Optical Fractional Fourier Transform - Experimental Implementation

Light processing plays a central role in quantum communication, since optical quantum networks that will allow for secure quantum communication [1] and linking quantum computers [2] are of significant scientific and engineering interest [3], [4]. In this work, we present the experimental implementation of optical Fractional Fourier Transform. The protocol is realised in gradient echo memory. Hermite-Gaussian modes of light are encoded in rubidium atoms with the coupling impulse linearly chirped in frequency - this corresponds to the temporal lens [5]. Then the ac-Stark beam is applied to the atoms which leads to them acquiring the spectral phase corresponding to the propagation through a spectral lens. This operation results in the rotation of the Wigner function of the input state [6] and is exactly the Fractional Fourier Transform (FrFT) of the input function. The Hermite-Gaussian modes of light are the eigenfunctions of FrFT.