Dark-Mode Theorems for Quantum Networks

TL;DR

This paper introduces theorems for identifying dark modes in linear quantum networks, providing a mathematical framework applicable to bosonic and fermionic systems, with implications for quantum information processing.

Contribution

The paper presents new theorems for determining dark modes in quantum networks by analyzing the coupling matrix structure, extending to fermionic systems and other Hamiltonians.

Findings

Theorems accurately predict dark modes in bosonic and fermionic networks.

Validation through ground-state cooling in optomechanical systems.

Method applicable to constructing decoherence-free subspaces.

Abstract

We propose and prove two theorems for determining the number of dark modes in linear two-component quantum networks composed of two types of bosonic modes. This is achieved by diagonalizing the two sub-networks of the same type of modes, mapping the networks to either a standard or a thick arrowhead matrix, and analyzing the linear dependence and independence between the column vectors associated with degenerate normal modes in the coupling matrix. We confirm the two theorems by checking the simultaneous ground-state cooling of the mechanical modes in linearized optomechanical networks. These results also work for linear fermionic networks and other networks described by quadratic coupled-mode Hamiltonian. The present method can be extended to study the dark-state effect in driven atom systems and to construct large decoherence-free subspaces for processing quantum information. This work will initiate the studies on dynamical, transport, and statistical properties of linear networks with decoupled subspaces.