Review: Quantum metrology and sensing with many-body systems

Quantum systems, fabricated across various spatial scales from nano to micrometers, are very delicate and naturally sensitive to the variations of their environment. These features make them excellent candidates for serving as sensors with wide range of applications. Indeed, the exceptional precision of quantum sensors arises from their compact size and inherent sensitivity, enabling measurements with unprecedented accuracy within highly localized regions. A key advantage of quantum sensors lies in their resource efficiency, as their achievable precision can scale super-linearly with respect to resources, such as system size, in contrast to the linear scaling characteristic of classical sensors. This phenomenon, commonly referred to as quantum-enhanced sensitivity, fundamentally depends on exploiting uniquely quantum mechanical features, including superposition, entanglement, and squeezing. Originally, quantum sensing was formulated for particles prepared in a special form of entangled states. Yet, certain realization of these probes may be susceptible to decoherence and interaction between particles may also be detrimental to their performance. An alternative framework for quantum sensing has been developed through exploiting quantum many-body systems, where the interaction between particles plays a crucial role. In this review, we investigate different aspects of the latter approach for quantum metrology and sensing. Many-body probes have been used for sensing purposes in both equilibrium and non-equilibrium scenarios. Quantum criticality, as a well-studied subject in many-body physics, has been identified as a resource for achieving quantum-enhanced sensitivity in both of these scenarios. In equilibrium, various types of criticalities, such as first order, second order, topological, and localization phase transitions have been exploited for sensing purposes. In non-equilibrium scenarios, quantum-enhanced sensitivity has been discovered for Floquet, dissipative, and time crystal phase transitions. While each type of these criticalities, either in equilibrium or non-equilibrium scenarios, has its own characteristics, the presence of one feature is crucial for achieving quantum-enhanced sensitivity and that is energy/quasi-energy gap closing. In non-equilibrium quantum sensing, time becomes another parameter which can affect the sensitivity of the probe.