Conservation of the total isotopic spin $S$ of a two-component Bose gas—such as ${}^{\mathrm{87}}\mathrm{R}\mathrm{b}$—has a dramatic impact on the structure of the ground state. In the case when $S$ is much smaller than the total number of particles $N$, the condensation of each of the two components occurs into at least two single-particle modes. The quantum wave function of such a ground state is a quantum superposition of the phase separated classical condensates, the most “probable” state in the superposition corresponding to the classical ground state in the sector of given $N$ and $S$.

A nonzero temperature generalization of the Fermi-Bose mapping theorem is used to study the exact quantum statistical dynamics of a one-dimensional gas of impenetrable bosons on a ring. We investigate the interference produced when an initially trapped gas localized on one side of the ring is released, split via an optical-dipole grating, and recombined on the other side of the ring. Nonzero temperature is shown not to be a limitation to obtaining high visibility fringes.

We investigate the sensitivity of quantum systems that are chaotic in a classical limit to small perturbations of their equations of motion. This sensitivity, originally studied in the context of defining quantum chaos, is relevant to decoherence when the environment has a chaotic classical counterpart.

We predict a dynamical classical superfluid-insulator transition in a Bose-Einstein condensate trapped in an optical and a magnetic potential. In the tight-binding limit, this system realizes an array of weakly coupled condensates driven by an external harmonic field. For small displacements of the parabolic trap about the equilibrium position, the condensates coherently oscillate in the array. For large displacements, the condensates remain localized on the side of the harmonic trap with a randomization of the relative phases. The superfluid-insulator transition is due to a discrete modulational instability, occurring when the condensate center of mass velocity is larger than a critical value.

We discuss the relations between the violation of the Clauser-Horne-Shimony-Holt (CHSH) Bell inequality for systems of two qubits on the one side and entanglement of formation, local filtering operations, and the entropy and purity on the other. We calculate the extremal Bell violations for a given amount of entanglement of formation and characterize the respective states, which turn out to have extremal properties also with respect to the entropy, purity, and several entanglement monotones. The optimal local filtering operations leading to the maximal Bell violation for a given state are provided, and the special role of the resulting Bell diagonal states in the context of Bell inequalities is discussed.

We propose the use of entangled pairs of neutral kaons, considered as a promising tool to close the well known loopholes affecting generic Bell’s inequality tests, in a specific Hardy-type experiment. Hardy’s contradiction without inequalities between local realism and quantum mechanics can be translated into a feasible experiment by requiring ideal detection efficiencies for only one of the observables to be alternatively measured. Neutral kaons are near to fulfill this requirement and therefore to close the efficiency loophole.

In this Letter we extend the concept of stochastic resonance. We show that in forced excitable systems noise can be responsible for the appearance of recurrences presenting a robust topological organization inequivalent to the periodic orbits of the deterministic system. As in stochastic resonance, these new structures are most pronounced at an optimal noise intensity.

We propose a new optimization method based on a demagnetization procedure well known in magnetism. We show how this procedure can be applied as a general tool to search for optimal solutions in any system where the configuration space is endowed with a suitable “distance.” We test the new algorithm on frustrated magnetic models and the traveling salesman problem. We find that the new method successfully competes with similar basic algorithms such as simulated annealing.

We report on the achievement of simultaneous quantum degeneracy in a mixed gas of fermionic ${}^{\mathrm{40}}\mathrm{K}$ and bosonic ${}^{\mathrm{87}}\mathrm{R}\mathrm{b}$. Potassium is cooled to 0.3 times the Fermi temperature by means of an efficient thermalization with evaporatively cooled rubidium. Direct measurement of the collisional cross-section confirms a large interspecies attraction. This interaction is shown to affect the expansion of the Bose-Einstein condensate released from the magnetic trap, where it is immersed in the Fermi sea.

We consider a diffusing particle, with diffusion constant $D^{\prime }$, moving in one dimension in an infinite sea of noninteracting mobile traps with diffusion constant $D$ and density $\rho$. We show that the asymptotic behavior of the survival probability, $P(t)$, satisfies $\underset{t\to \infty }{lim}[-\ln P(t)]/\sqrt{{\rho }^{2}Dt}=4/\sqrt{\pi }$, independent of $D^{\prime }$. The result comes from obtaining upper and lower bounds on $P(t)$, and showing that they coincide asymptotically. We also obtain exact results for $P(t)$ to first order in $D^{\prime }/D$ for an arbitrary finite number of traps.

We study transverse radial oscillations of an elongated Bose-Einstein condensate using finite-temperature simulations, in the context of a recent experiment at ENS [F. Chevy et al., Phys. Rev. Lett. 88, 250402 (2002)]. The mode observed experimentally corresponds to an in-phase collective oscillation of both the condensate and the thermal cloud. Our simulations are in excellent agreement with experiment, accounting for the very small damping rates observed. In contrast to other condensate modes, interatomic collisions are found to be the dominant damping mechanism in this case.

