The General Quantum Limit for and the Optimization of the Minimum Measurable Frequency Shift in a Laser

Abstract

We show that, contrary to conventional understanding, the minimum measurable frequency shift (MMFS) for a single-mode ideal laser is determined by a combination of phase diffusion caused by spontaneous emission and the shot noise caused by the vacuum mode. For all practical sensors, the MMFS is found to be given by the geometric mean of the measurement bandwidth and the Schwalow-Townes Linewidth, multiplied by a factor which can be much larger than unity under certain conditions. We determine the optimal values of the MMFS for three different sensing modalities, an unbalanced Mach-Zehnder Interferometer, a passive Fabry-Perot cavity (FPC), and heterodyning with a reference laser, and identify the conditions needed for reaching these values of the MMFS.