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 (6)

• Chiral tunneling and the Klein paradox in graphene
• 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

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• Cold atom simulation of interacting relativistic quantum field theories
• Electron fractionalization for two-dimensional Dirac fermions
• Synthetic band-structure engineering in polariton crystals with non-Hermitian topological phases
• Delocalization of relativistic Dirac particles in disordered one-dimensional systems and its implementation with cold atoms
• Floquet Semimetal with Floquet-band Holonomy
• Light scattering for thermometry of fermionic atoms in an optical lattice
• Quantum optics with quantum gases: controlled state reduction by designed light scattering
• Topological edge states in periodically-driven trapped-ion chains
• Simulation and measurement of the fractional particle number in one-dimensional optical lattices
• Topological effects and particle-physics analogies beyond the massless Dirac-Weyl fermion in graphene nanorings
• Particle number fractionalization of a one-dimensional atomic Fermi gas with synthetic spin-orbit coupling
• Quantum imaging of spin states in optical lattices
• Massive Jackiw-Rebbi Model
• Quantum simulation of topologically protected states using directionally unbiased linear-optical multiports
• Homodyne detection of matter-wave fields (shortened)
• Self-adjoint Dirac type Hamiltonians in one space dimension with a mass jump