We discuss a scheme for using entangled Bose-Einstein condensates to detect phase differences with a resolution better than the standard quantum limit. To date, schemes have shown that the enhancement in phase resolution gained by entangling condensates is lost when dissipation is present. Here we show how this can be overcome by using number correlated condensates, as have been produced recently in the laboratory. We also outline a scheme for measuring this phase that is not destroyed when the effects of finite detector efficiency are considered.

Spin relaxation in a strong-coupling regime (with respect to the spin system) is investigated in detail based on the spin-boson model in a stochastic limit. We find a bifurcation phenomenon in temperature dependence of relaxation constants, which is never observed in the weak-coupling regime. We also discuss inequalities among the relaxation constants in our model and show the well-known relation $2{\Gamma }_T\ge {\Gamma }_L$, for example, for a wider parameter region than before.

A Born-Markov master equation is used to investigate the decoherence of the state of a macroscopically occupied mode of a cold atom trap due to three-body loss. In the large-number limit only coherent states remain pure for times longer than the decoherence time: the time it takes for just three atoms to be lost from the trap. For large numbers of atoms ($N>{10}^4$) the decoherence time is found to be much faster than the phase-collapse time caused by intratrap atomic collisions.

The kinetic energy of an atom recoiling due to absorption of a photon was measured as a frequency, using an interferometric technique called “contrast interferometry.” Optical standing wave pulses were used to create a symmetric three-path interferometer with a Bose-Einstein condensate. Its recoil phase, measurable with a single shot, varies quadratically with additional recoils and is insensitive to errors from vibrations and ac Stark shifts. We have measured the photon recoil frequency of sodium to 7 ppm precision, using a simple realization of this scheme. Plausible extensions should yield sufficient precision to attain a ppb-level determination of $h/m$ and the fine structure constant $\alpha$.

Motivated by recent claims for rather unconventional first-order phase transitions in the two- and three-dimensional complex $|\psi {|}^4$ theory in certain parameter ranges we performed Monte Carlo simulation studies of this model. From our results in two and three dimensions we can unambiguously conclude that there is no evidence for a first-order transition, provided the measure of field fluctuations is treated properly. The origin of the discrepancy is traced by comparative simulations reproducing the erroneous results and by a transfer-matrix study of the one-dimensional case.

Alkali-metal magnetometers compete with SQUID detectors as the most sensitive magnetic field sensors. Their sensitivity is limited by relaxation due to spin-exchange collisions. We demonstrate a K magnetometer in which spin-exchange relaxation is completely eliminated by operating at high K density and low magnetic field. Direct measurements of the signal-to-noise ratio give a magnetometer sensitivity of $10\mathrm{f}\mathrm{T}\mathrm{H}{\mathrm{z}}^{\mathrm{-}\mathrm{1}\mathrm{/}\mathrm{2}}$, limited by magnetic noise produced by Johnson currents in the magnetic shields. We extend a previous theoretical analysis of spin exchange in low magnetic fields to arbitrary spin polarizations and estimate the shot-noise limit of the magnetometer to be $2\times {10}^{-18}\mathrm{T}\mathrm{H}{\mathrm{z}}^{\mathrm{-}\mathrm{1}\mathrm{/}\mathrm{2}}$.

We discuss the BCS-BEC crossover in a degenerate Fermi gas of two hyperfine states interacting close to a Feshbach resonance. We show that, by including fluctuation contributions to the free energy similar to that considered by Nozières and Schmitt-Rink, the character of the superfluid phase transition continuously changes from the BCS-type to the BEC-type, as the threshold of the quasimolecular band is lowered. In the BEC regime, the superfluid phase transition is interpreted in terms of molecules associated with both the Feshbach resonance and Cooper pairing.

We have studied the tunability of the interaction between permanent dipoles in Bose-Einstein condensates. Based on time-dependent control of the anisotropy of the dipolar interaction, we show that even the very weak magnetic dipole coupling in alkali gases can be used to excite collective modes. Furthermore, we discuss how the effective dipolar coupling in a Bose-Einstein condensate can be tuned from positive to negative values and even switched off completely by fast rotation of the orientation of the dipoles.

We propose and analyze two series of clustered quantum Hall states for rotating systems of spin-1 bosons. The first series [labeled $\mathrm{S}\mathrm{U}(4{)}_k$] includes the exact ground states of a model Hamiltonian at large angular momentum $L$, and also for $N=3k$ particles at $L=N$. The latter is a spin-singlet boson-triplet condensate. The second series, labeled $\mathrm{S}\mathrm{O}(5{)}_k$, includes exact ground states at large $L$ for different parameter values.