We study the transport of ultracold atoms in a tight optical lattice. For identical fermions the system is insulating under an external force while for bosonic atoms it is conducting. This reflects the different collisional properties of the particles and reveals the role of interparticle collisions in establishing a macroscopic transport in a perfectly periodic potential. Also in the case of fermions we can induce a transport by creating a collisional regime through the addition of bosons. We investigate the transport as a function of the collisional rate and observe a transition from a regime in which the mobility increases with increasing collisional rate to one in which it decreases. We compare our data with a theoretical model for electron transport in solids introduced by Esaki and Tsu.

The canonical thermodynamic properties of a one-dimensional system of interacting spin-$1/2$ fermions with an attractive zero-range pseudopotential are investigated within an exact approach. The density operator is evaluated as the statistical average of dyadics formed from a stochastic mean-field propagation of independent Slater determinants. For a harmonically trapped Fermi gas and for fermions confined in a 1D-like torus, we observe the transition to a quasi-BCS state with Cooper-like momentum correlations and an algebraic long-range order. For a few trapped fermions in a rotating torus, a dominant superfluid component with quantized circulation can be isolated.

The Berry phase in a composite system with one driven subsystem has been studied in this Letter. We choose two coupled spin-$\frac{1}{2}$ systems as the composite system; one of the subsystems is driven by a time-dependent magnetic field. We show how the Berry phases depend on the coupling between the two subsystems, and the relation between the Berry phases of the composite system and those of its subsystems.

Just as transition rates in a canonical ensemble must respect the principle of detailed balance, constraints exist on transition rates in driven steady states. I derive those constraints, by maximum information-entropy inference, and apply them to the steady states of driven diffusion and a sheared lattice fluid. The resulting ensemble can potentially explain nonequilibrium phase behavior and, for steady shear, gives rise to stress-mediated long-range interactions.

We consider a gas of cold fermionic atoms having two spin components with interactions characterized by their $s$-wave scattering length $a$. At positive scattering length the atoms form weakly bound bosonic molecules which can be evaporatively cooled to undergo Bose-Einstein condensation, whereas at negative scattering length BCS pairing can take place. It is shown that, by adiabatically tuning the scattering length $a$ from positive to negative values, one may transform the molecular Bose-Einstein condensate into a highly degenerate atomic Fermi gas, with the ratio of temperature to Fermi temperature $T/T_F\sim {10}^{-2}$. The corresponding critical final value of $k_F|a|$, which leads to the BCS transition, is found to be about one-half, where $k_F$ is the Fermi momentum.

Spatial correlations are observed in an ultracold gas of fermionic atoms close to a Feshbach resonance. The correlations are detected by inducing spin-changing rf transitions between pairs of atoms. We observe the process in the strongly interacting regime for attractive as well as for repulsive atom-atom interactions and both in the regime of high and low quantum degeneracy. The observations are compared with a two-particle model that provides theoretical predictions for the measured rf transition rates.

Bose-Einstein condensates of sodium atoms, prepared in an optical dipole trap, were distilled into a second empty dipole trap adjacent to the first one. The distillation was driven by thermal atoms spilling over the potential barrier separating the two wells and then forming a new condensate. This process serves as a model system for metastability in condensates, provides a test for quantum kinetic theories of condensate formation, and also represents a novel technique for creating or replenishing condensates in new locations.

We observe collective oscillations of a trapped, degenerate Fermi gas of ${}^6\mathrm{Li}$ atoms at a magnetic field just above a Feshbach resonance, where the two-body physics does not support a bound state. The gas exhibits a radial breathing mode at a frequency of 2837(05) Hz, in excellent agreement with the frequency of ${\nu }_H\equiv \sqrt{10{\nu }_x{\nu }_y/3}=2830(20)\mathrm{Hz}$ predicted for a hydrodynamic Fermi gas with unitarity-limited interactions. The measured damping times and frequencies are inconsistent with predictions for both the collisionless mean field regime and for collisional hydrodynamics. These observations provide the first evidence for superfluid hydrodynamics in a resonantly interacting Fermi gas.

Two particles, initially in a product state, become entangled when they come together and start to interact. Using semiclassical methods, we calculate the time evolution of the corresponding reduced density matrix ${\rho }_1$, obtained by integrating out the degrees of freedom of one of the particles. We find that entanglement generation sensitively depends (i) on the interaction potential, especially on its strength and range, and (ii) on the nature of the underlying classical dynamics. Under general statistical assumptions, and for short-ranged interaction potentials, we find that $\mathcal{P}(t)$ decays exponentially fast in a chaotic environment, whereas it decays only algebraically in a regular system. In the chaotic case, the decay rate is given by the golden rule spreading of one-particle states due to the two-particle coupling, but cannot exceed the system’s Lyapunov exponent.

We study the expansion of an atomic Fermi gas interacting attractively with a Bose-Einstein condensate. We observe a slower evolution of the radial-to-axial aspect ratio which reveals the importance of the mutual attraction between the two samples during the first phase of the expansion. For large atom numbers, we also observe a bimodal momentum distribution of the Fermi gas, which reflects the spatial distribution of the mixture in trap. This effect allows us to extract important information on the overlap of the two species across the collapse.

