Ultrafast electro-optic Time-Frequency Fractional Fourier Imaging at the Single-Photon Level

• URL: http://arxiv.org/abs/2307.01141v2
• Date: Sat, 28 Oct 2023 09:17:07 GMT
• Title: Ultrafast electro-optic Time-Frequency Fractional Fourier Imaging at the Single-Photon Level
• Authors: Micha{\l} Lipka and Micha{\l} Parniak
• Abstract summary: Fractional Fourier Transform (FRT) corresponds to an arbitrary-angle rotation in the phase space, e.g. the time-frequency (TF) space. A versatile low-noise single-photon-compatible implementation of the FRT is presented.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The Fractional Fourier Transform (FRT) corresponds to an arbitrary-angle rotation in the phase space, e.g. the time-frequency (TF) space, and generalizes the fundamentally important Fourier Transform. FRT applications range from classical signal processing (e.g. time-correlated noise optimal filtering) to emerging quantum technologies (e.g. super-resolution TF imaging) which rely on or benefit from coherent low-noise TF operations. Here a versatile low-noise single-photon-compatible implementation of the FRT is presented. Optical TF FRT can be synthesized as a series of a spectral disperser, a time-lens, and another spectral disperser. Relying on the state-of-the-art electro-optic modulators (EOM) for the time-lens, our method avoids added noise inherent to the alternatives based on non-linear interactions (such as wave-mixing, cross-phase modulation, or parametric processes). Precise control of the EOM-driving radio-frequency signal enables fast all-electronic control of the FRT angle. In the experiment, we demonstrate FRT angles of up to 1.63 rad for pairs of coherent temporally separated 11.5 ps-wide pulses in the near-infrared (800 nm). We observe a good agreement between the simulated and measured output spectra in the bright-light and single-photon-level regimes, and for a range of pulse separations (20 ps to 26.67 ps). Furthermore, a tradeoff is established between the maximal FRT angle and bandwidth, with the current setup accommodating up to 248 GHz of bandwidth. With the ongoing progress in EOM on-chip integration, we envisage excellent scalability and vast applications in all-optical TF processing both in the classical and quantum regimes.

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