We show that in an atomic Fermi gas near a Feshbach resonance the crossover between a Bose-Einstein condensate of diatomic molecules and a Bose-Einstein condensate of Cooper pairs occurs at positive detuning, i.e., when the molecular energy level lies in the two-atom continuum. We determine the crossover temperature as a function of the applied magnetic field and find excellent agreement with the experiment of C. A. Regal et al. [Phys. Rev. Lett. 92, 040403 (2004)] who has recently observed this crossover temperature.

Weak measurement is a new technique which allows one to describe the evolution of postselected quantum systems. It appears to be useful for resolving a variety of thorny quantum paradoxes, particularly when used to study properties of pairs of particles. Unfortunately, such nonlocal or joint observables often prove difficult to measure directly in practice (for instance, in optics—a common testing ground for this technique—strong photon-photon interactions would be needed to implement an appropriate von Neumann interaction). Here we derive a general, experimentally feasible, method for extracting these joint weak values from correlations between single-particle observables.

We predict that an ultracold Bose gas in an optical lattice can give rise to a new form of condensation, namely, nonspreading 3D wave packets that reflect the symmetry of the Laplacian with a negative effective mass along the lattice direction and are allowed to exist in the absence of any trapping potential even in the limit of noninteracting atoms. This result also has strong implications for optical propagation in periodic structures.

Symmetry implications for the decoherence of quantum oscillations of a two-state system in a solid are studied. When the oscillation frequency is small compared to the Debye frequency, the universal lower bound on the decoherence due to the atomic environment is derived in terms of the macroscopic parameters of the solid, with no unknown interaction constants.

In the continuous space and time limit, we show that the probability density to find the quantum random walk (QRW) driven by the Hadamard “coin” solves a hyperbolic evolution equation similar to the one obtained for a random two-velocity evolution with spatially inhomogeneous transition rates between the velocity states. In spite of the presence of a nonlinear drift term, it is remarkable that the QRW position can easily be described in simple analytical terms. This allows us to derive the quadratic time dependence of the variance typical for the QRW.

In this Letter we present a flat histogram algorithm based on the pruned and enriched Rosenbluth method. This algorithm incorporates in a straightforward manner microcanonical reweighting techniques, leading to “flat histogram” sampling in the chosen parameter space. As an additional benefit, our algorithm is completely parameter free and, hence, easy to implement. We apply this algorithm to interacting self-avoiding walks, the generic lattice model of polymer collapse.

We study numerically the structure of metastable states in the Sherrington-Kirkpatrick spin glass. We find that all nonparamagnetic stationary points of the free energy are organized into pairs, consisting of a minimum and an order 1 saddle, which coalesce in the thermodynamic limit. Within the annealed approximation, the entropic contribution of these states, that is the complexity, is compatible with the supersymmetry-breaking calculation performed by Bray and Moore [J. Phys. C 13, L469 (1980)]. This result indicates that the supersymmetry is spontaneously broken in the Sherrington-Kirkpatrick model.

The unknown state $\widehat{\rho }$ of a quantum system $S$ is determined by letting it interact with an auxiliary system $A$, the initial state of which is known. A one-to-one mapping can thus be realized between the density matrix $\widehat{\rho }$ and the probabilities of the occurrence of the eigenvalues of a single and factorized observable of $S+A$, so that $\widehat{\rho }$ can be determined by repeated measurements using a single apparatus. If $S$ and $A$ are spins, it suffices to measure simultaneously their $z$ components after a controlled interaction. The most robust setups are determined in this case for an initially pure or a completely disordered state of $A$. They involve an Ising or anisotropic Heisenberg coupling and an external field.

We have observed Bose-Einstein condensation of pairs of fermionic atoms in an ultracold ${}^6\mathrm{Li}$ gas at magnetic fields above a Feshbach resonance, where no stable ${}^6\mathrm{Li}_2$ molecules would exist in vacuum. We accurately determined the position of the resonance to be $822\pm 3\mathrm{G}$. Molecular Bose-Einstein condensates were detected after a fast magnetic field ramp, which transferred pairs of atoms at close distances into bound molecules. Condensate fractions as high as 80% were obtained. The large condensate fractions are interpreted in terms of preexisting molecules which are quasistable even above the two-body Feshbach resonance due to the presence of the degenerate Fermi gas.

We demonstrate a reversible conversion of a ${}^6\mathrm{Li}_2$ molecular Bose-Einstein condensate to a degenerate Fermi gas of atoms by adiabatically crossing a Feshbach resonance. By optical in situ imaging, we observe a smooth change of the cloud size in the crossover regime. On the Feshbach resonance, the ensemble is strongly interacting and the measured cloud size is $75(7)\%$ of the one of a noninteracting zero-temperature Fermi gas. The high condensate fraction of more than $90\%$ and the adiabatic crossover suggest our Fermi gas to be cold enough to form a superfluid.

