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We propose a new light source based on having alkaline-earth atoms in an optical lattice collectively emit photons on an ultra-narrow clock transition into the mode of a high Q-resonator. The resultant optical radiation has an extremely narrow linewidth in the mHz range, even smaller than that of the clock transition itself due to collective effects. A power level of order $10^{-12}W$ is possible, sufficient for phase-locking a slave optical local oscillator. Realizing this light source has the potential to improve the stability of the best clocks by two orders of magnitude., Comment: minor revisions + shortening; factor 2 algebra mistake corrected

Interferometry with Heisenberg limited phase resolution may play an important role in the next generation of atomic clocks, gravitational wave detectors, and in quantum information science. For experimental implementations the robustness of the phase resolution is crucial since any experimental realization will be subject to imperfections. In this article we study the robustness of phase reconstruction with two number states as input subject to fluctuations in the state preparation. We find that the phase resolution is insensitive to fluctuations in the total number of particles and robust against noise in the number difference at the input. The phase resolution depends on the uncertainty in the number difference in a universal way that has a clear physical interpretation: Fundamental noise due to the Heisenberg limit and noise due to state preparation imperfection contribute essentially independently to the total uncertainty in the phase. For number difference uncertainties less than one the first noise source is dominant and the phase resolution is essentially Heisenberg limited. For number difference uncertainties greater than one the noise due to state preparation imperfection is dominant and the phase resolution deteriorates linearly with the number difference uncertainty., Comment: 13 pages, 6 figures; high-resolution version can be obtained from authors

We study Bragg spectroscopy of a strongly interacting Bose-Einstein condensate using time-dependent Hartree-Fock-Bogoliubov theory. We include approximatively the effect of the momentum dependent scattering amplitude which is shown to be the dominant factor in determining the spectrum for large momentum Bragg scattering. The condensation of the Bragg scattered atoms is shown to significantly alter the observed excitation spectrum by creating a novel pairing channel of mobile pairs., Comment: 11 pages, 4 figures

We demonstrate that the process of evaporative cooling, as associated with the cooling of atomic gases, can also be employed to condense a system of photons giving rise to coherent properties of the light. The system we study consists of photons in a high-quality Fabry-Perot cavity with photon interactions mediated by a nonlinear atomic medium. We predict a macroscopic occupation of the lowest energy mode and evaluate the conditions for realizing a narrow spectral width indicative of a long coherence time for the field.

The ability to control spins in semiconductors is important in a variety of fields including spintronics and quantum information processing. Due to the potentially fast dephasing times of spins in the solid state [1-3], spin control operating on the picosecond or faster timescale may be necessary. Such speeds, which are not possible to attain with standard electron spin resonance (ESR) techniques based on microwave sources, can be attained with broadband optical pulses. One promising ultrafast technique utilizes single broadband pulses detuned from resonance in a three-level Lambda system [4]. This attractive technique is robust against optical pulse imperfections and does not require a fixed optical reference phase. Here we demonstrate the principle of coherent manipulation of spins theoretically and experimentally. Using this technique, donor-bound electron spin rotations with single-pulse areas exceeding pi/4 and two-pulses areas exceeding pi/2 are demonstrated. We believe the maximum pulse areas attained do not reflect a fundamental limit of the technique and larger pulse areas could be achieved in other material systems. This technique has applications from basic solid-state ESR spectroscopy to arbitrary single-qubit rotations [4, 5] and bang-bang control[6] for quantum computation., Comment: 15 pages, 4 figures, submitted 12/2008. Since the submission of this work we have become aware of related work: J. Berezovsky, M. H. Mikkelsen, N. G. Stoltz, L. A. Coldren, and D. D. Awschalom, Science 320: 349-352 (2008)

We prove that a class of one-dimensional maps with an arbitrary number of non-degenerate critical and singular points admits an induced Markov tower with exponential return time asymptotics. In particular the map has an absolutely continuous invariant probability measure with exponential decay of correlations for H\"{o}lder observations., Comment: 31 pages

