Keith Burnett

Phase diagram of bosonic atoms in two-color superlattices

We investigate the zero-temperature phase diagram of a gas of bosonic atoms in one- and two-color standing-wave lattices in the framework of the Bose-Hubbard model. We first introduce some relevant physical quantities; superfluid fraction, condensate fraction, quasimomentum distribution, and matter-wave interference pattern. We then discuss the relationships between them on the formal level and show that the superfluid fraction, which is the relevant order parameter for the superfluid to Mott-insulator transition, cannot be probed directly via the matter-wave interference patterns. The formal considerations are supported by exact numerical solutions of the Bose-Hubbard model for uniform one-dimensional systems. We then map out the phase diagram of bosons in nonuniform lattices. The emphasis is on optical two-color superlattices which exhibit a sinusoidal modulation of the well depth and can be easily realized experimentally. From the study of the superfluid fraction, the energy gap, and other quantities, we identify additional zero-temperature phases, including a localized and a quasi-Bose-glass phase, and discuss prospects for their experimental observation.

Collisional redistribution of radiation

Abstract The subject of this review is the collisional redistribution of resonance atomic radiation in dilute gases. The formation of scattered spectra in weak and intense fields is discussed and the formation that may be obtained from experiments is presented. The focus of recent work in the field is on radiative events taking place during collisions. Different aspects of the problem are presented using mainly the density matrix and correlation function approach. This work has shown what types of information on interatomic potentials and collision dynamics can be obtained using near-resonant light scattering from gases: this is highlighted in a discussion of light scattering in the presence of depolarizing collisions. We discuss the relationship of work on collisional redistribution to the various “half-collision” experiments that have recently come to the fore.

Bogoliubov Approach to Superfluidity of Atoms in an Optical Lattice

We use the Bogoliubov theory of atoms in an optical lattice to study the approach to the Mott-insulator transition. We derive an explicit expression for the superfluid density based on the rigidity of the system under phase variations. This enables us to explore the connection between the quantum depletion of the condensate and the quasi-momentum distribution on the one hand and the superfluid fraction on the other. The approach to the insulator phase may be characterized through the filling of the band by quantum depletion, which should be directly observable via the matter–wave interference patterns. We complement these findings by self-consistent Hartree–Fock–Bogoliubov–Popov calculations for one-dimensional lattices, including the effects of a parabolic trapping potential.

Quantum Encounters of the Cold Kind

Since the introduction of laser-cooling techniques for neutral atoms in the early 1980s, the study of collisional interactions between atoms and molecules has been extended to the regime of ultracold temperatures. With nanokelvin temperatures now attainable, our ability to probe the interactions, both experimentally and theoretically, has also progressed. Understanding of the subtle and often highly quantum-mechanical effects that are manifest at such low energies has advanced to the point where new precision measurements are matched by highly accurate theoretical calculations. Low-energy phenomena such as Bose–Einstein condensation and the photoassociation of atoms into bound molecules are now accurately described with no free parameters.

Microscopic quantum dynamics approach to the dilute condensed Bose gas

We derive quantum evolution equations for the dynamics of dilute condensed Bose gases. The approach contains, at different orders of approximation, for cases close to equilibrium, the Gross-Pitaevskii equation and the first-order Hartree-Fock-Bogoliubov theory. The proposed approach is also suited for the description of the dynamics of condensed gases that are far away from equilibrium. As an example the scattering of two Bose condensates is discussed.

Microscopic theory of atom-molecule oscillations in a Bose-Einstein condensate

In a recent experiment at JILA [E. A. Donley et al., Nature (London) 417, 529 (2002)] an initially pure condensate of {sup 85}Rb atoms was exposed to a specially designed time-dependent magnetic-field pulse in the vicinity of a Feshbach resonance. The production of additional components of the gas as well as their oscillatory behavior have been reported. We apply a microscopic theory of the gas to identify these components and determine their physical properties. Our time-dependent studies allow us to explain the observed dynamic evolution of all fractions, and to identify the physical relevance of the pulse shape. Based on ab initio predictions, our theory strongly supports the view that the experiments have produced a molecular condensate.

The Theory of Bose–Einstein Condensation of Dilute Gases

Bose‐Einstein condensation (BEC) has long been known to be a key element of macroscopic quantum phenomena such as superconductivity and superfluidity. BEC per se, however, eluded direct and unquestioned observation until 1995, when experimental groups produced condensates in dilute atomic alkali gases.

WHY A CONDENSATE CAN BE THOUGHT OF AS HAVING A DEFINITE PHASE

We present an argument for assigning a definite phase to an assembly of Bose-Einstein Condensed atoms. This relies on the demonstration that a coherent state of the condensed system is a robust state in the presence of interactions between the condensate and its environment.

Quantum phases of atomic boson-fermion mixtures in optical lattices

The zero-temperature phase diagram of a binary mixture of bosonic and fermionic atoms in a one-dimensional optical lattice is studied in the framework of the Bose-Fermi-Hubbard model. By exact numerical solution of the associated eigenvalue problems, ground state observables and the response to an external phase twist are evaluated. The stiffnesses under phase variations provide measures for the boson superfluid fraction and the fermionic Drude weight. Several distinct quantum phases are identified as functions of the strength of the repulsive boson-boson and the boson-fermion interactions. In addition to the bosonic Mott-insulator phase, two other insulating phases are found, where both the bosonic superfluid fraction and the fermionic Drude weight vanish simultaneously. One of these double-insulator phases exhibits a crystalline diagonal long-range order, while the other is characterized by spatial separation of the two species.

GENERALIZED MEAN FIELDS FOR TRAPPED ATOMIC BOSE-EINSTEIN CONDENSATES

We describe generalized time-dependent mean-field equations for partially condensed samples of trapped and evaporatively cooled atoms. These equations give a way of investigating the various order parameters that may be present as well as the existence of a mean value of the field due to condensed atoms. Our approach provides us with a closed system of self-consistent equations for the order parameters present. The equations we derive are shown to reduce to other treatments in the literature in various limits. We also show how the equation of motion method allows us to construct a formalism that can handle the evolution of these mean fields due to two-loop kinetics.