The resolution of a measurement system is fundamentally constrained by the wavelength of the used wave packet and the numerical aperture of the optical system. Overcoming these limits requires advanced interferometric techniques exploiting quantum correlations. While quantum interferometry can surpass the Heisenberg limit, it has been confined to the optical domain. Extending it to x-rays enables sub-angstrom spatial and zeptosecond temporal resolution, unlocking atomic-scale processes inaccessible to existing methods. Here, we demonstrate x-ray quantum interferometry using 17.5-kilo-electron volt ( [Formula: see text] = 70 picometers) photon pairs. Our approach introduces a phase measurement technique with exceptional noise resilience, mitigating the impact of mechanical instabilities, vibrations, and photonic noise-key challenges in x-ray interferometry. By generating and using entangled x-ray photons, we lay the foundation for next-generation techniques with unprecedented phase precision. This breakthrough carries far-reaching consequences for fundamental physics, high-resolution imaging, and spectroscopy, bringing to light quantum optical effects never before accessed in the x-ray regime.
The resolution of a measurement system is fundamentally constrained by the wavelength of the used wave packet and the numerical aperture of the optical system. Overcoming these limits requires advanced interferometric techniques exploiting quantum correlations. While quantum interferometry can surpass the Heisenberg limit, it has been confined to the optical domain. Extending it to x-rays enables sub-angstrom spatial and zeptosecond temporal resolution, unlocking atomic-scale processes inaccessible to existing methods. Here, we demonstrate x-ray quantum interferometry using 17.5-kilo-electron volt ( [Formula: see text] = 70 picometers) photon pairs. Our approach introduces a phase measurement technique with exceptional noise resilience, mitigating the impact of mechanical instabilities, vibrations, and photonic noise-key challenges in x-ray interferometry. By generating and using entangled x-ray photons, we lay the foundation for next-generation techniques with unprecedented phase precision. This breakthrough carries far-reaching consequences for fundamental physics, high-resolution imaging, and spectroscopy, bringing to light quantum optical effects never before accessed in the x-ray regime.
Quantum imaging encompasses a broad range of methods that exploit the quantum properties of light to capture information about an object. One such approach involves using a two-photon quantum state, where only one photon interacts with the object being imaged while its entangled partner carries spatial or temporal information. To implement this technique, it is necessary to generate specific quantum states of light and detect photons at the single-photon level. While this method has been successfully demonstrated in the visible electromagnetic spectrum, extending it to X-rays has faced significant challenges due to the difficulties in producing a sufficient rate of X-ray photon pairs and detecting them with adequate resolution. Here, we demonstrate record high rates of correlated X-ray photon pairs produced via a spontaneous parametric down-conversion process and we employ these photons to perform quantum correlation imaging of several objects, including a biological sample (E. cardamomum seedpod). Notably, we report an unprecedented detection rate of about 6,300 pairs per hour and the observation of energy anti-correlation for the X-ray photon pairs. We also present a detailed analysis of the properties of the down-converted X-ray photons, as well as a comprehensive study of the correlation imaging formation, including a study of distortions and corrections. These results mark a substantial advancement in X-ray quantum imaging, expanding the possibilities of X-ray quantum optical technologies, and illustrating the pathway towards enhancing biological imaging with reduced radiation doses.
Quantum correlation, such as entanglement and squeezing have shown to improve phase estimation in interferometric setups on one side, and non-interferometric imaging scheme of amplitude object on the other. In the last case, quantum correlation among a pair of beams leads to a sub-shot-noise readout of the image intensity pattern, where weak details, otherwise hidden in the noise, can be appreciated. In this paper we propose a technique which exploits entanglement to enhance quantitative phase retrieval of an object in a non-interferometric setting, i.e only measuring the propagated intensity pattern after interaction with the object. The method exploits existing technology, it operates in wide field mode, so does not require time consuming raster scanning and can operate with small spatial coherence of the incident field. This protocol can find application in optical microscopy and X-ray imaging, reducing the photon dose necessary to achieve a fixed signal-to-noise ratio.