Quantum projection noise will soon limit the best achievable precision of optical atomic clocks based on lattice-confined neutral atoms. Squeezing the collective atomic pseudo-spin via measurement of the clock state populations during Ramsey interrogation suppresses the projection noise. We show here that the lattice laser field can be used to perform ideal quantum non-demolition measurements without clock shifts or decoherence and explore the feasibility of such an approach in theory with the lattice field confined in a ring-resonator. Detection of the motional sideband due to the atomic vibration in the lattice wells can yield signal sizes a hundredfold above the projection noise limit., Comment: Substantially expanded version

Using the Kubo formalism, we demonstrate fractional quantum Hall features in a rotating Bose-Einstein condensate in a co-rotating two-dimensional optical lattice. The co-rotating lattice and trap potential allow for an effective magnetic field and compensation of the centrifugal potential. Fractional quantum Hall features are seen for the single-particle system and for few strongly interacting many-particle systems., Comment: 11 pages, 13 figures

We illustrate that open quantum systems composed of neutral, ultracold atoms in one-dimensional optical lattices can exhibit behavior analogous to semiconductor electronic circuits. A correspondence is demonstrated for bosonic atoms, and the experimental requirements to realize these devices are established. The analysis follows from a derivation of a quantum master equation for this general class of open quantum systems., Comment: Significantly Revised, and accepted for publication in PRL 2009

We observe millisecond spin-flip relaxation times of donor-bound electrons in high-purity n-GaAs . This is three orders of magnitude larger than previously reported lifetimes in n-GaAs . Spin-flip times are measured as a function of magnetic field and exhibit a strong power-law dependence for fields greater than 4 T . This result is in qualitative agreement with previously reported theory and measurements of electrons in quantum dots., Comment: 4 pages, 4 figures

Bose gases in rotating optical lattices combine two important topics in quantum physics: superfluid rotation and strong correlations. In this paper, we examine square two-dimensional systems at zero temperature comprised of strongly repulsive bosons with filling factors of less than one atom per lattice site. The entry of vortices into the system is characterized by jumps of 2 pi in the phase winding of the condensate wavefunction. A lattice of size L X L can have at most L-1 quantized vortices in the lowest Bloch band. In contrast to homogeneous systems, angular momentum is not a good quantum number since the continuous rotational symmetry is broken by the lattice. Instead, a quasi-angular momentum captures the discrete rotational symmetry of the system. Energy level crossings indicative of quantum phase transitions are observed when the quasi-angular momentum of the ground-state changes., Comment: 12 Pages, 13 Figures, Version 1

Atomtronics focuses on atom analogs of electronic materials, devices and circuits. A strongly interacting ultracold Bose gas in a lattice potential is analogous to electrons in solid-state crystalline media. As a consequence of the band structure, cold atoms in a lattice can exhibit insulator or conductor properties. P-type and N-type material analogs can be created by introducing impurity sites into the lattice. Current through an atomtronic wire is generated by connecting the wire to an atomtronic battery which maintains the two contacts at different chemical potentials. The design of an atomtronic diode with a strongly asymmetric current-voltage curve exploits the existence of superfluid and insulating regimes in the phase diagram. The atomtronic analog of a bipolar junction transistor exhibits large negative gain. Our results provide the building blocks for more advanced atomtronic devices and circuits such as amplifiers, oscillators and fundamental logic gates.

We report a novel hemispherical micro-cavity that is comprised of a planar integrated semiconductor distributed Bragg reflector (DBR) mirror, and an external, concave micro-mirror having a radius of curvature $50\mathrm{\mu m}$. The integrated DBR mirror containing quantum dots (QD), is designed to locate the QDs at an antinode of the field in order to maximize the interaction between the QD and the cavity. The concave micro-mirror, with high-reflectivity over a large solid-angle, creates a diffraction-limited (sub-micron) mode-waist at the planar mirror, leading to a large coupling constant between cavity mode and QD. The half-monolithic design gives more spatial and spectral tuning abilities, relatively to fully monolithic structures. This unique micro-cavity design will potentially enable us to both reach the cavity quantum electrodynamics (QED) strong coupling regime and realize the deterministic generation of single photons on demand., Comment: 15 pages, 17 figures, final version

