We discuss an integrable model of interacting fermions in one dimension that allows a complete description of the crossover from a BCS- to a Bose-like superfluid. This model bridges the Gaudin-Yang model of attractive spin $1/2$ fermions to the Lieb-Liniger model of repulsive bosons. Using a geometric resonance in the one-dimensional scattering length, the inverse coupling constant varies from $-\infty$ to $+\infty$ while the system evolves from a BCS-like state through a Tonks-Girardeau gas to a weakly interacting Bose gas of dimers. We study the ground state energy, the elementary density and spin excitations, and the correlation functions. An experimental realization with cold atoms of such a one-dimensional BCS-BEC crossover is proposed.

We report an experiment measuring simultaneously the temperature and the flux of ions produced by a cloud of triplet metastable helium atoms at the Bose-Einstein critical temperature. The onset of condensation is revealed by a sharp increase of the ion flux during evaporative cooling. Combining our measurements with previous measurements of ionization in a pure Bose-Einstein condensate, we extract an improved value of the scattering length $a={11.3}_{-1.0}^{+2.5}\mathrm{n}\mathrm{m}$. The analysis includes corrections that take into account the effect of atomic interactions on the critical temperature, and thus an independent measurement of the scattering length would allow a new test of these calculations.

We report the measurement of a Bell inequality violation with a single atom and a single photon prepared in a probabilistic entangled state. This is the first demonstration of such a violation with particles of different species. The entanglement characterization of this hybrid system may also be useful in quantum information applications.

We consider atomic Bose-Fermi mixtures in optical lattices and study the superfluidity of fermionic atoms due to $s$-wave pairing induced by boson-fermion interactions. We prove that the induced fermion-fermion coupling is always attractive if the boson-boson on-site interaction is repulsive, and predict the existence of an enhanced BEC-BCS crossover as the strength of the lattice potential is varied. We show that for direct on-site fermion-fermion repulsion, the induced attraction can give rise to superfluidity via $s$-wave pairing at striking variance with the case of pure systems of fermionic atoms with direct repulsive interactions.

We show that the rotation of trapped quantum mechanical particles with a repulsive interaction can lead to vortex formation, irrespective of whether the particles are bosons or (unpaired) fermions. The exact many-particle wave function constitutes similar structures in both cases, implying that this vortex formation is indeed universal.

Kovtun, Son, and Starinets proposed a bound on the shear viscosity of any fluid in terms of its entropy density. We argue that this bound is always saturated for gauge theories at large 't Hooft coupling, which admit holographically dual supergravity description.

We study equilibrium properties of a cold two-component Fermi gas confined in a quasi-one-dimensional trap of the transverse size $l_{\perp }$. In the dilute limit ($n{l}_{\perp }\ll 1$, where $n$ is the 1D density) the problem is exactly solvable for an arbitrary 3D fermionic scattering length $a_F$. When $l_{\perp }/a_F$ goes from $-\infty$ to $+\infty$, the system successively passes three regimes: weakly interacting Fermi gas, hard core Bose gas, and weakly coupled Bose gas. The regimes are separated by two crossovers at $a_F\sim \pm n{l}_{\perp }^2$. In conclusion, we discuss experimental implications of these results.

We study a genuine Brownian motor by hard disk molecular dynamics and calculate analytically its properties, including its drift speed and thermal conductivity, from microscopic theory.

Quantum phase slips (QPS) in narrow superfluid channels generate momentum by unwinding the supercurrent. In a uniform Bose gas, this momentum needs to be absorbed by quasiparticles (phonons). We show that this requirement results in an additional exponential suppression of the QPS rate (compared to the rate of QPS induced by a sharply localized perturbation). In BCS-paired fluids, momentum can be transferred to fermionic quasiparticles, and we find an interesting interplay between quasiparticle scattering on QPS and on disorder.

We discuss the behavior of weakly bound bosonic dimers formed in a two-component cold Fermi gas at a large positive scattering length $a$ for the interspecies interaction. We find the exact solution for the dimer-dimer elastic scattering and obtain a strong decrease of their collisional relaxation and decay with increasing $a$. The large ratio of the elastic to inelastic rate is promising for achieving Bose-Einstein condensation of the dimers and cooling the condensed gas to very low temperatures.

Among the most important parameters for the usefulness of quantum computers are the size of the quantum register and the decoherence time for the quantum information. The decoherence time is expected to get shorter with the number of correlated qubits, but experimental data are only available for small numbers of qubits. Solid-state nuclear magnetic resonance allows one to correlate large numbers of qubits (several hundred) and measure their decoherence rates. We use a modified magnetic dipole-dipole interaction to correlate the proton spins in a solid sample and observe the decay of the resulting highly correlated states. By systematically varying the number of correlated spins, we measure the increase of the decoherence rate with the size of the quantum register.

