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 time-frequency 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.

6 pages, 4 figures

References in corpus (6)

• Sorting photons by radial quantum number
• Continuous-Variable Quantum Computing in Optical Time-Frequency Modes using Quantum Memories
• Optical-domain spectral super-resolution via a quantum-memory-based time-frequency processor
• A quantum-bit encoding converter
• Time-frequency as quantum continuous variables
• Variable electro-optic shearing interferometry for ultrafast single-photon-level pulse characterization

Cited by in corpus (10)

• Integrated optical wave analyzer using the discrete fractional Fourier transform
• Fully solvable finite simplex lattices with open boundaries in arbitrary dimensions
• Ultrafast electro-optic Time-Frequency Fractional Fourier Imaging at the Single-Photon Level
• Gottesman-Kitaev-Preskill encoding in continuous modal variables of single photons
• Erecting time telescope for photonic quantum networks
• Long-lived collective Rydberg excitations in atomic gas achieved via ac-Stark lattice modulation
• Interferometric sorting of temporal Hermite-Gauss modes via temporal Gouy phase
• Spectrum-to-position mapping via programmable spatial dispersion implemented in an optical quantum memory
• Hybrid quantum memory leveraging slow-light and gradient-echo duality
• Time-resolved second-order autocorrelation function of parametric downconversion