arXiv subjects
Publications and source records attributed to J. Cooper.
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.
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.
This report documents the physics case for building a 2 MW, 8 GeV superconducting linac proton driver at Fermilab.
Consider the following problem: how many collinear triples of points must a transversal of (Z/nZ)^2 have? This question is connected with venerable issues in discrete geometry. We show that the answer, for n prime, is between (n-1)/4 and (n-1)/2, and consider an analogous question for collinear quadruples. We conjecture that the upper bound is the truth and suggest several other interesting problems in this area.
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.
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. Imamović-Tomasović and A. Griffin [arXiv:cond-mat/9911402].
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.
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.
We present a kinetic theory for Bose-Einstein condensation of a weakly interacting atomic gas in a trap. Starting from first principles, we establish a Markovian kinetic description for the evolution towards equilibrium. In particular, we obtain a set of self-consistent master equations for mean fields, normal densities, and anomalous fluctuations. These kinetic equations generalize the Gross-Pitaevskii mean-field equations, and merge them consistently with a quantum-Boltzmann equation approach.
We propose an experiment that would demonstrate nonlinear Josephson-type oscillations in the relative population of a driven, two-component Bose-Einstein condensate. An initial state is prepared in which two condensates exist in a magnetic trap, each in a different hyperfine state, where the initial populations and relative phase between condensates can be controlled within experimental uncertainty. A weak driving field is then applied, which couples the two internal states of the atom and consequently transfers atoms back and forth between condensates. We present a model of this system and investigate the effect of the mean field on the dynamical evolution.