavity surface emitting lasers is given. We report for the first time in an experimental work a complete characterization of the phenomenon based on the residence times probability density. We also give evidence of the bona fide resonance, clarifying this recently debated subject.

We discuss renormalization of the nonrelativistic three-body problem with short-range forces. The problem becomes nonperturbative at momenta of the order of the inverse of the two-body scattering length, and an infinite number of graphs must be summed. This summation leads to a cutoff dependence that does not appear in any order in perturbation theory. We argue that this cutoff dependence can be absorbed in a single three-body counterterm and compute the running of the three-body force with the cutoff. We comment on the relevance of this result for the effective field theory program in nuclear and molecular physics.

We have imaged an $18\mu \mathrm{K}$ cloud of ${}^{85}\mathrm{Rb}$ atoms bouncing freely on a horizontal, concave magnetic atom mirror (radius of curvature $R$). A high-quality image is observed even after 14 reflections. Initially compact, the cloud is alternately collimated (odd bounces) and brought back to a focus (even bounces) when dropped from a height $R/4\mathrm{}$. This multiple reconstruction of a thermally expanding cloud hinges on the microscopic reversal of the atomic motion. We discuss the factors limiting the resolution of the mirror and describe the method of construction.

We introduce a model able to reproduce the main features of $1/f$ noise: hyperuniversality (the power-law exponents are independent on the dimension of the system; we show here results in $d=1,2\mathrm{}$) and apparent lack of a low-frequency cutoff in the power spectrum. Essential ingredients of this model are an activation-deactivation process and dissipation.

We study an induced dynamics in the space of energy of single-spin-flip Monte Carlo algorithm. The method gives an efficient reweighting technique. This dynamics is shown to have relaxation times proportional to the specific heat. From this we argue for a logarithmic factor in the correlation time of the standard 2D Ising local dynamics.

A crucial assumption in the conventional description of thermal conduction is the existence of local thermal equilibrium. We test this assumption in two simple models of heat conduction: a linear chain of planar spins with nearest neighbor couplings and a Lorentz gas. We look at the steady state of the system when the two ends are connected to heat baths at temperatures $T_1$ and $T_2$. If $T_1{=T}_2$, the system reaches thermal equilibrium. If $T_1\ne T_2$, there is a heat current through the system, but there is no local thermal equilibrium, even in the limit of large system size, when the heat current goes to zero. We argue that this is due to the existence of an infinity of local conservation laws in their dynamics.

Analysis of directly measurable subsystems of quantum systems (i.e., prepared and measured observable, parameters of symmetry transformations), based on the Einstein-Podolsky-Rosen definition of physical reality, shows that such subsystems cannot be deterministic. This effect is not specifically quantum: a physically different but mathematically similar situation arises in classical decision-making systems obeying classical logic. Direct consequences of this phenomenon are nonclassical behavior of probabilities and irreversibility of measurements (or decisions).

Motivated by the recent success of optical trapping of alkali Bose condensate, we have studied the superfluid state of optically trapped alkali fermions, which can have Cooper pairs with total spin $J\ge 2$. In this paper, we shall discuss the general structure of these large spin Cooper pairs and their close relation with singlet Cooper pairs with nonzero orbital angular momentum. We also present the exact solution for the $J=2\mathrm{}$ pairing which shows a surprising change of ground state as the spin $f$ of the constituent fermion increases.

We analyze the dynamics of two trapped interacting Bose-Einstein condensates in the absence of thermal cloud and identify two regimes for the evolution: a regime of slow periodic oscillations and a regime of strong nonlinear mixing leading to the damping of the relative motion of the condensates. We compare our predictions with an experiment recently performed at JILA.

The oscillation frequencies of collective excitations of a trapped Bose-Einstein condensate, when calculated in the mean-field approximation and in the Thomas-Fermi limit, are independent of the scattering length $a$. We calculate the leading corrections to the frequencies from quantum fluctuations around the mean field. The semiclassical correction is proportional to $N^{1/5}{a}^{6/5}$, where $N$ is the number of atoms in the condensate. The correction is positive semidefinite and is zero for surface modes whose eigenfunctions have a vanishing Laplacian. The shift in the frequency of the lowest quadrupole mode for an axially symmetric trap is large enough that it should be measurable in future experiments.

While the use of continuum approximations to describe systems consisting of many molecules is well established, it is not known how such approximations fail as the number of molecular components decreases. We study the one-dimensional Fermi-Pasta-Ulam chain in order to determine the critical value of the system size below which the system's behavior deviates from the continuum limit, allowing us to delineate between “small” and “large” systems and define these terms precisely. For this system, the distinction between small and large is correlated with the appearance of an instability of the chain.

We propose a method for controlling the unitary evolution of quantum systems by switching on and off alternatively two distinct constant perturbations. We show how to find appropriate switching times in order to attain any desired evolution. We suggest an experimental realization of our method in controlling the translational motion of cold atoms.

We investigate the nonequilibrium stationary state of a translationally invariant one-dimensional driven lattice gas with short-range interactions. The phase diagram is found to exhibit a line of continuous transitions from a disordered phase to a phase with spontaneous symmetry breaking. At the phase transition the correlation length is infinite and density correlations decay algebraically. Depending on the parameters which define the dynamics, the transition either belongs to the universality class of directed percolation or to a universality class of a growth model which preserves the local minimal height. Consequences of mappings to other models are briefly discussed.