Exponential Expansion of Massive Schr\"{o}dinger Cats for Sensing and Entanglement

TL;DR

This paper introduces a protocol to exponentially expand Schr"{o}dinger cat states of levitated masses, enhancing their utility in sensing and entanglement, and demonstrates how this growth improves experimental feasibility for quantum gravity tests.

Contribution

It proposes a novel Gaussian dynamics-based method to exponentially enlarge superpositions and generate entanglement in qubit-mass systems, advancing quantum sensing and fundamental physics experiments.

Findings

Exponential superposition expansion enhances force sensing speed.

Full quantum dynamics analysis confirms entanglement growth.

Feasibility conditions for experiments are derived.

Abstract

Schr\"{o}dinger cat states of levitated masses have several applications in sensing and, offer an avenue to explore the fundamental nature -- classical vs nonclassical -- of gravity, eg, through gravitationally induced entanglement (GIE). The interaction between a qubit and a levitated mass is a convenient method to create such a cat state. The size of the superpositions is limited by weak mass-qubit interactions. To overcome this limitation, we propose a protocol that exponentially expands an initially small superposition via Gaussian dynamics and successfully recombines it to complete an interferometry. An unknown force can be sensed by the superposition exponentially fast in the expansion time. The entanglement between two such interferometers interacting via a quantum force is -- for the first time in qubit-based non-Gaussian protocols -- obtained by solving the full quantum dynamics using Gaussian techniques. GIE grows exponentially, thereby making it closer to experimental feasibility. Requirements of experimental precision and decoherence are obtained.