Hamiltonian Tomography of Photonic Lattices

Abstract

In this letter we introduce a novel approach to Hamiltonian tomography of non-interacting tight-binding photonic lattices. To begin with, we prove that the matrix element of the low-energy effective Hamiltonian between sites $i$ and $j$ may be obtained directly from $S_{ij}(\omega )$, the (suitably normalized) two-port measurement between sites $i$ and $j$ at frequency $\omega$. 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 actually 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 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.

7 pages, 5 figures

References in corpus (14)

• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Fractional quantum Hall states at zero magnetic field
• Observation of phononic helical edge states in a mechanical 'topological insulator'
• Bose-Einstein condensation of photons in an optical microcavity
• Chiral groundstate currents of interacting photons in a synthetic magnetic field
• Topological properties of linear circuit lattices
• Subwavelength vacuum lattices and atom-atom interactions in photonic crystals
• Observation of a dissipative phase transition in a one-dimensional circuit QED lattice
• Topological Photonic Quasicrystals: Fractal Topological Spectrum and Protected Transport
• Low-Disorder Microwave Cavity Lattices for Quantum Simulation with Photons
• Coupling strength estimation for spin chains despite restricted access
• Indirect Hamiltonian Identification through a small gateway
• Engineering topological materials in microwave cavity arrays
• Quantum Crystals and Laughlin Droplets of Cavity Rydberg Polaritons

Cited by in corpus (15)

• Topological Photonics
• A Dissipatively Stabilized Mott Insulator of Photons
• Random access quantum information processors
• Hamiltonian Tomography via Quantum Quench
• Measuring Electromagnetic and Gravitational Responses of Photonic Landau Levels
• Quantum Origami: Transversal Gates for Quantum Computation and Measurement of Topological Order
• Topological polarons, quasiparticle invariants and their detection in 1D symmetry-protected phases
• Origin and localization of topological band gaps in gyroscopic metamaterials
• Two-dimensional optical quasicrystal potentials for ultracold atom experiments
• Electric fields for light: Propagation of microwave photons along a synthetic dimension
• Building Flat-Band Lattice Models from Gram Matrices
• Stochastic approach for quantum metrology with generic Hamiltonians
• High-accuracy Hamiltonian learning via delocalized quantum state evolutions
• Analogue Quantum Simulation with Fixed-Frequency Transmon Qubits
• Tunneling Spectroscopy in Superconducting Circuit Lattices