Multi-Photon Synthetic Lattices in Multi-Port Waveguide Arrays: Synthetic Atoms and Fock Graphs

Abstract

Activating transitions between internal states of physical systems has emerged as an appealing approach to create lattices and complex networks. In such a scheme, the internal states or modes of a physical system are regarded as lattice sites or network nodes in an abstract space whose dimensionality may exceed the systems' apparent (geometric) dimensionality. This introduces the notion of synthetic dimensions, thus providing entirely novel pathways for fundamental research and applications. Here, we analytically show that the propagation of multi-photon states through multi-port waveguide arrays gives rise to synthetic dimensions where a single waveguide system generates a multitude of synthetic lattices. Since these synthetic lattices exist in photon-number space, we introduce the concept of pseudo-energy and demonstrate its utility for studying multi-photon interference processes. Specifically, the spectrum of the associated pseudo-energy operator generates a unique ordering of the relevant states. Together with generalized pseudo-energy ladder operators, this allows for representing the dynamics of multi-photon states by way of pseudo-energy term diagrams that are associated with a synthetic atom. As a result, the pseudo-energy representation leads to concise analytical expressions for the eigensystem of $N$ photons propagating through $M$ nearest-neighbor coupled waveguides. In the regime where $N>2$ and $M>2$, non-local coupling in Fock space gives rise to hitherto unknown all-optical dark states which display intriguing non-trivial dynamics.

Two-column layout, 11 pages, 8 figures

References in corpus (10)

• Synthetic Dimension in Photonics
• Topological quantum matter in synthetic dimensions
• Photonic Topological Insulator in Synthetic Dimensions
• Roadmap on STIRAP applications
• Multiphoton Quantum-State Engineering using Conditional Measurements
• Observation of momentum-space chiral edge currents in room-temperature atoms
• Superradiance Lattice
• Exceptional points of any order in a single, lossy, waveguide beamsplitter by photon-number-resolved detection
• Multiphoton Discrete Fractional Fourier Dynamics in Waveguide Beam Splitters
• Single-step fabrication of surface waveguides in fused silica with few-cycle laser pulses

Cited by in corpus (10)

• Giant Atoms in a Synthetic Frequency Dimension
• Generating high-order quantum exceptional points in synthetic dimensions
• Creating locally interacting Hamiltonians in the synthetic frequency dimension for photons
• Arbitrary synthetic dimensions via multi-boson dynamics on a one-dimensional lattice
• Fully solvable finite simplex lattices with open boundaries in arbitrary dimensions
• Emergent non-Hermitian localization phenomena in the synthetic space of zero-dimensional bosonic systems
• Multiphoton processes via conditional measurements in the two-field interaction
• Modelling quantum photonics on a quantum computer
• Liouville Fock state lattices and potential simulators
• Quantum coherent feedback control of an N-level atom with multiple excitations