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We discuss the use of time and frequency degrees of freedom of single photons in quantum optics. Such a degree of freedom is generally discretized into modes for experimental reasons, but it is not a physical requirement. The origin of the quantumness of the time and frequency variables can be explained because of the non-commutativity of time and frequency operators - which can be defined properly- when restricted to the one photon per mode subspace. As a consequence, We will show that frequency and time operators can be used to define a universal set of gates in this particular subspace and provide an experimental implementation of such a universal set of gates.
Nicolas Fabre
"Quantum optics with time-frequency degrees of freedom of single photons", Proc. SPIE 12570, Quantum Optics and Photon Counting 2023, 1257002 (6 June 2023); https://doi.org/10.1117/12.2665062
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Nicolas Fabre, "Quantum optics with time-frequency degrees of freedom of single photons," Proc. SPIE 12570, Quantum Optics and Photon Counting 2023, 1257002 (6 June 2023); https://doi.org/10.1117/12.2665062