Authors

Ruichao Ma, Clai Owens, Aman LaChapelle, David I. Schuster, Jonathan Simon

Abstract

In this paper we introduce an approach to Hamiltonian tomography of noninteracting tight-binding photonic lattices. To begin with, we prove that the matrix element of the low-energy effective Hamiltonian between sites \( \ensuremath{\alpha} \) and \( \ensuremath{\beta} \) may be obtained directly from \( {S}_{\ensuremath{\alpha}\ensuremath{\beta}[[:space:]]}(\ensuremath{\omega}) \), the (suitably normalized) two-port measurement between sites \( \ensuremath{\alpha} \) and \( \ensuremath{\beta} \) at frequency \( \ensuremath{\omega} \). This general result enables complete characterization of both on-site energies and tunneling matrix elements in arbitrary lattice networks by spectroscopy, and suggests that coupling between lattice sites is a topological property of the two-port spectrum. We further provide extensions of this technique for measurement of band projectors in finite, disordered systems with good band flatness ratios, and apply the tool to direct real-space measurement of the Chern number. Our approach demonstrates the extraordinary potential of microwave quantum circuits for exploration of exotic synthetic materials, providing a clear path to characterization and control of single-particle properties of Jaynes-Cummings-Hubbard lattices. More broadly, we provide a robust, unified method of spectroscopic characterization of linear networks from photonic crystals to microwave lattices and everything in between.

Citation

  • Journal: Physical Review A
  • Year: 2017
  • Volume: 95
  • Issue: 6
  • Pages:
  • Publisher: American Physical Society (APS)
  • DOI: 10.1103/physreva.95.062120

BibTeX

@article{Ma_2017,
  title={{Hamiltonian tomography of photonic lattices}},
  volume={95},
  ISSN={2469-9934},
  DOI={10.1103/physreva.95.062120},
  number={6},
  journal={Physical Review A},
  publisher={American Physical Society (APS)},
  author={Ma, Ruichao and Owens, Clai and LaChapelle, Aman and Schuster, David I. and Simon, Jonathan},
  year={2017}
}

Download the bib file

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