What is frequency entanglement? If frequency (or energy) is regarded as a quantum property, can one generate a pair of photons with frequency entanglement? What would be the uses of this type of entangelment in say, sensing? How would you describe it mathematically? And would you be able to give a bit of intuition?
 A: We are basically talking about time-energy entangled photons. This is used for quantum communication. The real term is frequency bin entanglement.
First, a monochromatic laser pump produces frequency entangled photons, where the frequency of each photon is uncertain, but the sum of their frequencies is well defined.
THen, narrow band frequency filters resolve the frequency of each photon.This leads to the concept of frequency bin, two photons whose frequency is so close, that they cannot be distinguished by the filters.
Then different frequency bins are made to interfere using electro optic phase modulators.


In this chapter, we introduce our method to manipulate energy-time entangled photons. First,we describe classical and single-photon schemes for manipulating the frequency degree of free-dom with EOPMs,  which create frequency sidebands.   These experiments can be viewed ashigh-dimensional  frequency  analogues  of  the  spatio-temporal  and  polarization  experimentspresented in section 1.3. Correspondence principles imply that classical interference translatesto single-photon interference, and single-photon interference translates to two-photon interfer-ence. We show how we can transpose the setup to the entangled-photon case, leading to the no-tion offrequency-bin entanglement. We also show how the high-dimensional interference patterncreated by EOPMs can be restricted to interference between effective two-dimensional states.We describe in detail our experimental tools —mainly composed of off-the-shelf components—to implement the method and acquire reliable data.  Finally, we present our experimental re-sults, i.e. high-visibility two-photon interference patterns in optical fibers at telecommunicationwavelengths, demonstrating that the method can be reliably implemented.


Please see here:
https://tel.archives-ouvertes.fr/tel-01743877/document
