Experimental determination of number–phase uncertainty relations

Abstract

An experimental determination of the uncertainty product for the phase and photon number of a mode of the electromagnetic field is performed. The expectation value of the commutator that sets the lower bound for the uncertainty product is also determined experimentally. This is accomplished by using optical homodyne tomography to measure the density matrix of a small-photon-number coherent state. The experimental results agree with the quantum-mechanical predictions.