Review: Quantum Metrology and Sensing with Many-Body Systems

The main power of quantum sensors is achieved when the probe is composed of several particles. In this situation, quantum features such as entanglement contribute to enhancing the precision of quantum sensors beyond the capacity of classical sensors. Originally, quantum sensing was formulated for non-interacting particles that are prepared in a special form of maximally entangled states. These probes are extremely sensitive to decoherence, and any interaction between particles is detrimental to their performance. An alternative framework for quantum sensing has been developed 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 in both equilibrium and non-equilibrium scenarios. Quantum criticality has been identified as a resource for achieving quantum-enhanced sensitivity in both 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 has its own characteristics, the presence of one feature is crucial for achieving quantum-enhanced sensitivity: the energy/quasi-energy gap closing. In non-equilibrium quantum sensing, time is another parameter that can affect the sensitivity of the probe. Typically, the sensitivity enhances as the probe evolves in time. In general, a more complete understanding of resources for non-equilibrium quantum sensors is now rapidly evolving. In this review, we provide an overview of recent progress in quantum metrology and sensing using many-body systems.