We develop a time-dependent mean-field theory to investigate the released momentum distribution and the released energy of an ultracold Fermi gas in the BCS-BEC crossover after the scattering length has been set to zero by a fast magnetic-field ramp. For a homogeneous gas we analyze the non-equilibrium dynamics of the system as a function of the interaction strength and of the ramp speed. For a trapped gas the theoretical predictions are compared with experimental results., Comment: 4 pages, 4 figures

Strongly interacting bosons in 2D in a rotating square lattice are investigated via a modified Bose-Hubbard Hamiltonian. Such a system corresponds to a rotating lattice potential imprinted on a trapped Bose-Einstein condensate. Second-order quantum phase transitions between states of different symmetries are observed at discrete rotation rates. For the square lattice we study, there are four possible ground-state symmetries., Comment: 4 pages, 5 figures, Accepted for publication in PRL v2: Replaced phase winding labels with symmetry eigenstate indices, replaced Gaussian Ansatz with more general treatment and other minor changes

Bose-Einstein condensates are studied in a potential of finite depth which supports both bound and quasi-bound states. This potential, which is harmonic for small radii and decays as a Gaussian for large radii, models experimentally relevant optical traps. The nonlinearity, which is proportional to both the number of atoms and the interaction strength, can transform bound states into quasi-bound ones. The latter have a finite lifetime due to tunnelling through the barriers at the borders of the well. We predict the lifetime and stability properties for repulsive and attractive condensates in one, two, and three dimensions, for both the ground state and excited soliton and vortex states. We show, via a combination of the variational and WKB approximations, that macroscopic quantum tunnelling in such systems can be observed on time scales of 10 milliseconds to 10 seconds., Comment: J. Phys. B: At. Mol. Opt. Phys. in press

We observe dramatic changes in the atomic momentum distribution of a Fermi gas in the region of the BCS-BEC crossover. We study the shape of the momentum distribution and the kinetic energy as a function of interaction strength. The momentum distributions are compared to a mean-field crossover theory, and the kinetic energy is compared to theories for the two weakly interacting limits. The temperature dependence of the distribution is also presented., Comment: Includes revisions to Figure 3 and references

The band structure of a Bose-Einstein condensate is studied for lattice traps of sinusoidal, Jacobi elliptic, and Kronig-Penney form. It is demonstrated that the physical properties of the system are independent of the choice of lattice. The Kronig-Penney potential, which admits a full exact solution in closed analytical form, is then used to understand in a novel way the swallowtails, or loops, that form in the band structure. Their appearance can be explained by adiabatically tuning a second lattice with half the period. Such a two-color lattice, which can be easily realized in experiments, has intriguing new physical properties. For instance, swallowtails appear even for weak nonlinearity, which is the experimental regime. We determine the stability properties of this system and relate them to current experiments.

In high-purity n-type GaAs under strong magnetic field, we are able to isolate a lambda system composed of two Zeeman states of neutral-donor bound electrons and the lowest Zeeman state of bound excitons. When the two-photon detuning of this system is zero, we observe a pronounced dip in the excited-state photoluminescence indicating the creation of the coherent population-trapped state. Our data are consistent with a steady-state three-level density-matrix model. The observation of coherent population trapping in GaAs indicates that this and similar semiconductor systems could be used for various EIT-type experiments., Comment: 5 pages, 4 figures replaced 6/25/2007 with PRL version

We propose a multi-band Fermi-Bose Hubbard model with on-site fermion-boson conversion and general filling factor in three dimensions. Such a Hamiltonian models an atomic Fermi gas trapped in a lattice potential and subject to a Feshbach resonance. We solve this model in the two state approximation for paired fermions at zero temperature. The problem then maps onto a coupled Heisenberg spin model. In the limit of large positive and negative detuning, the quantum phase transitions in the Bose Hubbard and Paired-Fermi Hubbard models are correctly reproduced. Near resonance, the Mott states are given by a superposition of the paired-fermion and boson fields and the Mott-superfluid borders go through an avoided crossing in the phase diagram., Comment: 4 pages, 3 figures

