Ultrafast imaging of photon statistics in two dimensions is a powerful tool for probing non-equilibrium and transient optical phenomena, yet it remains experimentally challenging due to the simultaneous need for high temporal resolution and statistical fidelity. In this work, we demonstrate spatially resolved single-shot measurements of photon number distributions using difference-frequency generation (DFG) in a nonlinear BBO crystal. We show that our platform can discriminate between coherent and thermal photon statistics across two spatial dimensions with picosecond resolution. At the same time, we find that the retrieved distributions deviate from the ideal ones, a consequence of vacuum contamination and the multimodal response of the amplifier. To explain this, we develop a temporal mode decomposition framework that captures the essential physics of signal amplification and fluorescence, and quantitatively reproduces the experimental findings. This establishes a robust approach for measuring two-dimensional photon statistics while clarifying the fundamental factors that limit the fidelity of such measurements.
Ultrafast imaging of photon statistics in two dimensions is a powerful tool for probing non-equilibrium and transient optical phenomena, yet it remains experimentally challenging due to the simultaneous need for high temporal resolution and statistical fidelity. In this work, we demonstrate spatially resolved single-shot measurements of photon number distributions using difference-frequency generation (DFG) in a nonlinear BBO crystal. We show that our platform can discriminate between coherent and thermal photon statistics across two spatial dimensions with picosecond resolution. At the same time, we find that the retrieved distributions deviate from the ideal ones, a consequence of vacuum contamination and the multimodal response of the amplifier. To explain this, we develop a temporal mode decomposition framework that captures the essential physics of signal amplification and fluorescence, and quantitatively reproduces the experimental findings. This establishes a robust approach for measuring two-dimensional photon statistics while clarifying the fundamental factors that limit the fidelity of such measurements.
We present a method for spatially resolved multiphoton counting based on an intensified camera with the retrieval of multimode photon statistics fully accounting for nonlinearities in the detection process. The scheme relies on one-time quantum tomographic calibration of the detector. Faithful, high-fidelity reconstruction of single- and two-mode statistics of multiphoton states is demonstrated for coherent states and their statistical mixtures. The results consistently exhibit classical values of the Mandel parameter and the noise reduction factor in contrast to raw statistics of camera photo-events. Detector operation is reliable for illumination levels up to the average of one detected photon per an event area-substantially higher than in previous approaches to characterize quantum statistical properties of light with spatial resolution.
Photonics offers the potential for large-scale, room-temperature, and ultrafast quantum operations. Multiplexing pulses of light allows for high throughput speeds and dense encoding, with tens of thousands of optical modes being present in a time as short as a microsecond. However, the measurement speed of electronic devices such as photodetectors is currently one bottleneck in such time-multiplexed scalability, because many quantum optical protocols rely on measurement, including state preparation, feed-forward, and feedback. Furthermore, characterization of quantum states and modes is essential for their effective use. Using nanophotonic optical parametric amplifiers (OPAs) presents one way to circumvent the measurement limitations of current quantum photonic schemes. Their large amplification bandwidth, enabled by dispersion engineering on nanophotonic integrated platforms, allows information encoded in femtosecond-scale, THz-bandwidth, multimode quantum optical states to be accessed with nonlinear optical interactions. In this work, we show how ultra-broadband integrated nanophotonic OPAs can be used to measure ultrafast and multimode quantum states of light. First, we explore the single-photon detection capabilities of OPAs, showing that current OPAs operating in the Gaussian regime are capable of 250 MHz photon count rates with 26% efficiency and a 2% dark count probability. We also show how non-Gaussian operation through pump depletion, with performance that approaches state-of-the-art photon detectors in terms of efficiency and dark count rate while retaining ultrafast operation, can become experimentally possible with a higher nonlinear coupling rate and lower loss. Next, we use nanophotonic OPAs to both generate and characterize multimode ultrafast squeezed vacuum. We use the photocurrent distribution of amplified squeezed vacuum to recover 2.41 dB of squeezing in one mode of a 154-fs multimode squeezed pulse and reconstruct its Wigner distribution. Finally, we investigate the capabilities of broadband nanophotonic OPAs to determine the temporal mode structure and quadrature variances of ultra-broadband temporally multimode quantum states by adapting frequency-resolved optical gating to the quantum regime. We numerically show the successful full characterization of a multimode squeezed state, even in the presence of noise. Together, these results establish OPAs as a valuable measurement device for measuring ultrafast quantum pulses and learning the structure of multimode quantum states, and they provide one building block towards a framework for scalable continuous-variable quantum photonics in which state generation, manipulation, and characterization occur within the same nanophotonic platform.
