Manipulating atoms in an optical lattice: fractional fermion number and its optical quantum measurement

Ruostekoski, J., Javanainen, J. and Dunne, G.V. (2008) Manipulating atoms in an optical lattice: fractional fermion number and its optical quantum measurement. Physical Review A, 77, (1), 013603-[18pp]. (doi:10.1103/PhysRevA.77.013603).


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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.

Item Type: Article
Digital Object Identifier (DOI): doi:10.1103/PhysRevA.77.013603
ISSNs: 1050-2947 (print)
1094-1622 (electronic)
Subjects: Q Science > QA Mathematics
Q Science > QC Physics
Divisions : University Structure - Pre August 2011 > School of Mathematics > Applied Mathematics
ePrint ID: 49971
Accepted Date and Publication Date:
3 January 2008Published
January 2008Submitted
Date Deposited: 08 Jan 2008
Last Modified: 31 Mar 2016 12:27

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