Difference-phase squeezing from amplitude squeezing by means of a beamsplitter

A classical analysis of two equal intensity coherent fields incident on a beamsplitter shows that the difference-phase noise of the output depends only on the noise in the difference of the amplitudes of the input fields and not on their phase noise. This suggests that in the quantum mechanical case squeezing in the amplitudes of the input beams can lead to squeezing in the phase difference of the output beams. We show that this is true. We also find the phase properties of the output when the input consists of two number states with an equal number of photons. The difference phase distribution consists of two narrow peaks, at theta = 0 and theta = pi. States with small phase difference noise should be useful in the measurement of phase shifts.