Generalized Collective Lamb Shift

TL;DR

This paper introduces techniques to efficiently analyze the collective Lamb shifts in hybrid quantum systems, enabling a comprehensive understanding of energy level hybridizations across all subspaces without restrictive approximations.

Contribution

The authors develop methods for a compact description of Lamb shift statistics across all collective subspaces, overcoming computational intractability.

Findings

Analyzed Lamb shifts in all subspaces and excitation manifolds.

Described average Lamb shift weighted over subspace degeneracies.

Provided a comprehensive framework for energy level hybridization analysis.

Abstract

Hybrid quantum systems consisting of an ensemble of two--level systems interacting with a single--mode electromagnetic field are important for the development of quantum information processors and other quantum devices. These systems are characterized by the set of energy level hybridizations, split by collective Lamb shifts, that occur when the ensemble and field mode interact coherently with high cooperativity. Computing the full set of Lamb shifts is generally intractable given the high dimensionality of many devices. In this work, we present a set of techniques that allow a compact description of the Lamb shift statistics across all collective angular momentum subspaces of the ensemble without using restrictive approximations on the state space. We use these techniques to both analyze the Lamb shift in all subspaces and excitation manifolds and to describe the average observed Lamb shift weighted over the degeneracies of all subspaces.