Quantum optical measurement of arbitrary fourth-order field moments via balanced homodyne correlation

Balanced homodyne correlation allows the measurement of moments of creation and annihilation operators with unequal or equal powers with high signal to noise ratios, thus giving access to high order moments. In this work we implement this method for the first time. Our realisation with eight detectors gives access to field moments up to fourth order. We use a laser direct written waveguide structures to implement the beam splitter cascade, and we use a photodiode array for multi-beam detection. The set-up is successfully verified with squeezed- and coherent states.