Squeezing by critical speeding up: Applications in quantum metrology

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.

Automated summary

This article presents an alternative protocol for preparing critical states that benefits from critical speeding up rather than critical slowing down, achieved by moving away from the critical point. The protocol is applied to quantum Rabi model, its classical oscillator limit, and the Lipkin-Meshkov-Glick model. The adiabatic speed-up protocol is discussed in quantum metrology and compared to critical quantum metrology, showing that critical quantum metrology is a suboptimal strategy. The article concludes that systems exhibiting a phase transition are interesting in quantum technologies, but the critical point may not be the most important aspect.