Quantization over boson operator spaces

TL;DR

This paper develops a third quantization framework for open bosonic systems, enabling diagonalization of the quantum Liouvillean for quadratic Hamiltonians with Lindblad couplings, advancing the analysis of open quantum many-body systems.

Contribution

It introduces a third quantization approach for open bosonic systems and provides explicit diagonalization methods for quadratic Hamiltonians with Lindblad couplings.

Findings

Diagonalization of quantum Liouvillean for quadratic bosonic Hamiltonians.

Explicit solution for a single boson case.

Framework applicable to arbitrary linear Lindblad couplings.

Abstract

The framework of third quantization - canonical quantization in the Liouville space - is developed for open many-body bosonic systems. We show how to diagonalize the quantum Liouvillean for an arbitrary quadratic n-boson Hamiltonian with arbitrary linear Lindblad couplings to the baths and, as an example, explicitly work out a general case of a single boson.