Nonlinear systems driven by state-dependent Poisson noise are introduced to model the persistence of climatic anomalies in land-atmosphere interaction caused by the soil-moisture dependence of the frequency of rainfall events. It is found that these systems may give rise to bimodal probability distributions, while the state variable randomly persists around the preferential states because of transient dynamics that are opposite to the long-term behavior. Mean-field analysis and numerical simulations of the spatially distributed systems reveal a symmetry-breaking bifurcation for sufficiently strong spatial diffusive couplings and intermediate noise intensities. In such conditions, the initial development of spatial patterns is followed by a stable configuration, selected on the bases of the initial conditions in correspondence of the remnants of the modes of the uncoupled system.

We present experimental and theoretical results showing that magnetic resonance transitions from the “end” sublevels of maximum or minimum spin in alkali-metal vapors are a promising alternative to the conventional 0-0 transition for small-size gas-cell atomic clocks. For these “end resonances,” collisional spin-exchange broadening, which often dominates the linewidth of the 0-0 resonance, decreases with increasing spin polarization and vanishes for 100% polarization. The end resonances also have much stronger signals than the 0-0 resonance, and are readily detectable in cells with high buffer-gas pressure.

Single-particle spectra are calculated in the superconducting state for a fermionic system with an attractive interaction, as functions of temperature and coupling strength from weak to strong. The fermionic system is described by a single-particle self-energy that includes pairing-fluctuation effects in the superconducting state. The theory reduces to the ordinary BCS approximation in weak coupling and to the Bogoliubov approximation for the composite bosons in strong coupling. Several features of the single-particle spectral function are shown to compare favorably with experimental data for cuprate superconductors.

We examine the collisional behavior of two-component Fermi gases released at zero temperature from a harmonic trap. Using a phase-space formalism to calculate the collision rate during expansion, we find that Pauli blocking plays only a minor role for momentum changing collisions. As a result, for a large scattering cross section, Pauli blocking will not prevent the gas from entering the collisionally hydrodynamic regime. In contrast to the bosonic case, hydrodynamic expansion at very low temperatures is therefore not evidence for fermionic superfluidity.

A single $l$-shell model is investigated for a system of fermions of spin $s$ and an attractive $s$-wave, spin channel independent, interaction. The spectra and eigenvectors are determined exactly for different $l,s$ values and particle numbers $N$. As a generalization of Cooper pairing it is shown that when $N=\mu (2s+1)$, $\mu =1,2,\dots ,2l+1$, the ground state consists of clusters of $(2s+1)$ particles. The relevance of the results for more general situations including the homogeneous system is briefly discussed.

We perform a systematic study of the thermodynamics of quantum gases in the unitarity limit. Our study is based on a “universality hypothesis” for the relevant energy scales which is supported by experiments and can be proven in the Boltzmann regime. It implies a universal form for the grand potential, which is specified by only a few universal numbers in the degenerate limit. This hypothesis provides a simple way to determine the density profile of a trapped fermion superfluid. It implies a superfluid bump in the density and gives the general expression of the second sound velocity of a homogeneous superfluid at unitarity.

Dynamics of a one-dimensional growing front with an unstable straight profile are analyzed. We argue that a coarsening process occurs if and only if the period $\lambda$ of the steady-state solution is an increasing function of its amplitude $A$. This statement is rigorously proved for two important classes of conserved and nonconserved models by investigating the phase diffusion equation of the steady pattern. We further provide clear numerical evidence for the growth equation of a stepped crystal surface.

We develop a theory describing neutral atom scattering at low energies in an optical lattice. We show that, for a repulsive interaction, as the microscopic scattering length increases the effective scattering amplitude approaches a limiting value which depends only on the lattice parameters. In the case of attractive interaction a geometric resonance occurs before reaching this limit. Close to the resonance, the effective interaction becomes repulsive and supports a weakly bound state, which can extend over several lattice sites.

The influence of intrinsic firing interspike interval correlations on the noise spectrum and information transfer is studied. This is done through the comparison of two simple firing models, one of which is a renewal process while the other displays interval correlations. These correlations are shown to shape the spike train power spectrum and, in particular, to decrease the noise power at low frequencies. Linear response theory and numerical simulations reveal how this shaping can increase the transmission of information about a time-varying signal. Our results are relevant to the analysis of nonrenewal point processes and signal detection in physics and biology.

In periodically driven systems, near a bifurcation (critical) point the period-averaged escape rate $\overline{W}$ scales with the field amplitude $A$ as $|\ln \overline{W}|\propto (A_c-A{)}^{\xi }$, where $A_c$ is a critical amplitude. We find three scaling regions. With increasing field frequency or decreasing $|A_c-A|$, the critical exponent $\xi$ changes from $\xi =3/2$ for a stationary system to a dynamical value $\xi =2$ and then again to $\xi =3/2$. Monte Carlo simulations agree with the scaling theory.