Measuring the polarization of a single photon typically results in its destruction. We propose, demonstrate, and completely characterize a quantum nondemolition (QND) scheme for realizing such a measurement nondestructively. This scheme uses only linear optics and photodetection of ancillary modes to induce a strong nonlinearity at the single-photon level, nondeterministically. We vary this QND measurement continuously into the weak regime and use it to perform a nondestructive test of complementarity in quantum mechanics. Our scheme realizes the most advanced general measurement of a qubit to date: it is nondestructive, can be made in any basis, and with arbitrary strength.

We investigate the correlation properties of a one-dimensional interacting Bose gas by loading a magnetically trapped Bose-Einstein condensate (BEC) into a deep two-dimensional optical lattice. We measure the three-body recombination rate for both the BEC in the magnetic trap and the BEC loaded into the optical lattice. The recombination rate coefficient is a factor of 7 smaller in the lattice, which we interpret as a reduction in the local three-body correlation function in the 1D case. This is a signature of correlation intermediate between that of the uncorrelated, phase coherent, 1D, mean-field regime and the strongly correlated Tonks-Girardeau regime.

We study nonlinear localization of a two-component Bose-Einstein condensate (BEC) in a one-dimensional optical lattice. Our theory shows that spin-dependent optical lattices can be used to effectively manipulate the nonlinear interactions between the BEC components, and to observe composite localized states of a BEC in both bands and gaps of the matter-wave spectrum.

We investigate the lifetime of macroscopic entanglement under the influence of decoherence. For Greenberger-Horne-Zeilinger–type superposition states, we find that the lifetime decreases with the size of the system (i.e., the number of independent degrees of freedom), and the effective number of subsystems that remain entangled decreases with time. For a class of other states (e.g., cluster states), however, we show that the lifetime of entanglement is independent of the size of the system.

Guided systems for coherent matter waves are expected to offer substantial improvements over unguided systems, but adiabatic coupler proposals have proven difficult to realize. We outline instead considerations for a coherence-preserving diabatic approach enabling filters, couplers, and interferometers that can accept multimode guide inputs of up to magneto-optical-trap temperatures.

We study the transport of vortices in superconductors with triangular arrays of boomerang- or V-shaped asymmetric pinning wells, when applying an alternating electrical current. The asymmetry of the pinning landscape induces a very efficient “diode” effect, that allows the sculpting at will of the magnetic field profile inside the sample. We present the first quantitative study of magnetic “lensing” of fluxons inside superconductors. Our proposed vortex lens provides a near threefold increase of the vortex density at its “focus” regions. The main numerical features have been derived analytically.

In this Letter we experimentally implement a single photon Bell test based on the ideas of S. Tan et al. [Phys. Rev. Lett. 66, 252 (1991)] and L. Hardy [Phys. Rev. Lett. 73, 2279 (1994)]. A double homodyne measurement is used to measure correlations in the Fock space spanned by zero and one photons. Local oscillators used in the correlation measurement are distributed to two observers by copropagating it in an orthogonal polarization mode. This method eliminates the need for interferometrical stability in the setup, consequently making it a robust and scalable method.

The dissociation of ultracold molecules was studied by ramping an external magnetic field through a Feshbach resonance. The observed dissociation energies directly yielded the strength of the atom-molecule coupling. They showed nonlinear dependence on the ramp speed.  This was explained by a Wigner threshold law which predicts that the decay rate of the molecules above threshold increases with the density of states.  In addition, inelastic molecule-molecule and molecule-atom collisions were characterized.

We formulate a simple additivity principle allowing one to calculate the whole distribution of current fluctuations through a large one dimensional system in contact with two reservoirs at unequal densities from the knowledge of its first two cumulants. This distribution (which in general is non-Gaussian) satisfies the Gallavotti-Cohen symmetry and generalizes the one predicted recently for the symmetric simple exclusion process. The additivity principle can be used to study more complex diffusive networks including loops.

Excitation spectroscopy of vortex lattices in rotating Bose-Einstein condensates is described. We numerically obtain the Bogoliubov–de Gennes quasiparticle excitations for a broad range of energies and analyze them in the context of the complex dynamics of the system. Our work is carried out in a regime in which standard hydrodynamic assumptions do not hold, and includes features not readily contained within existing treatments.

We investigate the fermionic $\mathrm{SU}(N)$ Hubbard model on the two-dimensional square lattice for weak to moderate interactions using renormalization group and mean-field methods. For the repulsive case $U>0$ at half filling and small $N$ the dominant tendency is towards breaking of the $\mathrm{SU}(N)$ symmetry. For $N>6$ staggered flux order takes over as the dominant instability, in agreement with the large-$N$ limit. Away from half filling for $N=3$ two flavors remain half filled by cannibalizing the third flavor. For $U<0$ and odd $N$ a full Fermi surface coexists with a superconductor. These results may be relevant to future experiments with cold fermionic atoms in optical lattices.

