Multiconfigurational HartreeFock theory for identical bosons in a double well
Abstract
Multiconfigurational HartreeFock theory is presented and implemented in an investigation of the fragmentation of a BoseEinstein condensate made of identical bosonic atoms in a doublewell potential at zero temperature. The approach builds in the effects of the condensate mean field and of atomic correlations by describing generalized manybody states that are composed of multiple configurations which incorporate atomic interactions. Nonlinear and linear optimization is utilized in conjunction with the variational and HylleraasUndheim theorems to find the optimal ground and excited states of the interacting system. The resulting energy spectrum and associated eigenstates are presented as a function of doublewell barrier height. Delocalized and localized single configurational states are found in the extreme limits of the simple and fragmented condensate ground states, while multiconfigurational states and macroscopic quantum superposition states are revealed throughout the full extent of barrier heights. Comparison is made to existing theories that either neglect mean field or correlation effects and it is found that contributions from both interactions are essential in order to obtain a robust microscopic understanding of the condensate's atomic structure throughout the fragmentation process.
 Authors:
 Department of Chemistry, University of Washington, Seattle, Washington 981951700 (United States)
 Department of Physics, University of Washington, Seattle, Washington 981951560 (United States)
 (United States)
 Publication Date:
 OSTI Identifier:
 20786361
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physical Review. A; Journal Volume: 72; Journal Issue: 6; Other Information: DOI: 10.1103/PhysRevA.72.063624; (c) 2005 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 74 ATOMIC AND MOLECULAR PHYSICS; ATOMS; BOSEEINSTEIN CONDENSATION; BOSONS; COMPARATIVE EVALUATIONS; CORRELATIONS; DISSOCIATION; EIGENSTATES; ENERGY SPECTRA; EXCITED STATES; GROUND STATES; HARTREEFOCK METHOD; MANYBODY PROBLEM; MEANFIELD THEORY; NONLINEAR PROBLEMS; OPTIMIZATION; POTENTIALS; VARIATIONAL METHODS
Citation Formats
Masiello, D., McKagan, S. B., Reinhardt, W. P., and Department of Physics, University of Washington, Seattle, Washington 981951560. Multiconfigurational HartreeFock theory for identical bosons in a double well. United States: N. p., 2005.
Web. doi:10.1103/PHYSREVA.72.0.
Masiello, D., McKagan, S. B., Reinhardt, W. P., & Department of Physics, University of Washington, Seattle, Washington 981951560. Multiconfigurational HartreeFock theory for identical bosons in a double well. United States. doi:10.1103/PHYSREVA.72.0.
Masiello, D., McKagan, S. B., Reinhardt, W. P., and Department of Physics, University of Washington, Seattle, Washington 981951560. Thu .
"Multiconfigurational HartreeFock theory for identical bosons in a double well". United States.
doi:10.1103/PHYSREVA.72.0.
