Phase amplification microscopy with femtometer-level accuracy

Abstract

We demonstrate a major breakthrough in laser interferometry and microscopy achieving femtometer-level measurement accuracy and beyond, termed Phase Amplification microscopy ({\Phi}-Amp). By exploiting the native silicide substrate as a phase cavity, our phase-gain theory predicts that weak sub-atomic phase signals can be magnified over 1000-fold, thus bypassing the shot-noise limit. We experimentally achieved a 158.2-fold phase gain for graphene in ambient air, corresponding ~ 730 femtometer accuracy. To fully unleash the potential of {\Phi}-Amp for atomic fabrication and quantum measurement, we quantified interlayer spacing differences between AB-stacked and 30-degree-twisted bilayer graphene to be ~ 0.77 Angstroms and further detected atomic impurities and defects on large atomic structures. As the first wide-field metrology tool, we envision {\Phi}-Amp may accelerate the scaling up of atomic quantum devices.