Photons emitted by incoherent sources exhibit temporal bunching, a fundamental manifestation of Bose-Einstein statistics first observed by Hanbury Brown and Twiss (HBT). While intensity correlation measurements originated in astronomy and are now central across quantum technologies, biophysics, and spectroscopy, observing temporal bunching in broadband thermal light remains limited by detector temporal resolution. Conventional approaches - such as streak cameras or optical upconversion - introduce severe trade-offs in efficiency, bandwidth, or setup versatility. Here, we propose and demonstrate a third route: pre-detection temporal magnification of the optical field prior to measuring its intensity autocorrelation function in a conventional HBT setup. Using an electro-optic time lens with a temporal magnification of 660, we resolve the temporal intensity autocorrelation of broadband thermal light generated via non-degenerate spontaneous parametric down-conversion with a bandwidth of 250 GHz. This enables direct observation of thermal photon bunching on sub-3.5 picosecond timescales without narrow spectral filtering, establishing pre-detection temporal imaging as a general platform for broadband statistical optics, with applications spanning ultrafast quantum optics, biophysical imaging, and potentially stellar intensity interferometry.
High-dimensional encoding in time-frequency and photon-number degrees of freedom promises photon-efficient quantum communication, but requires detectors that are both temporal-mode selective and photon-number resolving. Here we demonstrate time-correlated single-photon detection combining both capabilities. A train of shaped pump pulses drives quantum frequency up-conversion to select a chosen temporal mode, and the converted photons are counted with a photon-number-resolving detector. Applying to a photon-pair source by spontaneous parametric downconversion into signal and idler bands, we demonstrate direct sampling of the high-dimensional correlated quantum states on compound time-frequency and photon number bases. Our measurements show that the up-converted photons in each band exhibit thermal photon-number statistics, indicating strong single-mode selection. We reconstruct joint temporal intensities conditioned on one and two photon pairs, revealing signal-idler correlations in both time-frequency and photon number. Together, these results establish a unified technology framework linking high-dimensional quantum correlations, mode-selective photon measurement, and photon-number resolved detection. This approach provides a route to characterizing multimode photon-pair sources and to larger time-frequency and photon-number alphabets for high-dimensional quantum communication and information processing.
High-dimensional encoding in time-frequency and photon-number degrees of freedom promises photon-efficient quantum communication, but requires detectors that are both temporal-mode selective and photon-number resolving. Here we demonstrate time-correlated single-photon detection combining both capabilities. A train of shaped pump pulses drives quantum frequency up-conversion to select a chosen temporal mode, and the converted photons are counted with a photon-number-resolving detector. Applying to a photon-pair source by spontaneous parametric downconversion into signal and idler bands, we demonstrate direct sampling of the high-dimensional correlated quantum states on compound time-frequency and photon number bases. Our measurements show that the up-converted photons in each band exhibit thermal photon-number statistics, indicating strong single-mode selection. We reconstruct joint temporal intensities conditioned on one and two photon pairs, revealing signal-idler correlations in both time-frequency and photon number. Together, these results establish a unified technology framework linking high-dimensional quantum correlations, mode-selective photon measurement, and photon-number resolved detection. This approach provides a route to characterizing multimode photon-pair sources and to larger time-frequency and photon-number alphabets for high-dimensional quantum communication and information processing.
Quantum correlations of ultrafast quantum optical states in the time–frequency domain manifest prominently on femtosecond time scales, an elusive challenging regime. We develop a new method to probe the time–frequency mode structure of ultrafast two-photon states utilizing dual-comb-based asynchronously overlapping pulses with single-photon frequency upconversion through femtosecond optical sampling. This method enables quick, highly precise joint temporal intensity measurements over a broad temporal dynamic range with only a single linear scanning stage. We demonstrate full characterization of time–frequency entangled two-photon states in both time and frequency domains. We quantified the time–frequency mode structure in both time and frequency domains through Schmidt decomposition, resulting in temporal and spectral purities of 87.7% and 76.9%, respectively, for heralded single-photons without any spectral filtering. Furthermore, through the simple control of pump spectral bandwidth, we demonstrate the ability to tailor time–frequency entanglement, verifying the two-dimensional Fourier duality. This method paves the way for a substantial upgrade to ultrafast quantum optical techniques, enabling a rapid, detailed, and multi-dimensional characterization of entangled states with potential applications in quantum metrology and photon-deficient fluorescence imaging.