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Quantum 2.0 Conference and Exhibition

How to perform the optical Fractional Fourier Transform?

Marcin Jastrzębski, Bartosz Niewelt, Stanisław Kurzyna, Jan Nowosielski, Wojciech Wasilewski, Mateusz Mazelanik, Michal P. Parniak

Published Jan 1, 2023• 0 citations
Publisher

Abstract

We present the Fractional Fourier Transform (FrFT) realised in quantum memory. We achieve this transformation by applying two temporal and one spectral lenses and measure the Hermite-Gaussian modes which are the eigenfunctions of FrFT.
DOI
10.1364/quantum.2023.qth4a.6

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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.
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Fractional Fourier transform (FrFT) is an important tool used in signal processing. It is usually utilized to filter the noise in acoustic signals and it is generalization of Fourier transform. In recent years it was also presented that it has a crucial role in optics, especially mode sorting [2]. One of the important interpretations of FrFT is rotation of the Wigner distribution in time-frequency domain called chronocyclic Wigner function. We have shown that it is possible to perform rotation of arbitrary angleφ\varphiφcoresponding to angle of FrFT. Despite its usefulness, it is still very difficult to perform FrFT in the time-frequency domain. Our experiment is based on the gradient echo memory built around cloud of ultracold rubidium 87 atoms trapped in the magneto-optical trap. The memory protocol uses two-photon Raman transition to store signal pulses in atomic coherence. By applying spatial lens with ac-Stark modulation and imposing two temporal lenses in specific order [1]. We have experimentally performed FrFT in spectro-temporal domain for the cat state.