Boson-fermion coherence in a spherically symmetric harmonic trap

Takahiko Miyakawa, Pierre Meystre

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

We consider the photoassociation of a low-density gas of quantum-degenerate trapped fermionic atoms into bosonic molecules in a spherically symmetric harmonic potential. For a dilute system and the photoassociation coupling energy small compared to the level separation of the trap, only those fermions in the single shell with Fermi energy are coupled to the bosonic molecular field. Introducing a collective pseudospin operator formalism we show that this system can then be mapped onto the Tavis-Cummings Hamiltonian of quantum optics, with an additional pairing interaction. By exact diagonalization of the Hamiltonian, we examine the ground state and low excitations of the Bose-Fermi system, and study the dynamics of the coherent coupling between atoms and molecules. In a semiclassical description of the system, the pairing interaction between fermions is shown to result in a self-trapping transition in the photoassociation, with a sudden suppression of the coherent oscillations between atoms and molecules. We also show that the full quantum dynamics of the system is dominated by quantum fluctuations in the vicinity of the self-trapping solution.

Original languageEnglish (US)
Article number033624
JournalPhysical Review A
Volume71
Issue number3
DOIs
StatePublished - Mar 1 2005

Fingerprint

bosons
fermions
traps
harmonics
trapping
atoms
molecules
rarefied gases
quantum optics
retarding
interactions
formalism
operators
oscillations
ground state
energy
excitation

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • Physics and Astronomy(all)

Cite this

Boson-fermion coherence in a spherically symmetric harmonic trap. / Miyakawa, Takahiko; Meystre, Pierre.

In: Physical Review A, Vol. 71, No. 3, 033624, 01.03.2005.

Research output: Contribution to journalArticle

@article{11da278b834a4583934305f4f5633aaa,
title = "Boson-fermion coherence in a spherically symmetric harmonic trap",
abstract = "We consider the photoassociation of a low-density gas of quantum-degenerate trapped fermionic atoms into bosonic molecules in a spherically symmetric harmonic potential. For a dilute system and the photoassociation coupling energy small compared to the level separation of the trap, only those fermions in the single shell with Fermi energy are coupled to the bosonic molecular field. Introducing a collective pseudospin operator formalism we show that this system can then be mapped onto the Tavis-Cummings Hamiltonian of quantum optics, with an additional pairing interaction. By exact diagonalization of the Hamiltonian, we examine the ground state and low excitations of the Bose-Fermi system, and study the dynamics of the coherent coupling between atoms and molecules. In a semiclassical description of the system, the pairing interaction between fermions is shown to result in a self-trapping transition in the photoassociation, with a sudden suppression of the coherent oscillations between atoms and molecules. We also show that the full quantum dynamics of the system is dominated by quantum fluctuations in the vicinity of the self-trapping solution.",
author = "Takahiko Miyakawa and Pierre Meystre",
year = "2005",
month = "3",
day = "1",
doi = "10.1103/PhysRevA.71.033624",
language = "English (US)",
volume = "71",
journal = "Physical Review A",
issn = "2469-9926",
publisher = "American Physical Society",
number = "3",

}

TY - JOUR

T1 - Boson-fermion coherence in a spherically symmetric harmonic trap

AU - Miyakawa, Takahiko

AU - Meystre, Pierre

PY - 2005/3/1

Y1 - 2005/3/1

N2 - We consider the photoassociation of a low-density gas of quantum-degenerate trapped fermionic atoms into bosonic molecules in a spherically symmetric harmonic potential. For a dilute system and the photoassociation coupling energy small compared to the level separation of the trap, only those fermions in the single shell with Fermi energy are coupled to the bosonic molecular field. Introducing a collective pseudospin operator formalism we show that this system can then be mapped onto the Tavis-Cummings Hamiltonian of quantum optics, with an additional pairing interaction. By exact diagonalization of the Hamiltonian, we examine the ground state and low excitations of the Bose-Fermi system, and study the dynamics of the coherent coupling between atoms and molecules. In a semiclassical description of the system, the pairing interaction between fermions is shown to result in a self-trapping transition in the photoassociation, with a sudden suppression of the coherent oscillations between atoms and molecules. We also show that the full quantum dynamics of the system is dominated by quantum fluctuations in the vicinity of the self-trapping solution.

AB - We consider the photoassociation of a low-density gas of quantum-degenerate trapped fermionic atoms into bosonic molecules in a spherically symmetric harmonic potential. For a dilute system and the photoassociation coupling energy small compared to the level separation of the trap, only those fermions in the single shell with Fermi energy are coupled to the bosonic molecular field. Introducing a collective pseudospin operator formalism we show that this system can then be mapped onto the Tavis-Cummings Hamiltonian of quantum optics, with an additional pairing interaction. By exact diagonalization of the Hamiltonian, we examine the ground state and low excitations of the Bose-Fermi system, and study the dynamics of the coherent coupling between atoms and molecules. In a semiclassical description of the system, the pairing interaction between fermions is shown to result in a self-trapping transition in the photoassociation, with a sudden suppression of the coherent oscillations between atoms and molecules. We also show that the full quantum dynamics of the system is dominated by quantum fluctuations in the vicinity of the self-trapping solution.

UR - http://www.scopus.com/inward/record.url?scp=18444387690&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=18444387690&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.71.033624

DO - 10.1103/PhysRevA.71.033624

M3 - Article

AN - SCOPUS:18444387690

VL - 71

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 3

M1 - 033624

ER -