We study the simplest irreversible ballistically controlled reaction, whereby particles having an initial continuous velocity distribution annihilate upon colliding. In the framework of the Boltzmann equation, expressions for the exponents characterizing the density and typical velocity decay are explicitly worked out in arbitrary dimension. These predictions are in excellent agreement with the complementary results of extensive Monte Carlo and molecular dynamics simulations. We finally discuss the definition of universality classes indexed by a continuous parameter for this far from equilibrium dynamics with no conservation laws.

We have produced a macroscopic quantum system in which a ${}^6\mathrm{Li}$ Fermi sea coexists with a large and stable ${}^{23}\mathrm{Na}$ Bose-Einstein condensate. This was accomplished using interspecies sympathetic cooling of fermionic ${}^6\mathrm{Li}$ in a thermal bath of bosonic ${}^{23}\mathrm{Na}$. The system features rapid thermalization and long lifetimes.

The conjecture that the scaling limit of the two-dimensional self-avoiding walk (SAW) in a half plane is given by the stochastic Loewner evolution (SLE) with $\kappa =8/3\mathrm{}$ leads to explicit predictions about the SAW. A remarkable feature of these predictions is that they yield not just critical exponents but also probability distributions for certain random variables associated with the self-avoiding walk. We test two of these predictions with Monte Carlo simulations and find excellent agreement, thus providing numerical support to the conjecture that the scaling limit of the SAW is ${\mathrm{SLE}}_{8/3}$.

We show that the dipole-dipole interatomic forces induced by an off-resonant running laser beam can lead to a self-bound pencil-shaped Bose condensate, even if the laser beam is a plane wave. For an appropriate laser intensity the ground state has a quasi-one-dimensional density modulation—a Bose-Einstein “supersolid.”

The invariant information, introduced by Č. Brukner and A. Zeilinger [Phys. Rev. Lett. 83, 3354 (1999)], is reconsidered from the point of view of quantum state estimation. We show that this quantity is directly related to the mean error of the standard reconstruction from the measurement of a complete set of mutually complementary observables. We give its generalization in terms of the Fisher information. Provided that the optimum reconstruction is adopted, the information loses its invariant character.

We report a measurement of the excitation spectrum $\omega \left(k\right)$ and the static structure factor $S\left(k\right)$ of a Bose-Einstein condensate. The excitation spectrum displays a linear phonon regime, as well as a parabolic single-particle regime. The linear regime provides an upper limit for the superfluid critical velocity, by the Landau criterion. The excitation spectrum agrees well with the Bogoliubov spectrum in the local density approximation, even close to the long-wavelength limit of the region of applicability. Feynman’s relation between $\omega \left(k\right)$ and $S\left(k\right)$ is verified, within an overall constant.

We study quantum dynamical tunneling between two symmetry-related islands of stability in the phase space of a classically chaotic system. The setting for these experiments is the motion of carefully prepared samples of cesium atoms in an amplitude-modulated standing wave of light. We examine the dependence of the tunneling dynamics on the system parameters and indicate how the observed features provide evidence for chaos-assisted (three-state) tunneling. We also observe the influence of a noisy perturbation of the standing-wave intensity, which destroys the tunneling oscillations, and we show that the tunneling is more sensitive to the noise for a smaller value of the effective Planck constant.

Diffusion is often accompanied by a reaction or sorption which can induce temperature inhomogeneities. Monte Carlo simulations of Lennard-Jones atoms in zeolite NaCaA are reported with a hot zone presumed to be created by a reaction. Our simulations show that localized hot regions can alter both the kinetic and transport properties. Further, enhancement of the diffusion constant is greater for larger barrier height, a surprising result of considerable significance to many chemical and biological processes. We find an unanticipated coupling between reaction and diffusion due to the presence of hot zone in addition to that which normally exists via concentration.

It is shown that radiation pressure can be profitably used to entangle macroscopic oscillators like movable mirrors, using present technology. We prove a new sufficient criterion for entanglement and show that the achievable entanglement is robust against thermal noise. Its signature can be revealed using common optomechanical readout apparatus.

We study the quantum and the mean-field Gross-Pitaevskii (GP) dynamics of a Bose-Einstein condensate gas confined in a toroidal trap. According to GP, if the interatomic interaction is attractive, the rotational states of the system can be dynamically stable or unstable depending on the strength of the mean-field energy. The full quantum analysis, however, reveals that the condensate is always unstable. Quantum fluctuations are particularly important close to the GP stability borderline, even for systems with a relatively large number of condensate atoms.

