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Title: Coherence and entanglement in the ground state of a bosonic Josephson junction: From macroscopic Schroedinger cat states to separable Fock states

Abstract

We consider a bosonic Josephson junction made of N ultracold and dilute atoms confined by a quasi-one-dimensional double-well potential within the two-site Bose-Hubbard model framework. The behavior of the system is investigated at zero temperature by varying the interatomic interaction from the strongly attractive regime to the repulsive one. We show that the ground state exhibits a crossover from a macroscopic Schroedinger-cat state to a separable Fock state through an atomic coherent regime. By diagonalizing the Bose-Hubbard Hamiltonian we characterize the emergence of the macroscopic cat states by calculating the Fisher information F, the coherence by means of the visibility {alpha} of the interference fringes in the momentum distribution, and the quantum correlations by using the entanglement entropy S. Both Fisher information and visibility are shown to be related to the ground-state energy by employing the Hellmann-Feynman theorem. This result, together with a perturbative calculation of the ground-state energy, allows simple analytical formulas for F and {alpha} to be obtained over a range of interactions, in excellent agreement with the exact diagonalization of the Bose-Hubbard Hamiltonian. In the attractive regime the entanglement entropy attains values very close to its upper limit for a specific interaction strength lying in the regionmore » where coherence is lost and self-trapping sets in.« less

Authors:
;  [1];  [1];  [2];  [3]
  1. Dipartimento di Fisica 'Galileo Galilei' and Consorzio Nazionale Interuniversitario per la Scienze Fisiche della Materia (CNISM), Universita di Padova, Via Marzolo 8, I-35122 Padova (Italy)
  2. (INO) del Consiglio Nazionale delle Ricerche (CNR), via G. Sansone 1, I-50019 Sesto Fiorentino (Italy)
  3. Dipartimento di Fisica e Matematica and CNISM, Universita dell'Insubria, Via Valleggio 11, I-22100 Como (Italy)
Publication Date:
OSTI Identifier:
21546820
Resource Type:
Journal Article
Resource Relation:
Journal Name: Physical Review. A; Journal Volume: 83; Journal Issue: 5; Other Information: DOI: 10.1103/PhysRevA.83.053607; (c) 2011 American Institute of Physics
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 74 ATOMIC AND MOLECULAR PHYSICS; BOSONS; CORRELATIONS; ENTROPY; FOCK REPRESENTATION; GROUND STATES; HAMILTONIANS; HUBBARD MODEL; INFORMATION; INTERACTIONS; INTERFERENCE; JOSEPHSON JUNCTIONS; MANY-BODY PROBLEM; ONE-DIMENSIONAL CALCULATIONS; POTENTIALS; QUANTUM ENTANGLEMENT; QUANTUM STATES; QUANTUM WELLS; SCHROEDINGER PICTURE; TRAPPING; CRYSTAL MODELS; ENERGY LEVELS; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; NANOSTRUCTURES; PHYSICAL PROPERTIES; QUANTUM OPERATORS; SUPERCONDUCTING JUNCTIONS; THERMODYNAMIC PROPERTIES

Citation Formats

Mazzarella, G., Toigo, F., Salasnich, L., Istituto Nazionale di Ottica, and Parola, A.. Coherence and entanglement in the ground state of a bosonic Josephson junction: From macroscopic Schroedinger cat states to separable Fock states. United States: N. p., 2011. Web. doi:10.1103/PHYSREVA.83.053607.
Mazzarella, G., Toigo, F., Salasnich, L., Istituto Nazionale di Ottica, & Parola, A.. Coherence and entanglement in the ground state of a bosonic Josephson junction: From macroscopic Schroedinger cat states to separable Fock states. United States. doi:10.1103/PHYSREVA.83.053607.
Mazzarella, G., Toigo, F., Salasnich, L., Istituto Nazionale di Ottica, and Parola, A.. 2011. "Coherence and entanglement in the ground state of a bosonic Josephson junction: From macroscopic Schroedinger cat states to separable Fock states". United States. doi:10.1103/PHYSREVA.83.053607.
@article{osti_21546820,
title = {Coherence and entanglement in the ground state of a bosonic Josephson junction: From macroscopic Schroedinger cat states to separable Fock states},
author = {Mazzarella, G. and Toigo, F. and Salasnich, L. and Istituto Nazionale di Ottica and Parola, A.},
abstractNote = {We consider a bosonic Josephson junction made of N ultracold and dilute atoms confined by a quasi-one-dimensional double-well potential within the two-site Bose-Hubbard model framework. The behavior of the system is investigated at zero temperature by varying the interatomic interaction from the strongly attractive regime to the repulsive one. We show that the ground state exhibits a crossover from a macroscopic Schroedinger-cat state to a separable Fock state through an atomic coherent regime. By diagonalizing the Bose-Hubbard Hamiltonian we characterize the emergence of the macroscopic cat states by calculating the Fisher information F, the coherence by means of the visibility {alpha} of the interference fringes in the momentum distribution, and the quantum correlations by using the entanglement entropy S. Both Fisher information and visibility are shown to be related to the ground-state energy by employing the Hellmann-Feynman theorem. This result, together with a perturbative calculation of the ground-state energy, allows simple analytical formulas for F and {alpha} to be obtained over a range of interactions, in excellent agreement with the exact diagonalization of the Bose-Hubbard Hamiltonian. In the attractive regime the entanglement entropy attains values very close to its upper limit for a specific interaction strength lying in the region where coherence is lost and self-trapping sets in.},
doi = {10.1103/PHYSREVA.83.053607},
journal = {Physical Review. A},
number = 5,
volume = 83,
place = {United States},
year = 2011,
month = 5
}
  • A Comment on the Letter by M. H. Devoret, J. M. Martinis, and J. Clarke, Phys. Rev. Lett. 55, 1908 (1985).
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