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arXiv:1111.3460 · Physical Review B

Classical realization of two-site Fermi-Hubbard systems

Stefano Longhi, Giuseppe Della Valle, Vittorio Foglietti

Published Jul 18, 2011• 7 citations
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Abstract

A classical wave optics realization of the two-site Hubbard model, describing the dynamics of interacting fermions in a double-well potential, is proposed based on light transport in evanescently coupled optical waveguides.
DOI
10.1103/physrevb.84.033102

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A classical analog simulator of the two-site Hubbard-Holstein model, describing the dynamics of two correlated electrons coupled with local phonons, is proposed based on light transport in engineered optical waveguide arrays. Our photonic analog simulator enables us to map the temporal dynamics of the quantum system in Fock space into spatial propagation of classical light waves in the evanescently coupled waveguides of the array. In particular, in the strong correlation regime the periodic temporal dynamics, related to the excitation of Holstein polarons with equal energy spacing, can be visualized as a periodic self-imaging phenomenon of the light beam along the waveguide array and explained in terms of generalized Bloch oscillations of a single particle in a semi-infinite inhomogeneous tight-binding lattice.
We have prepared two ultracold fermionic atoms in an isolated double-well potential and obtained full control over the quantum state of this system. In particular, we can independently control the interaction strength between the particles, their tunneling rate between the wells and the tilt of the potential. By introducing repulsive (attractive) interparticle interactions we have realized the two-particle analog of a Mott-insulating (charge-density-wave) state. We have also spectroscopically observed how second-order tunneling affects the energy of the system. This work realizes the first step of a bottom-up approach to deterministically create a single-site addressable realization of a ground-state Fermi-Hubbard system.
We have studied strong correlation effects and localization in metallic systems. Strong correlation effects and localization occurred in metallic systems due to strong electron-electron interactions and strong electron phonon coupling. Strong electron-phonon interactions have been found in such materials as cuprates, fullerides and manganites. The interplay of electronelectron and electron-phonon interactions in these correlated systems leaded to coexistence of or competition between various phases such as super conductivity, charge-density-wave or spin-density wave phases or formation of novel non Fermi liquid phases, polarons, bipolarons and so on. We have considered Holstein-Hubbard model for our work. The Holstein-Hubbard model provides on over simplified description of both electron-electron and electron-phonon interactions, it retains to be the relevant ingredients of a system in which electrons experience simultaneously an instantaneous short range repulsion and a phononmediated retarded attraction. In spite of its formal simplicity, it is not exactly solvable even in one dimension. So quantum simulators of Fermi-Hubbard modes based on either fermionic atoms inoptical lattice or electrons in artificial quantum dot crystals have been used. In our work a classical analog simulator was theoretically proposed for the two site Holstein-Hubbard model based on light transport in engineered waveguide lattices, which is capable of reproducing the temporal dynamics of the quantum model in Fock space as spatial evolution in photonic lattice. We have found that in the strong correlation regime the periodic temporal dynamics exhibited by the Holstein-Hubbard Hamiltonian, related to the excitation Holstein polarons has been explained in terms of generalized Bloch oscillations of a single particle in a semi-infinite inhomogeneous tight binding lattice. Light transport in two dimensional photonic lattices simulated in Fock space the hopping dynamics of two correlated electrons on a one dimensional lattice and exploited to visualize such phenomena as correlated tunneling of bond electron-electron molecules and their coherent motion under the action of d.c. or a.c. fields. The obtained results were found in good agreement with previous results.