Photonic de Broglie Waves

Abstract

In quantum optics an ensemble of photons is treated as a Bose condensate which has a de Broglie wavelength given by l 0 ͞N where l 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 1͞ p N. Finally we show that the interferometer is Heisenberg limited in sensitivity (Df min 1͞N) and thus forms a new class of interferometers operating at the fundamental quantum limit.

Multiphoton entanglement and interferometry

“…These experiments demonstrated an interesting feature of NOON states: the effective de Broglie wavelength of the multiphoton state is by 1/N shorter than the wavelength of the single photon (Jacobson et al, 1995). Nagata et al have not only measured the reduced de Broglie wavelength of four-entangled photons, but also shown a visibility that exceeds the threshold to beat the standard quantum limit (see the original paper for details).…”

Quantum diffraction and interference of spatially correlated photon pairs and its Fourier-optical analysis

“…This work has been developed into one of the fields of quantum imaging. Meanwhile, the concept of the "photonic de Broglie wave" has been proposed as an intuitive and essential way to understand the interferometric properties of a multiphoton state [6]. Within this concept, the photonic de Broglie wavelength of an ensemble photons with wavelength λ and number of photons n can be measured to be λ/n.…”

Demonstration of the three-photon de Broglie wavelength by projection measurement

“…NOON state of the form in Eq. (1) for N = 2 case was realized with two photons from parametric downconversion, which led to the demonstrations of twophoton de Broglie wavelength [7,8]. For N > 2, however, it is not easy to generate the NOON state.…”

“…Early work by Jacobson et al [1] utilized a special beam splitter that sends a whole incident coherent state to either one of the outputs thus creating a Schödinger-cat like state. The equivalent de Broglie wavelength in this case was shown to be λ/ n with n as the average photon number of the coherent state.…”