Combining critical and quantum metrology

​Critical metrology relies on the precise preparation of a system's ground state near the quantum phase transition point. This facilitates the creation of quantum correlations, known for their ability to enhance the quantum Fisher information and thus improve measurement precision within the confines of the Cramér-Rao bound. Essentially, critical metrology involves encoding information about the unknown parameter within the system's ground state. Conversely, in conventional metrology methods like Ramsey interferometry, the eigenstates of the system remain unchanged, and information about the unknown parameter is stored within the phase accumulated during free evolution. I will introduce an approach that combines these two methodologies into a unified protocol applicable to both closed and driven-dissipative systems. To achieve this, I will concentrate on the squeezing Hamiltonian, which characterizes the thermodynamic limit of Dicke and Lipkin-Meshkov-Glick Hamiltonians.