Photonic de Broglie Waves

In quantum optics an ensemble of photons is treated as a Bose condensate which has a de Broglie wavelength given by ₀/N where ₀ and N are the wavelength and average number of constituent photons, respectively. We describe an interferometer which is capable of measuring this de Broglie wavelength. We show specifically that a coherent state input has a de Broglie coherence length proportional to 1/N. Finally we show that the interferometer is Heisenberg limited in sensitivity (₌₈₍0ex{0ex}=0ex{0ex}1/N) and thus forms a new class of interferometers operating at the fundamental quantum limit.