The full set of stationary states of the mean field of a Bose-Einstein condensate in the presence of a potential step or point-like impurity are presented in closed analytic form. The nonlinear Schr\"odinger equation in one dimension is taken as a model. The nonlinear analogs of the continuum of stationary scattering states, as well as evanescent waves, are discussed. The solutions include asymmetric soliton trains and other wavefunctions of novel form, such as a pair of dark solitons bound by an impurity.

All Bloch states of the mean field of a Bose-Einstein condensate in the presence of a one dimensional lattice of impurities are presented in closed analytic form. The band structure is investigated by analyzing the stationary states of the nonlinear Schr\"odinger, or Gross-Pitaevskii, equation for both repulsive and attractive condensates. The appearance of swallowtails in the bands is examined and interpreted in terms of the condensates superfluid properties. The nonlinear stability properties of the Bloch states are described and the stable regions of the bands and swallowtails are mapped out. We find that the Kronig-Penney potential has the same properties as a sinusoidal potential; Bose-Einstein condensates are trapped in sinusoidal optical lattices. The Kronig-Penney potential has the advantage of being analytically tractable, unlike the sinusoidal potential, and, therefore, serves as a good model for experimental phenomena., Comment: Version 2. Fixed typos, added reference

The entropy and kinetic, potential, and interaction energies of an atomic Fermi gas in a trap are studied under the assumption of thermal equilibrium for finite temperature. A Feshbach resonance can cause the fermions to pair into diatomic molecules. The entropy and energies of mixtures of such molecules with unpaired atoms are calculated, in relation to recent experiments on molecular Bose-Einstein condensates produced in this manner. It is shown that, starting with a Fermi gas of temperature $T= 0.1 T_F^0$, where $T_F^0$ is the non-interacting Fermi temperature, an extremely cold degenerate Fermi gas of temperature $T \lesssim 0.01 T_F^0$ may be produced without further evaporative cooling. This requires adiabatic passage of the resonance, subsequent sudden removal of unpaired atoms, and adiabatic return. We also calculate the ratio of the interaction energy to the kinetic energy, a straightforward experimental signal which may be used to determine the temperature of the atoms and indicate condensation of the molecules., Comment: 12 pages, 5 figures

Feshbach scattering resonances are being utilized in atomic gases to explore the entire crossover region from a Bose-Einstein Condensation (BEC) of composite bosons to a Bardeen-Cooper-Schrieffer (BCS) of Cooper pairs. Several theoretical descriptions of the crossover have been developed based on an assumption that the fermionic interactions are dependent only on the value of a single microscopic parameter, the scattering length for the interaction of fermion particles. Such a picture is not universal, however, and is only applicable to describe a system with an energetically broad Feshbach resonance. In the more general case in which narrow Feshbach resonances are included in the discussion, one must consider how the energy dependence of the scattering phase shift affects the physical properties of the system. We develop a theoretical framework which allows for a tuning of the scattering phase shift and its energy dependence, whose parameters can be fixed from realistic scattering solutions of the atomic physics. We show that BCS-like nonlocal solutions may build up in conditions of resonance scattering, depending on the effective range of the interactions., Comment: 8 pages,7 figures

Correlations between a composite boson and a fermion pair are considered in the context of the crossover theory of fermionic to bosonic superfluidity. It is shown that such correlations are the minimal ingredients needed in a many-body theory to generate the right boson-boson scattering length in the Bose-Einstein limit of the crossover., Comment: 4 pages, no figures

We study the superfluid state of atomic Fermi gases using a BCS-BEC crossover theory. Our approach emphasizes non-condensed fermion pairs which strongly hybridize with their (Feshbach-induced) molecular boson counterparts. These pairs lead to pseudogap effects above $T_c$ and non-BCS characteristics below. We discuss how these effects influence the experimental signatures of superfluidity., Comment: 4 pages, 3 figures, submitted to PRA Rapid Communications; introduction rewritten, figure replaced

