Manipulating atoms in an optical lattice: Fractional fermion number and its optical quantum measurement
arXiv:0709.2187 · doi:10.1103/PhysRevA.77.013603
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.
arXiv comment18 pages, 9 figures
References in corpus (36)
- Two-Dimensional Gas of Massless Dirac Fermions in Graphene
- Experimental Observation of Quantum Hall Effect and Berry's Phase in Graphene
- Chiral tunneling and the Klein paradox in graphene
- Cold bosonic atoms in optical lattices
- Transition from a strongly interacting 1D superfluid to a Mott insulator
- Observation of the e/3 Fractionally Charged Laughlin Quasiparticles
- Controlled Collisions for Multiparticle Entanglement of Optically Trapped Atoms
- Creation of effective magnetic fields in optical lattices: The Hofstadter butterfly for cold neutral atoms
- Non-Abelian gauge potentials for ultra-cold atoms with degenerate dark states
- Quantum Phases of Vortices in Rotating Bose-Einstein Condensates
- Excitation of phonons in a Bose-Einstein condensate by light scattering
- Cold atoms in non-Abelian gauge potentials: From the Hofstadter "moth" to lattice gauge theory
- Simulation and detection of Dirac fermions with cold atoms in an optical lattice
- Creating vortex rings and three-dimensional skyrmions in Bose-Einstein condensates
- Realization of a Laughlin quasiparticle interferometer: Observation of fractional statistics
- Strongly inhibited transport of a 1D Bose gas in a lattice
- Artificial electromagnetism for neutral atoms: Escher staircase and Laughlin liquids
- Probing quantum phases of ultracold atoms in optical lattices by transmission spectra in cavity QED
- Energetically stable particle-like Skyrmions in a trapped Bose-Einstein condensate
- Particle number fractionization of an atomic Fermi-Dirac gas in an optical lattice
- Monopole core instability and Alice rings in spinor Bose-Einstein condensates
- Cavity enhanced light scattering in optical lattices to probe atomic quantum statistics
- 't Hooft-Polyakov Monopoles in an Antiferromagnetic Bose-Einstein Condensate
- Macroscopic superpositions of Bose-Einstein condensates
- Bragg spectroscopy of the multi-branch Bogoliubov spectrum of elongated Bose-Einstein condensates
- Engineering vortex rings and systems for controlled studies of vortex interactions in Bose-Einstein condensates
- Stable particlelike solitons with multiply-quantized vortex lines in Bose-Einstein condensates
- Optical linewidth of a low density Fermi-Dirac gas
- Non-destructive optical measurement of relative phase between two Bose condensates
- Optical detection of fractional particle number in an atomic Fermi-Dirac gas
- Optical response of superfluid state in dilute atomic Fermi-Dirac gases
- Probing the statistical properties of Bose-Einstein condensates with light
- Nontopological Finite Temperature Induced Fermion Number
- Thermal Fluctuations of Induced Fermion Number
- The Electric Charge of a Dirac Monopole at Nonzero Temperature
- On the Fractional Electric Charge of a Magnetic Monopole at Nonzero Temperature
Cited by in corpus (37)
- Light-induced gauge fields for ultracold atoms
- Topological Quantum Matter with Ultracold Gases in Optical Lattices
- Topological quantum matter with cold atoms
- Cold atom simulation of interacting relativistic quantum field theories
- Synthetic spin-orbit coupling in an optical lattice clock
- Geometrical pumping with a Bose-Einstein condensate
- The Nonlinear Dirac Equation in Bose-Einstein Condensates: Foundation and Symmetries
- Electron fractionalization for two-dimensional Dirac fermions
- Optical Kagome lattice for ultra-cold atoms with nearest neighbor interactions
- 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
- On the effective Dirac dynamics of ultracold atoms in bichromatic optical lattices
- Topological phases of quasi-one-dimensional fermionic atoms with a synthetic gauge field
- Light scattering for thermometry of fermionic atoms in an optical lattice
- Topological bound states of a quantum walk with cold atoms
- Quantum optics with quantum gases: controlled state reduction by designed light scattering
- Topological edge states in periodically-driven trapped-ion chains
- Robustness of symmetry-protected topological states against time-periodic perturbations
- Topological phase transition in a stretchable photonic crystal
- Light scattering by ultracold atoms in an optical lattice
- 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
- A Complete Spectral Analysis of the Jackiw-Rebbi Model, Including its Zero Mode
- Imaging of quantum Hall states in ultracold atomic gases
- Light scattering from ultracold atomic gases in optical lattices at finite temperature
- Particle number fractionalization of a one-dimensional atomic Fermi gas with synthetic spin-orbit coupling
- Massive Jackiw-Rebbi Model
- Quantum imaging of spin states in optical lattices
- Quantum simulation of topologically protected states using directionally unbiased linear-optical multiports
- Finite temperature fermion condensate, charge and current densities in a (2+1)-dimensional conical space
- Optical lattices with large scattering length: Using few-body physics to simulate an electron-phonon system
- Optical signatures of antiferromagnetic ordering of fermionic atoms in an optical lattice
- Homodyne detection of matter-wave fields (shortened)
- Light scattering from ultracold gases in disordered optical lattices
- Self-adjoint Dirac type Hamiltonians in one space dimension with a mass jump
- Edge Modes and Teleportation in a Topologically Insulating Quantum Wire