Initial states of qubit-boson models leading to conserved quantities

TL;DR

This paper explores how specific initial states in qubit-boson systems can ensure the conservation of certain qubit observables during evolution, even without associated symmetries, providing a general construction and examples.

Contribution

It introduces a general method to identify initial states that lead to conserved qubit observables in qubit-boson models, expanding understanding beyond symmetry-based conservation.

Findings

Constructed the subspace of initial states leading to conserved quantities.

Applied the method to Jaynes-Cummings and multi-photon Rabi models.

Demonstrated conservation without symmetry in these models.

Abstract

It is possible to prepare a composite qubit-environment system so that its time evolution will guarantee the conservation of a preselected qubit's observable. In general, this observable is not associated with a symmetry. The latter may not even be present in the subsystem. The initial states which lead to such a quantity conserved dynamics form a subspace of the qubit-environment space of states. General construction of this subspace is presented and illustrated by two examples. The first one is the exactly soluble Jaynes-Cummings model and the second is the multi-photon Rabi model.