Multiple photon Hamiltonian in linear quantum optical networks

TL;DR

This paper derives an explicit effective Hamiltonian for multiple photons in linear quantum optical networks using a group theory approach, providing insights into device properties and photon evolution.

Contribution

It introduces an alternative derivation of the multi-photon Hamiltonian based on single-photon Hamiltonians and Lie group theory, offering a new perspective on quantum optical network analysis.

Findings

Explicit formula for multi-photon Hamiltonian derived

Group theory approach elucidates properties of two-port devices

Method applicable to complex quantum optical systems

Abstract

We give an alternative derivation for the explicit formula of the effective Hamiltonian describing the evolution of the quantum state of any number of photons entering a linear optics multiport. The description is based on the effective Hamiltonian of the optical system for a single photon and comes from relating the evolution in the Lie group that describes the unitary evolution matrices in the Hilbert space of the photon states to the evolution in the Lie algebra of the Hamiltonians for one and multiple photons. We give a few examples of how a group theory approach can shed light on some properties of devices with two input ports.