@article{osti_20786361,
title = {Multiconfigurational HartreeFock theory for identical bosons in a double well},
author = {Masiello, D. and McKagan, S. B. and Reinhardt, W. P. and Department of Physics, University of Washington, Seattle, Washington 981951560},
abstractNote = {Multiconfigurational HartreeFock theory is presented and implemented in an investigation of the fragmentation of a BoseEinstein condensate made of identical bosonic atoms in a doublewell potential at zero temperature. The approach builds in the effects of the condensate mean field and of atomic correlations by describing generalized manybody states that are composed of multiple configurations which incorporate atomic interactions. Nonlinear and linear optimization is utilized in conjunction with the variational and HylleraasUndheim theorems to find the optimal ground and excited states of the interacting system. The resulting energy spectrum and associated eigenstates are presented as a function of doublewell barrier height. Delocalized and localized single configurational states are found in the extreme limits of the simple and fragmented condensate ground states, while multiconfigurational states and macroscopic quantum superposition states are revealed throughout the full extent of barrier heights. Comparison is made to existing theories that either neglect mean field or correlation effects and it is found that contributions from both interactions are essential in order to obtain a robust microscopic understanding of the condensate's atomic structure throughout the fragmentation process.},
doi = {10.1103/PHYSREVA.72.0},
journal = {Physical Review. A},
number = 6,
volume = 72,
place = {United States},
year = {Thu Dec 15 00:00:00 EST 2005},
month = {Thu Dec 15 00:00:00 EST 2005}
}

A timedependent multiconfigurational selfconsistent field theory is presented to describe the manybody dynamics of a gas of identical bosonic atoms confined to an external trapping potential at zero temperature from first principles. A set of generalized evolution equations are developed, through the timedependent variational principle, which account for the complete and selfconsistent coupling between the expansion coefficients of each configuration and the underlying onebody wave functions within a restricted two state Fock space basis that includes the full effects of the condensate's mean field as well as atomic correlation. The resulting dynamical equations are a classical Hamiltonian system and, bymore »

Multiconfigurational timedependent Hartree method for mixtures consisting of two types of identical particles
We specify the formally exact multiconfigurational timedependent Hartree method originally developed for systems of distinguishable degrees of freedom to mixtures consisting of two types of identical particles. All three cases, FermiFermi, BoseBose, and BoseFermi mixtures, are treated on an equal footing making explicit use of the reduced one and twobody density matrices of the mixture. The theory naturally contains as specific cases the versions of the multiconfigurational timedependent Hartree method for singlespecies fermions and bosons. Explicit and compact equations of motion are derived and their properties and usage are briefly discussed. 
Multiconfigurational HartreeFock calculations of hyperfineinduced transitions in heliumlike ions
We are investigating the hyperfine quenching of 1[ital s]2[ital p] [sup 3][ital P][sub 0][sup [ital o]] for the three heliumlike ions [sup 19]F[sup 7+], [sup 23]Na[sup 9+], and [sup 27]Al[sup 11+] in the multiconfigurational HartreeFockBreitPauli scheme. The configuration expansions are generated with the activespace method and are increased in a systematic way, allowing the convergence of the calculated parameters to be studied. A careful comparison is done with the pioneering work of Mohr using a perturbation approach [[ital Beam][ital Foil] [ital Spectroscopy], [ital Atomic] [ital Structure] [ital and] [ital Lifetimes], edited by I. Sellin and D. Pegg (Plenum, New York,more » 
Large multiconfigurational HartreeFock calculations on the hyperfinestructure constants of the sup 7 Li 2 s sup 2 S and 2 p sup 2 P states
Accurate hyperfinestructure parameters for the ground and first excited states of lithium are reported. Hyperfine parameters are calculated from multiconfiguration HartreeFock (MCHF) wave functions using a recently written hyperfinestructure program, being a part of the MCHF Atomic Structure Package. Convergence of the hyperfinestrucure parameters is studied as the active set of orbitals is increased. The relativistic, finitenuclearsize, and finitenuclearmasscorrected values of the magnetic hyperfinestructure constants of the 2{ital s} {sup 2}{ital S}{sub 1/2} and 2{ital p} {sup 2}{ital P}{sub 1/2,3/2} states of {sup 7}Li were determiend to be {ital A}{sub 1/2}=401.70 MHz and {ital A}{sub 1/2}=45.94 MHz, {ital A}{sub 3/2}=3.098more » 
Large multiconfigurational HartreeFock calculations on the hyperfine structure of Li( sup 2 S ) and Li( sup 2 P )
Extensive multiconfigurational HartreeFock (MCHF) calculations on the {sup 2}{ital S} ground state and the {sup 2}{ital P} excited state of lithium are reported. MCHF problems involving full configurationinteraction calculations within up to 85 orbitals are solved numerically using the finiteelement method. Systematic studies of the convergence of the hyperfine parameters with respect to the size of the active space are given. The Fermi contact term of Li({sup 2}{ital S}) has an accuracy of 0.07%. The Fermi contact, the orbital, the spindipolar, and the electric quadrupole terms of Li({sup 2}{ital P}) have an estimated inaccuracy of 0.7%, 0.13%, 0.15%, and 0.35%,more »