We propose increasing the fractional quantum Hall gap of a rapidly rotating Bose gas by increasing the interatomic interactions via a Feshbach resonance. The generation of molecules by the resonance causes pair correlations to grow throughout the system effecting the ground state. By an extension of the usual Chern-Simons theory, built of composite atoms and molecules, we are able to account for these resonance effects. We find that the resulting ground state evolves from a Laughlin wavefunction to a unique paired wavefunction as one approaches the resonance.

We investigate the quantum state of burst atoms seen in the recent Rb-85 experiments at JILA. We show that the presence of a resonance scattering state can lead to a pairing instability generating an outflow of atoms with energy comparable to that observed. A resonance effective field theory is used to study this dynamical process in an inhomogeneous system with spherical symmetry.

We present a unified kinetic theory that describes the finite-temperature, non-equilibrium dynamics of a Bose-Einstein condensed gas interacting with a thermal cloud. This theory includes binary interactions to second order in the interaction potential and reduces to a diagonal quantum Boltzmann equation for Bogoliubov quasiparticles. The Hartree-Fock-Bogoliubov interactions include the pairing field and are expressed as many-body $T$ matrices to second order. The interactions thus include the correct renormalized scattering physics. This renormalized theory is automatically gapless. Thus, the excited Bogoliubov modes are naturally orthogonal to the condensate ground state., Comment: 12 pgs, 3 figs, RevTeX4, submitted to PRA

In a recent experiment, a Feshbach scattering resonance was exploited to observe Ramsey fringes in a $^{85}$Rb Bose-Einstein condensate. The oscillation frequency corresponded to the binding energy of the molecular state. We show that the observations are remarkably consistent with predictions of a resonance field theory in which the fringes arise from oscillations between atoms and molecules., Comment: 5 pages, 5 figures

We present a description of the behavior of a superfluid gas of fermions in the presence of a Feshbach resonance over the complete range of magnetic field detunings. Starting from a resonance Hamiltonian, we exploit a functional method to describe the continuous behavior from Bardeen-Cooper-Schrieffer to Bose-Einstein condensation type superfluidity. Our results show an ability for a resonance system to exhibit a high critical temperature comparable to the Fermi temperature. The results are derived in a manner that is shown to be consistent with the underlying microscopic scattering physics.

Using the prescription of the nonequilibrium statistical operator method, we derive a non-Markovian generalization to the kinetic theory described by Walser {\sl et al.} [Phys. Rev. A {\bf 59}, 3878 (1999)]. Quasi-particle damping and effects arising from the finite duration of a collision are introduced to include terms beyond the Born approximation. Such a self-consistent theory is shown to conserve energy to second order in the interaction strength, even in the Markov limit. This kinetic theory is applied to a simple model of a Bose gas confined in a spherical trap to study the full real-time evolution towards equilibrium. A modified form for the damping function, is seen to strongly improve the energy conservation. Based on a linear response calculation, we predict the damping rates and frequencies of the collective excitations. We demonstrate the emergence of differing time scales for damping and equilibration., Comment: 11 figures, submitted to Phys. Rev. A

We derive a theory of superfluidity for a dilute Fermi gas that is valid when scattering resonances are present. The treatment of a resonance in many-body atomic physics requires a novel mean-field approach starting from an unconventional microscopic Hamiltonian. The mean-field equations incorporate the microscopic scattering physics, and the solutions to these equations reproduce the energy-dependent scattering properties. This theory describes the high-$T_c$ behavior of the system, and predicts a value of $T_c$ which is a significant fraction of the Fermi temperature. It is shown that this novel mean-field approach does not break down for typical experimental circumstances, even at detunings close to resonance. As an example of the application of our theory we investigate the feasibility for achieving superfluidity in an ultracold gas of fermionic $^6$Li., Comment: 15 pages, 10 figures

