Stroboscopic quantum nondemolition measurements for enhanced entanglement generation between atomic ensembles

TL;DR

This paper introduces a formalism for stroboscopic quantum nondemolition measurements that enhances entanglement between atomic ensembles without relying on approximations, enabling precise state evolution analysis.

Contribution

It develops an exact measurement operator formalism for QND entanglement, including a sequence of projections in different bases, improving understanding of entanglement dynamics.

Findings

Sequence of QND projections enhances entanglement

Exact state evolution derived without Holstein-Primakoff approximation

Mathematical identities simplify the analysis of state dynamics

Abstract

We develop a measurement operator formalism to handle quantum nondemolition (QND) measurement induced entanglement generation between two atomic gases. We first derive how the QND entangling scheme reduces to a positive operator-valued measure, and consider its limiting case when it can be used to construct a projection operator that collapses the state to a total spin projection state. We then analyze how a stroboscopic sequence of such projections made in the x and z basis evolves the initial wave function. Such a sequence of QND projections can enhance the entanglement between the atomic ensembles and makes the state converge towards a highly entangled state. We show several mathematical identities which greatly simplify the state evolution in the projection sequence and allow one to derive the exact state in a highly efficient manner. Our formalism does not use the Holstein-Primakoff approximation as is conventionally done, and treats the spins of the atomic gases in an exact way.