Adaptive measurements and optimal states for quantum interferometry

Summary form only given. Interferometry is the basis of many high-precision measurements. The ultimate limit to the precision is due to quantum effects. This limit is most easily explored for a Mach-Zehnder interferometer The outputs of this device can be measured to yield an estimate φ of the phase difference φ between the two arms of the interferometer. It is well known that this can achieve the standard quantum limit for phase variance when an N-photon number state enters one input port. Several authors have proposed ways of reducing the phase variance to the Heisenberg limit. In this paper we show that there is a physical measurement scheme using photodetectors and feedback that is almost as good as the optimal measurement. The fundamental idea is that, in addition to the unknown phase we wish to measure, φ, in one arm of the interferometer, we introduce a known phase shift, Φ, into the other arm of the interferometer. After each photodetection we adjust this introduced phase shift in order to minimize the expected uncertainty of our best phase estimate φ after the next photodetection. This feedback process is uniquely defined using Bayesian statistics, and can be solved exactly for moderate photon numbers.