In this letter, we predict a direct and observable signature of the superfluid phase in a quantum Fermi gas, in a temperature regime already accessible in current experiments. We apply the theory of resonance superfluidity to a gas confined in a harmonic potential and demonstrate that a significant increase in density will be observed in the vicinity of the trap center., Comment: 4 pages, 4 figures

We discuss the equivalence of two non-equilibrium kinetic theories that describe the evolution of a dilute, Bose-Einstein condensed atomic gas in a harmonic trap. The second-order kinetic equations of Walser et al. [PRA 63, 013607 (2001)] reduce to the Gross-Pitaevskii equation and the quantum Boltzmann equation in the low and high temperature limits, respectively. These kinetic equations can thus describe the system in equilibrium (finite temperature) as well as in non-equilibrium (real time). We have found this theory to be equivalent to the non-equilibrium Green's function approach originally proposed by Kadanoff and Baym and more recently applied to inhomogeneous trapped systems by M. Imamovi\'c-Tomasovi\'c and A. Griffin [arXiv:cond-mat/9911402]., Comment: REVTeX3, 6 pages, 2 eps figures, published version, minor changes

We consider the superfluid phase transition that arises when a Feshbach resonance pairing occurs in a dilute Fermi gas. We apply our theory to consider a specific resonance in potassium-40, and find that for achievable experimental conditions, the transition to a superfluid phase is possible at the high critical temperature of about 0.5 T_F. Observation of superfluidity in this regime would provide the opportunity to experimentally study the crossover from the superfluid phase of weakly-coupled fermions to the Bose-Einstein condensation of strongly-bound composite bosons., Comment: 4 pages, 3 figures

We realized an equivalent Hanbury Brown and Twiss experiment for a beam of electrons in a two dimensional electron gas in the quantum Hall regime. A metallic split gate serves as a tunable beam splitter which is used to partition the incident beam into transmitted and reflected partial beams. The current fluctuations in the reflected and transmitted beam are fully anticorrelated demonstrating that fermions tend to exclude each other (anti-bunching). If the occupation probability of the incident beam is lowered by an additional gate, the anticorrelation is reduced and disappears in the classical limit of a highly diluted beam.

We have experimentally studied shot noise of chaotic cavities defined by two quantum point contacts in series. The cavity noise is determined as 1/4*2e|I| in agreement with theory and can be well distinguished from other contributions to noise generated at the contacts. Subsequently, we have found that cavity noise decreases if one of the contacts is further opened and reaches nearly zero for a highly asymmetric cavity., Comment: 4 pages, 4 figures, REVTeX

We derive the frequency of precession and conditions for stability for a quantized vortex in a single-component and a two-component Bose-Einstein condensate. The frequency of precession is proportional to the gradient of the free energy with respect to displacement of the vortex core. In a two-component system, it is possible to achieve a local minimum in the free energy at the center of the trap. The presence of such a minimum implies the existence of a region of energetic stability where the vortex cannot escape and where one may be able to generate a persistent current., Comment: 6 Pages, 6 Figures

In this paper, we show that pair-correlations may play an important role in the quantum statistical properties of a Bose-Einstein condensed gas composed of an atomic field resonantly coupled with a corresponding field of molecular dimers. Specifically, pair-correlations in this system can dramatically modify the coherent and incoherent transfer between the atomic and molecular fields., Comment: 4 pages, 4 figures

We have formulated a kinetic theory for a condensed atomic gas in a trap, i.e., a generalized Gross-Pitaevskii equation, as well as a quantum-Boltzmann equation for the normal and anomalous fluctuations [R. Walser et al., Phys. Rev. A, 59, 3878 (1999)]. In this article, the theory is applied to the case of an isotropic configuration and we present numerical and analytical results for the reversible real-time propagation, as well as irreversible evolution towards equilibrium., Comment: 15 pages RevTeX, 8 figures, reviewed PRA resubmission

