Pulse characterization at the single-photon level through chronocyclic $Q$-function measurements

TL;DR

This paper introduces a novel method for characterizing the spectral amplitude of single-photon-level light pulses by measuring their chronocyclic Q-function, enabling detailed spectral phase and coherence analysis without prior information.

Contribution

The authors demonstrate a new approach using quantum state tomography techniques to retrieve complex spectral information of single-photon pulses through chronocyclic Q-function measurements.

Findings

Accurately recovers spectral phase features including phase jumps.

Resistant to regions with zero spectral intensity.

Provides unambiguous spectral amplitude estimates without prior assumptions.

Abstract

The characterization of the complex spectral amplitude that is, the spectrum and spectral phase, of single-photon-level light fields is a crucial capability for modern photonic quantum technologies. Since established pulse characterisation techniques are not applicable at low intensities, alternative approaches are required. Here, we demonstrate the retrieval of the complex spectral amplitude of single-photon-level light pulses through measuring their chronocyclic $Q-$function. Our approach draws inspiration from quantum state tomography by exploiting the analogy between quadrature phase space and time-frequency phase space. In the experiment, we perform time-frequency projections with a quantum pulse gate, which directly yield the chronocyclic $Q-$function. We evaluate the data with maximum likelihood estimation, which is the established technique for quantum state tomography. This yields not only an unambigious estimate of the complex spectral amplitude of the state under test that does not require any \textit{a priori} information, but also allows for, in principle, estimating the spectral-temporal coherence properties of the state. Our method accurately recovers features such as jumps in the spectral phase and is resistant against regions with zero spectral intensity, which makes it immediately beneficial also for classical pulse characterization problems.