We form ultracold ${\mathrm{Na}}_2$ molecules by single-photon photoassociation of a Bose-Einstein condensate, measuring the photoassociation rate, linewidth, and light shift of the $J=1\mathrm{}$, $v=135\mathrm{}$ vibrational level of the $A^1{\Sigma }_u^{+}$ molecular state. The photoassociation rate constant increases linearly with intensity, even where it is predicted that many-body effects might limit the rate. Our observations are in good agreement with a two-body theory having no free parameters.

Multisimultaneity is a causal model of relativistic quantum physics which assigns a real time ordering to any set of events, much in the spirit of the pilot-wave picture. Contrary to standard quantum mechanics, it predicts a disappearance of the correlations in a Bell-type experiment when both analyzers are in relative motion such that each one, in its own inertial reference frame, is first to select the output of the photons. We tested this prediction using acousto-optic modulators as moving beam splitters and interferometers separated by 55 m. We did not observe any disappearance of the correlations, in agreement with quantum mechanics.

We consider acoustic propagation in an irrotational vortex, using the technical machinery of differential geometry to investigate the “acoustic geometry” that is probed by the sound waves. The acoustic space-time curvature of a constant circulation hydrodynamical vortex leads to deflection of phonons at appreciable distances from the vortex core. The scattering angle for phonon rays is shown to be quadratic in the small quantity $\Gamma /2\mathrm{}\pi \mathrm{cb}$, where $\Gamma$ is the vortex circulation, $c$ the speed of sound, and $b$ the impact parameter.

An atomic grating generated by a pulsed standing-wave laser field is proposed to manipulate the superfluid state in a quantum degenerate gas of fermionic atoms. We show that in the presence of atomic Cooper pairs, the density oscillations of the gas caused by the atomic grating exhibit a much longer coherence time than that in the normal Fermi gas. Our result indicates that the technique of a pulsed atomic grating is a potential candidate to detect the atomic superfluid state in a quantum degenerate Fermi gas.

Atoms can be trapped and guided with electromagnetic fields, using nanofabricated structures. We describe the fundamental features of an interferometer for guided matter waves, built of two combined Y-shaped beam splitters. We find that such a device is expected to exhibit high contrast fringes even in a multimode regime, analogous to a white light interferometer.

We solve the joint open problems of photon localization and single-photon wave functions in the context of spontaneous emission from an excited atom in free space. Our wave functions are well-defined members of a discrete orthonormal function set. Both the degree and shape of the localization are controlled by entanglement mapping onto the atom wave function, even though the atom is remote from the photon.

A three-dimensional generalization of the sign-change ( $\pi$ phase shift) rule for adiabatic cycles of spin-1/2 or two-state wave functions encircling a degeneracy in the parameter space of the Hamiltonian yields a Dirac-type singularity wherein any closed circuit of the adiabatic cycle in which the degeneracy is “looped” results in an observable $\pm 2\pi$ phase shift. It is concluded that an interferometer loop similarly taken around a magnetic monopole of strength $n/2\mathrm{}$ yields an observable $\pm 2n\pi$ phase shift, $n$ being an integer.

We demonstrate a near-field Talbot-Lau interferometer for ${\mathrm{C}}_{70}$ fullerene molecules. Such interferometers are particularly suitable for larger masses. Using three free-standing gold gratings of $1\mu \mathrm{m}$ period and a transversally incoherent but velocity-selected molecular beam, we achieve an interference fringe visibility of $40\%$ with high count rate. Both the high visibility and its velocity dependence are in good agreement with a quantum simulation that takes into account the van der Waals interaction of the molecules with the gratings and are in striking contrast to a classical moiré model.

One of the computational “grand challenges” is to develop methodology capable of sampling conformational equilibria in systems with rough energy landscapes. Here, a significant step forward is made by combining molecular dynamics with a novel variable transformation designed to enhance sampling by reducing barriers without introducing bias and, thus, to preserve, perfectly, equilibrium properties.

We propose a method to create a monopole structure in a multicomponent condensate by applying the basic methods used to create vortices and solitons experimentally in single-component condensates. We also show that by using a two-component structure for a monopole, we can avoid many problems related to the previously suggested three-component monopole. We discuss the observation and dynamics of such a monopole structure, and note that the dynamics of the two-component monopole differs from the dynamics of the three-component monopole.