Measurement of numberphase uncertainty relations of optical fields
Abstract
We have experimentally determined all of the quantities involved in the uncertainty relation for the phase and photon number of a mode of the electromagnetic field when the field mode is in a coherent state of small average photon number. This is accomplished by determining the quantum state of the field using optical homodyne tomography, which uses measured distributions of electricfield quadrature amplitude to determine the Wigner function and hence the density matrix. The measured state is then used to calculate the uncertainty product for the number and phase, as well as the expectation value of the commutator of the number and phase operators. The experimental results agree with the quantummechanical predictions. We also present measured phase and photonnumber distributions for these weak coherent states, as well as their measured complex wave functions.
 Publication:

Physical Review A
 Pub Date:
 October 1993
 DOI:
 10.1103/PhysRevA.48.3159
 Bibcode:
 1993PhRvA..48.3159S
 Keywords:

 42.50.Wm;
 03.65.Bz