We present a novel method for the calculation of the energy density of states $D(E)$ for systems described by classical statistical mechanics. The method builds on an extension of a recently proposed strategy that allows the free-energy profile of a canonical system to be recovered within a preassigned accuracy [A. Laio and M. Parrinello, Proc. Natl. Acad. Sci. U.S.A. 99, 12562 (2002)]. The method allows a good control over the error on the recovered system entropy. This fact is exploited to obtain $D(E)$ more efficiently by combining measurements at different temperatures. The accuracy and efficiency of the method are tested for the two-dimensional Ising model (up to size $50\times 50$) by comparison with both exact results and previous studies. This method is a general one and should be applicable to more realistic model systems.

The theory of decoherent histories is checked for the requirement of statistical independence of subsystems. Strikingly, this is satisfied only when the decoherence functional is diagonal in both its real and imaginary parts. Although the weakened condition of consistency (or weak decoherence), allowing a nondiagonal imaginary part, is sufficient for the assignment of probabilities, it may easily violate the statistical independence of subsystems. Therefore, weakened consistency conditions and various related generalizations of the concept of decoherent histories appear to be ruled out. The same conclusion is obtained independently, by claiming a plausible dynamical robustness of decoherent histories.

We report on a matter wave interferometer realized with entangled pairs of trapped ${}^{87}\mathrm{Rb}$ atoms. Each pair of atoms is confined at a single site of an optical lattice potential. The interferometer is realized by first creating a coherent spin superposition of the two atoms and then tuning the interstate scattering length via a Feshbach resonance. The selective change of the interstate scattering length leads to an entanglement dynamics of the two-particle state that can be detected in a Ramsey interference experiment. This entanglement dynamics is employed for a precision measurement of atomic interaction parameters. Furthermore, the interferometer allows us to separate lattice sites with one or two atoms in a nondestructive way.

The motion of two interacting species of small particles, coupled differently to their environment, is studied both analytically and via numerical simulations. We find three ways of controlling the particle motion of one (passive) $B$ species by means of another (active) $A$ species: (i) dragging the target particles $B$ by driving the auxiliary particles $A$, (ii) rectifying the motion of the $B$ species on the asymmetric potential created by the $A\mathrm{\text{−}}B$ interactions, and (iii) dynamically modifying (pulsating) this potential by controlling the motion of the $A$ particles. This allows easy control of the magnitude and direction of the velocity of the target particles by changing the ac drive(s).

The motion of extended defects in materials is often resisted by interaction with diffusing impurities. The defect undergoes a transition from slow to fast migration, or vice versa. This transition is commonly hysteretic, with the defect jumping back and forth between these kinetic states. We explore such hysteresis within a kinetic Monte Carlo simulation. After identifying the slow variables, we construct an effective potential that quantitatively describes the stable and metastable states of the system (a bifurcation diagram) and the kinetics of the transitions between these. This description provides a means to determine whether hysteresis will be observed in a particular simulation and the detailed nature of this hysteresis (switching times).

We study bosonic atoms near a Feshbach resonance and predict that, in addition to standard normal and atomic superfluid phases, this system generically exhibits a distinct phase of matter: a molecular superfluid, where molecules are superfluid while atoms are not. We explore zero- and finite-temperature properties of the molecular superfluid (a bosonic, strong-coupling analog of a BCS superconductor), and study quantum and classical phase transitions between the normal, molecular superfluid, and atomic superfluid states.

The low temperature dynamics of a vortex in a trapped quasi-two-dimensional Bose-Einstein condensate are studied quantitatively. Precession of an off-centered vortex in a dimple trap, embedded in a weaker harmonic trap, leads to the emission of sound in a dipolar radiation pattern. Sound emission and reabsorption can be controlled by varying the depth of the dimple. In a shallow dimple, the power emitted is proportional to the vortex acceleration-squared over the precession frequency, whereas for a deep dimple, periodic sound reabsorption stabilizes the vortex against radiation-induced decay.

We show that, apart from a difference in scale, all of the surprising recently observed properties of a degenerate Fermi gas near a Feshbach resonance persist in the high temperature Boltzmann regime. In this regime, the Feshbach resonance is unshifted. By sweeping across the resonance, a thermal distribution of bound states (molecules) can be reversibly generated. Throughout this process, the interaction energy is negative and continuous. We also show that this behavior must persist at lower temperatures unless there is a phase transition as the temperature is lowered. We rigorously demonstrate universal behavior near the resonance.

We present a mean-field theory numerical study of Tkachenko waves of a vortex lattice in trapped atomic Bose-Einstein condenstates. Our results show remarkable qualitative and quantitative agreement with recent experiments at the Joint Institute for Laboratory Astrophysics. We extend our calculations beyond the conditions of the experiment, probing deeper into the incompressible regime where we find excellent agreement with analytical results. In addition, bulk excitations observed in the experiment are discussed.