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Pulse Characterization by spectral correlation function measurement with a quantum pulse gate

Abhinandan Bhattacharjee, Laura Serino, Patrick Folge, Benjamin Brecht, Christine Silberhorn

Published Jan 1, 2024• 0 citations
Publisher

Abstract

We measure the two-point spectral correlation function to completely characterize an ultrafast pulse with arbitrary level of coherence using a quantum pulse gate. Our method is readily applicable to single-photon pulses.
DOI
10.1364/cleo_fs.2024.fm4k.5

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Temporal-spectral modes of light provide a fundamental window into the nature of quantum systems and offer a robust means for information encoding. Methods to precisely characterize the temporal-spectral state of light at the single-photon level thus play a central role in understanding single-photon sources and their applications in emerging optical quantum technologies. Here we demonstrate an optical reference-free method, which melds techniques from ultrafast metrology and single-photon spectral detection, to characterize the pulse-mode structure of heralded single photons.
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 characterization 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 (QPG), which directly yield the chronocyclic Q −function. We evaluate the complex spectral amplitude from the measured chronocyclic Q −function data with maximum likelihood estimation (MLE), which is the established technique for quantum state tomography. The MLE yields not only an unambigious estimate of the complex spectral amplitude of the state under test that does not require any 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 for classical pulse characterization problems.
Single photons are a natural platform for quantum technologies as they support entanglement in many degrees of freedom and are inherently well protected from a detrimental type of noise called decoherence. In order to fully exploit photons for quantum technologies, it will be necessary to be able to shape, control, and measure their properties in all degrees of freedom: space, time, frequency, and polarization. \n \n The time-frequency degree of freedom of light is of particular interest for quantum information tasks as it supports various encodings, including frequency bins and time bins, and is intrinsically robust for propagation through long-distance fibre links. Applications which harness quantum correlations in this degree of freedom, referred to as energy-time entanglement, include dispersion cancellation and high-dimensional quantum key distribution. However, detection of this entanglement and observation of these effects requires time resolution beyond the capabilities of current photon detectors. Thus, for operations on ultrafast time scales, more powerful and complex methods are required. \n \n In this thesis, we use a nonlinear technique known as optical gating to surpass the limitations in current detectors and measure single photon pairs, improving the time resolution by two orders of magnitude. When a single photon enters a nonlinear medium at the same time as a strong laser pulse, it may upconvert to a higher energy photon. The strong laser pulse effectively acts as an ultrafast shutter or gate and this creates a high resolution snapshot of the photon in time. Optical gating in conjunction with single photon spectrometers then allow us to measure both the spectral and temporal features of photons on subpicosecond time scales. \n \n These high resolution measurements enable us to explore a host of quantum effects which remained previously inaccessible. First, we directly observe energy-time entanglement, analogous to Einstein-Rosen-Podolsky correlations but \\emph{in frequency and time}. Then, with full control over the dispersion of each photon, we observe nonlocal dispersion cancellation on femtosecond time scales. We also explore ultrafast interferometry in the quantum domain by temporally resolving two-photon interference from a Franson interferometer and observe a violation of the CHSH-Bell inequality. Finally, we show that, using these measurements, it is possible to reconstruct a two-photon energy-time entangled state. Such measurement capabilities will be essential to precisely control both the spectral and temporal shape of entangled photons and to develop new applications in quantum state engineering.
The generation of ultrafast laser pulses and the reconstruction of their electric fields is essential for many applications in modern optics. Quantum optical fields can also be generated on ultrafast timescales; however, the tools and methods available for strong laser pulses are not appropriate for measuring the properties of weak, possibly entangled pulses. Here, we demonstrate a method to reconstruct the joint-spectral amplitude of a two-photon energy-time entangled state from joint measurements of the frequencies and arrival times of the photons, and the correlations between them. Our reconstruction method is based on a modified Gerchberg-Saxton algorithm. Such techniques are essential to measure and control the shape of ultrafast entangled photon pulses.
Single-photon sources are a fundamental resource in quantum optics and quantum information science. Photons with differing spectral and temporal shapes do not interfere well and inhibit the performance of quantum applications such as linear optics quantum computing, boson sampling, and quantum networks. Indistinguishability and purity of photons emitted from different sources are crucial properties for many quantum applications. The ability to determine the state of single-photon sources therefore provides a means to assess their quality, compare different sources, and provide feedback for source tuning. Here, we propose and demonstrate a single-configuration experimental method enabling complete characterization of the spectral-temporal state of a pulsed single-photon source having both pure and mixed states. The method involves interference of the unknown single-photon source with a reference at a balanced beam splitter followed by frequency-resolved coincidence detection at the outputs. Fourier analysis of the joint-spectral two-photon interference pattern reveals the density matrix of the single-photon source in the frequency basis. We present an experimental realization of this method for pure and mixed state pulsed single-photon sources.