Multiphoton, multimode state classification for nonlinear optical circuits

TL;DR

This paper introduces a new classification scheme for multimode photon states in nonlinear optical circuits, based on polynomial factorizability, and explores how to generate and analyze these states using advanced interferometer designs.

Contribution

It presents a novel classification method for multimode photon states based on polynomial factorizability and proposes experimental designs for generating these states.

Findings

Classification invariant under unitary transformations

Designs for generating states of different classes

Benchmarking robustness of quantum states

Abstract

We introduce a new classification of multimode states with a fixed number of photons. This classification is based on the factorizability of homogeneous multivariate polynomials and is invariant under unitary transformations. The classes physically correspond to field excitations in terms of single and multiple photons, each of which being in an arbitrary irreducible superposition of quantized modes. We further show how the transitions between classes are rendered possible by photon addition, photon subtraction, and photon-projection nonlinearities. We explicitly put forward a design for a multilayer interferometer in which the states for different classes can be generated with state-of-the-art experimental techniques. Limitations of the proposed designs are analyzed using the introduced classification, providing a benchmark for the robustness of certain states and classes.