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Title: Multiconfigurational Hartree-Fock theory for identical bosons in a double well

Abstract

Multiconfigurational Hartree-Fock theory is presented and implemented in an investigation of the fragmentation of a Bose-Einstein condensate made of identical bosonic atoms in a double-well potential at zero temperature. The approach builds in the effects of the condensate mean field and of atomic correlations by describing generalized many-body states that are composed of multiple configurations which incorporate atomic interactions. Nonlinear and linear optimization is utilized in conjunction with the variational and Hylleraas-Undheim 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 double-well 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:
 [1];  [2];  [1];  [3]
  1. Department of Chemistry, University of Washington, Seattle, Washington 98195-1700 (United States)
  2. Department of Physics, University of Washington, Seattle, Washington 98195-1560 (United States)
  3. (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; BOSE-EINSTEIN CONDENSATION; BOSONS; COMPARATIVE EVALUATIONS; CORRELATIONS; DISSOCIATION; EIGENSTATES; ENERGY SPECTRA; EXCITED STATES; GROUND STATES; HARTREE-FOCK METHOD; MANY-BODY PROBLEM; MEAN-FIELD 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 98195-1560. Multiconfigurational Hartree-Fock 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 98195-1560. Multiconfigurational Hartree-Fock 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 98195-1560. Thu . "Multiconfigurational Hartree-Fock theory for identical bosons in a double well". United States. doi:10.1103/PHYSREVA.72.0.
@article{osti_20786361,
title = {Multiconfigurational Hartree-Fock 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 98195-1560},
abstractNote = {Multiconfigurational Hartree-Fock theory is presented and implemented in an investigation of the fragmentation of a Bose-Einstein condensate made of identical bosonic atoms in a double-well potential at zero temperature. The approach builds in the effects of the condensate mean field and of atomic correlations by describing generalized many-body states that are composed of multiple configurations which incorporate atomic interactions. Nonlinear and linear optimization is utilized in conjunction with the variational and Hylleraas-Undheim 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 double-well 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 time-dependent multiconfigurational self-consistent field theory is presented to describe the many-body 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 time-dependent variational principle, which account for the complete and self-consistent coupling between the expansion coefficients of each configuration and the underlying one-body 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 » construction, form a well-defined initial value problem. They are implemented in an efficient numerical algorithm. An example is presented, highlighting the generality of the theory, in which the ballistic expansion of a fragmented condensate ground state is compared to that of a macroscopic quantum superposition state, taken here to be a highly entangled number state, upon releasing the external trapping potential. Strikingly different many-body matter-wave dynamics emerge in each case, accentuating the role of both atomic correlation and mean-field effects in the two condensate states.« less
  • We specify the formally exact multiconfigurational time-dependent Hartree method originally developed for systems of distinguishable degrees of freedom to mixtures consisting of two types of identical particles. All three cases, Fermi-Fermi, Bose-Bose, and Bose-Fermi mixtures, are treated on an equal footing making explicit use of the reduced one- and two-body density matrices of the mixture. The theory naturally contains as specific cases the versions of the multiconfigurational time-dependent Hartree method for single-species fermions and bosons. Explicit and compact equations of motion are derived and their properties and usage are briefly discussed.
  • 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 Hartree-Fock-Breit-Pauli scheme. The configuration expansions are generated with the active-space 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 » 1976), Vol. 1, pp. 97--103]. In the present calculations the orbital and spin-dipole magnetic contributions, which were previously neglected, are added to the dominant Fermi contact interaction term and a detailed analysis of the hyperfine induced transition rate is done in order to learn how to get an accurate description of the property in the multiconfiguration Hartree-Fock-Breit-Pauli approximation.« less
  • Accurate hyperfine-structure parameters for the ground and first excited states of lithium are reported. Hyperfine parameters are calculated from multiconfiguration Hartree-Fock (MCHF) wave functions using a recently written hyperfine-structure program, being a part of the MCHF Atomic Structure Package. Convergence of the hyperfine-strucure parameters is studied as the active set of orbitals is increased. The relativistic, finite-nuclear-size, and finite-nuclear-mass-corrected values of the magnetic hyperfine-structure 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 » MHz, respectively. The final values are compared with experiments and with the most reliable theoretical values obtained with other methods.« less
  • Extensive multiconfigurational Hartree-Fock (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 configuration-interaction calculations within up to 85 orbitals are solved numerically using the finite-element 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 spin-dipolar, 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 » respectively.« less