1,000-fold amplification in time-holography phase metrology

Conventional interferometers provide uniform phase sensitivity across the measurement range. However, for applications involving small phase changes, amplifying the response within a specific phase range—at the expense of reduced sensitivity elsewhere—can be advantageous. A key example is the Gires-Tournois etalon, used in gravitational wave interferometers. In this work, we introduce an ultrasensitive phase measurement system based on time-holographic recording with a conventional Mach-Zehnder interferometer, operated near the intensity minimum at the dark output port. Phase fluctuations in the milliradian range around this point are converted into rad-sized dark output phases, with amplification factors exceeding 1,000. The adjustable imbalance between the interferometer arms controls this magnification, which is revealed by heterodyning the output with a frequency-shifted beam. Phase is digitally retrieved from the time-hologram using Fourier processing, with noise subtraction for correction. The system achieves phase sensitivities better than λ/3,000, enabling sub-nanometer precision for dimensional measurements. This versatile platform provides powerful tools for ultrasensitive phase measurements in a wide range of scientific and technological applications.