Experimental implementation of the optical fractional Fourier transform in the time-frequency domain

Abstract

The fractional Fourier transform (FrFT), a fundamental operation in physics that corresponds to a rotation of phase space by any angle, is also an indispensable tool employed in digital signal processing for noise reduction. Processing of optical signals in their time-frequency degree of freedom bypasses the digitization step and presents an opportunity to enhance many protocols in quantum and classical communication, sensing and computing. In this letter, we present the experimental realization of the fractional Fourier transform in the timefrequency domain using an atomic quantum-optical memory system with processing capabilities. Our scheme performs the operation by imposing programmable interleaved spectral and temporal phases. We have verified the FrFT by analyses of chroncyclic Wigner functions measured via a shot-noise limited homodyne detector. Our results hold prospects for achieving temporal-mode sorting, processing and super-resolved parameter estimation.

Quantum optics with time-frequency degrees of freedom of single photons

“…An alternative method was performed experimentally in Ref. 13 Note that also, frequency displacement operation can be achieved using linear optics, which can be efficiently applied to single photon states Ref 14 . By using electro-optic phase modulation synchronized with the pulses, a spectral shift µ is achieved.…”