Measurement of two independent phase shifts using coupled parametric amplifiers

In this paper, we demonstrate a scheme capable of two-phase measurement, i.e. the simultaneous measurement of two phase shifts occurring in two independent Mach-Zehnder interferometers using one intensity detector. Our scheme utilizes dark-state-enhanced coupled parametric amplifiers in an atomic medium to mix the multiple fields probing the various arms of the interferometers in parallel. The two phase differences are then encoded in separate continuous-variable parameters in the spectral waveform of the parametrically amplified atom-radiated signal field, which can be directly decoupled in a single intensity measurement. Besides resolving two phase differences in parallel, this method can also be used to increase the channel capacity in optical and quantum communication by the simultaneous use of phase modulation and amplitude modulation.