Squeezing by Critical Speeding-up: Applications in Quantum Metrology

TL;DR

This paper introduces a protocol that leverages critical speeding-up by preparing states away from the critical point, enhancing quantum metrology performance and challenging the effectiveness of critical quantum metrology.

Contribution

It proposes an alternative adiabatic protocol exploiting critical speeding-up and compares its effectiveness with traditional critical quantum metrology approaches.

Findings

Critical quantum metrology with the Lipkin-Meshkov-Glick model does not surpass the standard quantum limit.

Critical metrology can be suboptimal compared to other strategies.

Systems with phase transitions are valuable for quantum technologies, but the critical point itself may not be the best focus.

Abstract

We present an alternative protocol allowing for the preparation of critical states that instead of suffering from the critical slowing-down benefits from the critical speeding-up. Paradoxically, we prepare these states by going away from the critical point which allows for the speed-up. We apply the protocol to the paradigmatic quantum Rabi model and its classical oscillator limit as well as the Lipkin-Meshkov-Glick model. Subsequently, we discuss the application of the adiabatic speed-up protocol in quantum metrology and compare its performance with critical quantum metrology. We show that critical quantum metrology with the Lipkin-Meshkov-Glick model cannot even overcome the standard quantum limit, and we argue that, even though critical metrology protocols can overcome it in some cases, critical metrology is a suboptimal metrological strategy. Finally, we conclude that systems exhibiting a phase transition are indeed interesting from the viewpoint of quantum technologies, however, it may not be the critical point that should attract the most attention.