We derive a quantum theory of evaporative cooling for a degenerate Fermi gas with two constituents and show that the optimum cooling trajectory is influenced significantly by the quantum statistics of the particles. The cooling efficiency is reduced at low temperatures due to Pauli blocking of available final states in each binary collision event. We compare the theoretical optimum trajectory with experimental data on cooling a quantum degenerate cloud of potassium-40, and show that temperatures as low as 0.3 times the Fermi temperature can now be achieved., Comment: 6 pages, 4 figures

The burgeoning field of Bose-Einstein condensation in dilute alkali and hydrogen gases has stimulated a great deal of research into the statistical physics of weakly interacting quantum degenerate systems. The recent experiments offer the possibility for exploring fundamental properties of low temperature physics in a very controllable and accessible way. One current goal of experimenters in this field is to observe superfluid-like behavior in these trapped Bose gases, analogous to persistent currents in superfluid liquid helium, which flow without observable viscosity, and electric currents in superconductors, which flow without observable resistance. These ``super'' properties of Bose-condensed systems occur because the macroscopic occupation of a quantized mode provides a stabilizing mechanism that inhibits decay due to thermal relaxation. Here we solve the time-dependent Gross-Pitaevskii equation of motion of the condensate involving two hyperfine atomic states and show how to generate, with extremely high fidelity, topological modes such as vortices that open the door to the study of superfluidity in these new systems. Our approach is inspired by recent experiments investigating a trapped condensate with two strongly coupled internal states. We show how the interplay between the internal and motional dynamics can be utilized to prepare the condensate in a variety of interesting configurations., Comment: 5 pages, 5 figures

We study the Coulomb pseudogap for tunneling into the two-dimensional electron system of high-mobility (Al,Ga)As/GaAs heterojunctions subjected to a quantizing magnetic field at filling factor $\nu \leq 1$. Tunnel current-voltage characteristics show that for the double maximum observed in the tunnel resistance at $\nu \approx 1$ the pseudogap is linear in energy with a slope that depends on filling factor, magnetic field, and temperature. We give a qualitative account of the filling factor dependence of the pseudogap slope and we confirm the recently reported appearance of another relaxation time for tunneling at $\nu \approx 1$. For the tunnel resistance peaks at $\nu=1/3$ and 2/3 a completely different behaviour of the current-voltage curves is found and interpreted as manifestation of the fractional gap., Comment: 7 pages, 9 figures included. Accepted to PRB

The order parameter of a condensate with two internal states can continuously distort in such a way as to remove twists that have been imposed along its length. We observe this effect experimentally in the collapse and recurrence of Rabi oscillations in a magnetically trapped, two-component Bose-Einstein condensate of ^87Rb.

Two internal hyperfine states of a Bose-Einstein condensate in a dilute magnetically trapped gas of ${}^{87}$Rb atoms are strongly coupled by an external field that drives Rabi oscillations between the internal states. Due to their different magnetic moments and the force of gravity, the trapping potentials for the two states are offset along the vertical axis, so that the dynamics of the internal and external degrees of freedom are inseparable. The rapid cycling between internal atomic states in the displaced traps results in an adiabatic transfer of population from the condensate ground state to its first antisymmetric topological mode. This has a pronounced effect on the internal Rabi oscillations, modulating the fringe visibility in a manner reminiscent of collapses and revivals. We present a detailed theoretical description based on zero-temperature mean-field theory., Comment: 10 pages, 8 eps figures included; submitted to PRA

We have measured independently both s-wave and p-wave cross-dimensional thermalization rates for ultracold potassium-40 atoms held in a magnetic trap. These measurements reveal that this fermionic isotope has a large positive s-wave triplet scattering length in addition to a low temperature p-wave shape resonance. We have observed directly the p-wave threshold law which, combined with the Fermi statistics, dramatically suppresses elastic collision rates at low temperatures. In addition, we present initial evaporative cooling results that make possible these collision measurements and are a precursor to achieving quantum degeneracy in this neutral, low-density Fermi system., Comment: 5 pages, 3 figures, 1 table