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

Manipulating atoms in an optical lattice: fractional fermion number and its optical quantum measurement
Manipulating atoms in an optical lattice: fractional fermion number and its optical quantum measurement
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.
1050-2947
013603-[18pp]
Ruostekoski, J.
2beb155e-64b0-4ee9-9cfe-079947a9c9f4
Javanainen, J.
10bc75aa-ad97-421b-8434-0b9e9a502318
Dunne, G.V.
479c42ee-7116-4584-be2b-c0b87ec2d616
Ruostekoski, J.
2beb155e-64b0-4ee9-9cfe-079947a9c9f4
Javanainen, J.
10bc75aa-ad97-421b-8434-0b9e9a502318
Dunne, G.V.
479c42ee-7116-4584-be2b-c0b87ec2d616

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).

Record type: Article

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.

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Submitted date: January 2008
Published date: 3 January 2008
Organisations: Applied Mathematics

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Local EPrints ID: 49971
URI: http://eprints.soton.ac.uk/id/eprint/49971
ISSN: 1050-2947
PURE UUID: 67c9fbeb-a94b-4cdc-b5b7-22d476f96cb5

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Date deposited: 08 Jan 2008
Last modified: 09 Nov 2021 09:16

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Contributors

Author: J. Ruostekoski
Author: J. Javanainen
Author: G.V. Dunne

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