Nucleation of vortex rings accompanies the collapse of ultrasound bubbles in superfluids. Using the Gross-Pitaevskii equation for a uniform condensate we elucidate the various stages of the collapse of a stationary spherically symmetric bubble and establish conditions necessary for vortex nucleation. The minimum radius of the stationary bubble, whose collapse leads to vortex nucleation, was found to be $28\pm 1$ healing lengths. The time after which the nucleation becomes possible is determined as a function of the bubble’s radius. We show that vortex nucleation takes place in moving bubbles of even smaller radius if the motion makes them sufficiently oblate.

We discuss a recently proposed extension of Bohmian mechanics to quantum field theory. For more or less any regularized quantum field theory there is a corresponding theory of particle motion, which, in particular, ascribes trajectories to the electrons or whatever sort of particles the quantum field theory is about. Corresponding to the nonconservation of the particle number operator in the quantum field theory, the theory describes explicit creation and annihilation events: the world lines for the particles can begin and end.

A kinematic approach to the geometric phase for mixed quantal states in nonunitary evolution is proposed. This phase is manifestly gauge invariant and can be experimentally tested in interferometry. It leads to well-known results when the evolution is unitary.

We have measured the precession frequency of a vortex lattice in a Bose-Einstein condensate of ${\mathrm{R}\mathrm{b}}^{87}$ atoms. The observed mode corresponds to a collective motion in which all the vortices in the array are tilted by a small angle with respect to the $z$ axis (the symmetry axis of the trapping potential) and synchronously rotate about this axis. This motion corresponds to excitation of a Kelvin wave along the core of each vortex and we have verified that it has the handedness expected for such helical waves, i.e., precession in the opposite sense to the rotational flow around the vortices.

We demonstrate complete characterization of a two-qubit entangling process—a linear optics controlled-not gate operating with coincident detection—by quantum process tomography. We use a maximum-likelihood estimation to convert the experimental data into a physical process matrix. The process matrix allows an accurate prediction of the operation of the gate for arbitrary input states and a calculation of gate performance measures such as the average gate fidelity, average purity, and entangling capability of our gate, which are 0.90, 0.83, and 0.73, respectively.

We prove a generalization of Kirchhoff’s matrix-tree theorem in which a large class of combinatorial objects are represented by non-Gaussian Grassmann integrals. As a special case, we show that unrooted spanning forests, which arise as a $q\to 0$ limit of the Potts model, can be represented by a Grassmann theory involving a Gaussian term and a particular bilocal four-fermion term. We show that this latter model can be mapped, to all orders in perturbation theory, onto the $N$-vector model at $N=-1$ or, equivalently, onto the $\sigma$ model taking values in the unit supersphere in ${\mathbb{R}}^{1|2}$. It follows that, in two dimensions, this fermionic model is perturbatively asymptotically free.

We consider a regular chain of quantum particles with nearest neighbor interactions in a canonical state with temperature $T$. We analyze the conditions under which the state factors into a product of canonical density matrices with respect to groups of $n$ particles each and under which these groups have the same temperature $T$. In quantum mechanics the minimum group size $n_{\mathrm{m}\mathrm{i}\mathrm{n}}$ depends on the temperature $T$, contrary to the classical case. We apply our analysis to a harmonic chain and find that $n_{\mathrm{m}\mathrm{i}\mathrm{n}}=\mathrm{c}\mathrm{o}\mathrm{n}\mathrm{s}\mathrm{t}$ for temperatures above the Debye temperature and $n_{\mathrm{m}\mathrm{i}\mathrm{n}}\propto T^{-3}$ below.

In a benchmark dynamical-lattice model in three dimensions, the discrete nonlinear Schrödinger equation, we find discrete vortex solitons with various values of the topological charge $S$. Stability regions for the vortices with $S=0,1,3$ are investigated. The $S=2$ vortex is unstable and may spontaneously rearranging into a stable one with $S=3$. In a two-component extension of the model, we find a novel class of stable structures, consisting of vortices in the different components, perpendicularly oriented to each other. Self-localized states of the proposed types can be observed experimentally in Bose-Einstein condensates trapped in optical lattices and in photonic crystals built of microresonators.

We consider a single atom in an optical lattice, subject to a harmonic trapping potential. The problem is treated in the tight-binding approximation, with an extra parameter $\kappa$ denoting the strength of the harmonic trap. It is shown that the $\kappa \to 0$ limit of this problem is singular, in the sense that the density of states for a very shallow trap ($\kappa \to 0$) is qualitatively different from that of a translationally invariant lattice ($\kappa =0$). The physics of this difference is discussed, and densities of states and wave functions are exhibited and explained.