Quantumentanglement of photons doubles microscope resolution Caltech NatureComms
The balanced pathlengths require symmetry in the optical paths of the signal and idler photons from the source Fourier plane to the detection planes, such that the paired photons are correlated in positions and momentums concurrently, and the phases of the paired photons can be combined. This requirement, however, cannot be satisfied through classical sources because two unentangled photons can only be correlated in either position or momentum in accordance with the uncertainty principle.
The signal photon on the object plane can be scattered by the object, leading to different wavevectors between the signal and idler photons. In Fig., in the paraxial approximation, photons traversing the same position on the object plane would arrive at the same position on the detection plane, indicating identical optical pathlengths according to Fermat’s principle.
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