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Type: Journal article
Title: Manipulating atoms in an optical lattice: fractional fermion number and its optical quantum measurement
Author: Ruostekoski, J.
Javanainen, J.
Dunne, Gerald Vincent
Citation: Physical Review A, 2008; 77(1):013603
Publisher: American Physical Society
Issue Date: 2008
ISSN: 1050-2947
School/Discipline: School of Chemistry and Physics
Statement of
J. Ruostekoski, J. Javanainen and G. V. Dunne
Abstract: We provide a detailed analysis of our previously proposed scheme [ J. Ruostekoski, G. V. Dunne and J. Javanainen Phys. Rev. Lett. 88 180401 (2002)] to engineer the profile of the hopping amplitudes for atomic gases in a one-dimensional optical lattice so that the particle number becomes fractional. We consider a constructed system of a dilute two-species gas of fermionic atoms where the two components are coupled via a coherent electromagnetic field with a topologically nontrivial phase profile. We show both analytically and numerically how the resulting atomic Hamiltonian in a prepared dimerized optical lattice with a defect in the pattern of alternating hopping amplitudes exhibits a fractional fermion number. In particular, in the low-energy limit we demonstrate the equivalence of the atomic Hamiltonian to a relativistic Dirac Hamiltonian describing fractionalization in quantum field theory. Expanding on our earlier argument [ J. Javanainen and J. Ruostekoski Phys. Rev. Lett. 91 150404 (2003)] we show how the fractional eigenvalues of the particle number operator can be detected via light scattering. In particular, we show how scattering of far-off resonant light can convey information about the counting and spin statistics of the atoms in an optical lattice, including state-selective atom density profiles and atom number fluctuations. Optical detection could provide a truly quantum mechanical measurement of the particle number fractionalization in a dilute atomic gas.
Keywords: Eigenvalues and eigenfunctions; electromagnetic fields; optical lattices; quantum field theory; quantum optics
Rights: © 2008 The American Physical Society
RMID: 0020080223
DOI: 10.1103/PhysRevA.77.013603
Appears in Collections:Chemistry and Physics publications

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