Quantum metrology of hopping strength in one-dimensional chains

We propose a critical quantum metrology protocol for high-precision estimation of electron hopping strength in a light–matter coupling platform. The system comprises a cavity coupled to an electronic chain, which exhibits a pseudo-superradiant phase transition. With the cavity ground state prepared in a squeezed vacuum state, this state serves as a quantum probe that achieves high-precision estimation of the hopping strength, saturating the ultimate quantum bound in both lossy and lossless regimes. Remarkably, in the presence of chain dissipation, increasing the electron current further enhances the measurement precision. Additionally, our results demonstrate that enlarging the chain size can, in principle, lead to significant precision enhancement. This work provides an optical readout scheme for high-precision measurement of hopping strengths in electronic chains, offering potential applications in cavity-QED-based critical quantum metrology and optical quantum sensing.