We present the first experimental demonstration of quantum enhanced detection at x-ray wavelengths.We show that x-ray pairs that are generated by spontaneous down-conversion can be used for the generation of heralded x-ray photons and directly measure the sub-Poissonian statistics of the single photons by using photon number resolving detectors.We utilize the properties of the strong time-energy correlations of the down-converted photons to demonstrate the ability to improve the visibility and the signal-to-noise ratio of an image with a small number of photons in an environment with a noise level that is higher than the signal by many orders of magnitude.A long-term goal of this work is to demonstrate x-ray photon entanglement.However, given the technical challenges, which are much greater than in the visible regime, we take a first step in demonstrating nonclassical (sub-Poisson) photon correlations.In our work, we demonstrate a new protocol for the measurement of quantum effects with x rays using advantages such as background-free measurements that the x-ray regime offers for experiments aiming at testing fundamental concepts in quantum optics.
Abstract We demonstrate the generation of a train of attosecond XUV pulses that are in a superposition of wavefront states. Such superposition yields a high precision, self-referencing, common path XUV interferometer setup to produce pairs of spatially separated and independently controllable XUV pulses that are locked in phase and time with a temporal jitter of 3.5 zs (zs = zeptoseconds = 10 − 21 s ). In our approach, we can independently control the relative phase/delay of the two optical beams with a resolution of 52 zs. Since the jitter is on the order of the Compton time scale τ C = λ C / m e c 2 , we explore the level of correlation between the non-local photons by comparing different spatial mode superpositions. Further, thanks to the stability of the interferometer we can retrieve the interference pattern through photon counting. Through post-selection of different particle events we can analyze one, two or more photon events. We argue that this zeptosecond level of temporal precision will open the door for new dynamical quantum electrodynamics (QED) tests at lower intensities while photon counting experiments can also have an impact on the emerging field of quantum light in strong fields. We also discuss the potential impact on other areas, such as time-dependent QED, imaging, measurements of non-locality, and molecular quantum tomography.
Quantum-enhanced interferometers utilize non-classical states of light in order to surpass the limitations imposed by classical physics on phase measurement sensitivity and resolution. We review key scientific developments in this growing field of research and derive fundamental metrology concepts, namely the Cram\'{e}r-Rao bound and the Fisher information, which are used to analyze the metrological performance of quantum states of light. We propose a supersensitive quantum interferometry protocol that can be amplified to the macroscopic realm (i.e. the mean number of photons of the probe state can reach approximately 100,000 photons) using contemporary techniques of spontaneous parametric down conversion. The parity measurement on the output field asymptotically saturates the quantum Cram\'{e}r-Rao bound, which scales like the Heisenberg limit. We uncover the role of photon statistics on phase sensitivity and rule out the necessity of mode entanglement for quantum-enhanced interferometry. Based on these insights we outline a practical metrology technique (independent of mode entanglement) that measures a phase delay of a single-mode anti-squeezing operation. This scheme can also be scaled macroscopically using contemporary techniques and is shown to significantly surpass the shot-noise limit (SNL) in the presence of realistic losses. Finally, the physical resources that enable quantum-enhanced interferometry is studied by analyzing the quantum Fisher information (QFI) using the first quantization and the second quantization formalisms of quantum mechanics. It is shown that increasing the intra-mode correlations of an interferometer (as quantified by the second order Glauber coherence function) can be conducive to attaining a quantum advantage in phase estimation; whereas, introducing mode entanglement can reduce phase sensitivity. Using the first quantization description, we derive a formula for the QFI that shows explicitly how the Heisenberg scaling term depends on particle entanglement.
Entangled photons have the remarkable ability to be more sensitive to signal and less sensitive to noise than classical light. Joint photons can sample an object collectively, resulting in faster phase accumulation and higher spatial resolution, while common components of noise can be subtracted. Even more, they can accomplish this while physically separate, due to the nonlocal properties of quantum mechanics. Indeed, nearly all quantum optics experiments rely on this separation, using individual point detectors that are scanned to measure coincidence counts and correlations. Scanning, however, is tedious, time consuming, and ill-suited for imaging. Moreover, the separation of beam paths adds complexity to the system while reducing the number of photons available for sampling, and the multiplicity of detectors does not scale well for greater numbers of photons and higher orders of entanglement. We bypass all of these problems here by directly imaging collinear photon pairs with an electron-multiplying CCD camera. We show explicitly the benefits of quantum nonlocality by engineering the spatial entanglement of the illuminating photons and introduce a new method of correlation measurement by converting time-domain coincidence counting into spatial-domain detection of selected pixels. We show that classical transport-of-intensity methods are applicable in the quantum domain and experimentally demonstrate nearly optimal (Heisenberg-limited) phase measurement for the given quantum illumination. The methods show the power of direct imaging and hold much potential for more general types of quantum information processing and control.