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.
View Article and Find Full Text PDFDespite the multitude of available methods, the characterization of ultrafast pulses remains a challenging endeavor, especially at the single-photon level. We introduce a pulse characterization scheme that maps the magnitude of its short-time Fourier transform. Contrary to many well-known solutions it does not require nonlinear effects and is therefore suitable for single-photon-level measurements.
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