The usual Kondo effect is associated with the formation of a many-body ground state that contains a quantum-mechanical entanglement between a (localized) fermion and the free fermions. We show, however, that also a bosonic form of the Kondo effect can occur in degenerate atomic Fermi gases near a Feshbach resonance, if the energy of the diatomic molecular level associated with the Feshbach resonance approaches twice the Fermi energy of the atoms.

For calculating low-energy properties of a dilute gas of atoms interacting via a Feshbach resonance, we develop an effective theory in which the parameters that enter are an atom-molecule coupling strength and the magnetic moment of the molecular resonance. We demonstrate that, for resonances in the fermionic systems ${}^6\mathrm{Li}$ and ${}^{40}\mathrm{K}$ that are under experimental investigation, the coupling is so strong that many-body effects are appreciable even when the resonance lies at an energy large compared with the Fermi energy. We calculate a number of many-body effects, including the effective mass and the lifetime of atomic quasiparticles in the gas.

We measure spin mixing of $F=1$ and $F=2$ spinor condensates of ${}^{87}\mathrm{Rb}$ atoms confined in an optical trap. We determine the spin mixing time to be typically less than 600 ms and observe spin population oscillations. The equilibrium spin configuration in the $F=1$ manifold is measured for different magnetic fields and found to show ferromagnetic behavior for low field gradients. An $F=2$ condensate is created by microwave excitation from the $F=1$ manifold, and this spin-2 condensate is observed to decay exponentially with time constant 250 ms. Despite the short lifetime in the $F=2$ manifold, spin mixing of the condensate is observed within 50 ms.

We discuss the possibility of inhibiting three-body recombination in atomic Bose-Einstein condensates via the application of resonant $2\pi$ laser pulses. These pulses result in the periodic change in the phase of the molecular state by $\pi$, which leads to destructive interference between the decay amplitudes following successive pulses. We show that the decay rate can be reduced by several orders of magnitude under realistic conditions.

The puzzle of how time-reversible microscopic equations of mechanics lead to the time-irreversible macroscopic equations of thermodynamics has been a paradox since the days of Boltzmann. Boltzmann simply sidestepped this enigma by stating “as soon as one looks at bodies of such small dimension that they contain only very few molecules, the validity of this theorem [the second law of thermodynamics and its description of irreversibility] must cease.” Today we can state that the transient fluctuation theorem (TFT) of Evans and Searles is a generalized, second-law-like theorem that bridges the microscopic and macroscopic domains and links the time-reversible and irreversible descriptions. We apply this theorem to a colloidal particle in an optical trap. For the first time, we demonstrate the TFT in an experiment and show quantitative agreement with Langevin dynamics.

We show that a two-dimensional (2D) array of 1D interacting boson tubes has a deconfinement transition between a 1D Mott insulator and a 3D superfluid for commensurate fillings and a dimensional crossover for the incommensurate case. We determine the phase diagram and excitations of this system and discuss the consequences for Bose condensates loaded in 2D optical lattices.

Classical particles driven through periodically modulated potential energy landscapes are predicted to follow a devil’s staircase hierarchy of commensurate trajectories depending on the orientation of the driving force. Recent experiments on colloidal spheres flowing through arrays of optical traps do indeed reveal such a hierarchy, but not with the predicted structure. The microscopic trajectories, moreover, appear to be random, with commensurability emerging only in a statistical sense. We introduce an idealized model for periodically modulated transport in the presence of randomness that captures both the structure and statistics of such statistically locked-in states.

We study 1D trapped Bose gases in the strongly interacting regime. The systems are created in an optical lattice and are subject to a longitudinal periodic potential. Bragg spectroscopy enables us to investigate the excitation spectrum in different regimes. In the superfluid phase a broad continuum of excitations is observed which calls for an interpretation beyond the Bogoliubov spectrum taking into account the effect of strong interactions. In the Mott insulating phase a discrete spectrum is measured. Both phases are compared to the 3D situation and to the crossover regime from 1D to 3D. The coherence length and coherent fraction of the gas are measured in all configurations. We observe signatures for increased fluctuations characteristic for 1D systems. Moreover, the collective oscillations cease near the transition to the Mott insulator phase.

We generalize the correlation functions of the Clauser-Horne-Shimony-Holt (CHSH) inequality to arbitrarily high-dimensional systems. Based on this generalization, we construct the general CHSH inequality for bipartite quantum systems of arbitrarily high dimensionality, which takes the same simple form as CHSH inequality for two dimensions. This inequality is optimal in the same sense as the CHSH inequality for two-dimensional systems, namely, the maximal amount by which the inequality is violated consists of the maximal resistance to noise. We also discuss the physical meaning and general definition of the correlation functions. Furthermore, by giving another specific set of the correlation functions with the same physical meaning, we realize the inequality presented by Collins et al. [Phys. Rev. Lett. 88, 040404 (2002)].

Using recent fluctuation theorems from nonequilibrium statistical mechanics, we extend the theory for voltage fluctuations in electric circuits to power and heat fluctuations. They could be of particular relevance for the functioning of small circuits. This is done for a parallel resistor and capacitor with a constant current source for which we use the analogy with a Brownian particle dragged through a fluid by a moving harmonic potential, where circuit-specific analogs are needed on top of the Brownian-Nyquist analogy. The results may also hold for other circuits as another example shows.