Transformation design and nonlinear Hamiltonians

TL;DR

This paper explores a class of nonlinear Hamiltonians in quantum optics, analyzing their entanglement properties and demonstrating their use in tasks like conditional state swapping for generating optical cat states.

Contribution

Introduces a new class of nonlinear Hamiltonians derived from beam splitter Hamiltonians, with applications in entanglement and quantum state manipulation.

Findings

Eigenstates exhibit significant entanglement.

Hamiltonians enable conditional state swapping.

Applications include generating optical cat states.

Abstract

We study a class of nonlinear Hamiltonians, with applications in quantum optics. The interaction terms of these Hamiltonians are generated by taking a linear combination of powers of a simple `beam splitter' Hamiltonian. The entanglement properties of the eigenstates are studied. Finally, we show how to use this class of Hamiltonians to perform special tasks such as conditional state swapping, which can be used to generate optical cat states and to sort photons.