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

Abstract

We provide a detailed analysis of our previously proposed scheme [Phys. Rev. Lett. 88, 180401, (2002)] to engineer the profile of the hopping amplitudes for atomic gases in a 1D 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 [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 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.

18 pages, 9 figures

References in corpus (5)

• Non-Abelian gauge potentials for ultra-cold atoms with degenerate dark states
• Simulation and detection of Dirac fermions with cold atoms in an optical lattice
• Realization of a Laughlin quasiparticle interferometer: Observation of fractional statistics
• Probing quantum phases of ultracold atoms in optical lattices by transmission spectra in cavity QED
• Cavity enhanced light scattering in optical lattices to probe atomic quantum statistics

Cited by in corpus (4)

• Electron fractionalization for two-dimensional Dirac fermions
• Delocalization of relativistic Dirac particles in disordered one-dimensional systems and its implementation with cold atoms
• Light scattering for thermometry of fermionic atoms in an optical lattice
• Quantum optics with quantum gases: controlled state reduction by designed light scattering