TEMPUS, a Timepix4-based system for the event-based detection of X-rays.

TEMPUS is a new detector system being developed for photon science. It is based on the Timepix4 chip and, thus, it can be operated in two distinct modes: a photon-counting mode, which allows for conventional full-frame readout at rates up to 40 kfps; and an event-driven time-stamping mode, which allows excellent time resolution in the nanosecond regime in measurements with moderate X-ray flux. In this paper, the initial prototype, a single-chip device, is introduced, and the readout system described. Moreover, and in order to evaluate its capabilities, some tests were performed at PETRA III and ESRF for which results are also presented.

Speckle contrast of interfering fluorescence X-rays.

With the development of X-ray free-electron lasers (XFELs), producing pulses of femtosecond durations comparable with the coherence times of X-ray fluorescence, it has become possible to observe intensity-intensity correlations due to the interference of emission from independent atoms. This has been used to compare durations of X-ray pulses and to measure the size of a focusedX-ray beam, for example. Here it is shown that it is also possible to observe the interference of fluorescence photons through the measurement of the speckle contrast of angle-resolved fluorescence patterns. Speckle contrast is often used as a measure of the degree of coherence of the incident beam or the fluctuations of the illuminated sample as determined from X-ray diffraction patterns formed by elastic scattering, rather than from fluorescence patterns as addressed here. Commonly used approaches to estimate speckle contrast were found to suffer when applied to XFEL-generated fluorescence patterns due to low photon counts and a significant variation of the excitation pulse energy from shot to shot. A new method to reliably estimate speckle contrast under such conditions, using a weighting scheme, is introduced. The method is demonstrated by comparing the speckle contrast of fluorescence observed with pulses of 3 fs to 15 fs duration.

Imaging via Correlation of X-Ray Fluorescence Photons.

We demonstrate that x-ray fluorescence emission, which cannot maintain a stationary interference pattern, can be used to obtain images of structures by recording photon-photon correlations in the manner of the stellar intensity interferometry of Hanbury Brown and Twiss. This is achieved utilizing femtosecond-duration pulses of a hard x-ray free-electron laser to generate the emission in exposures comparable to the coherence time of the fluorescence. Iterative phasing of the photon correlation map generated a model-free real-space image of the structure of the emitters. Since fluorescence can dominate coherent scattering, this may enable imaging uncrystallised macromolecules.

Imaging Trapped Ion Structures via Fluorescence Cross-Correlation Detection.

Cross-correlation signals are recorded from fluorescence photons scattered in free space off a trapped ion structure. The analysis of the signal allows for unambiguously revealing the spatial frequency, thus the distance, as well as the spatial alignment of the ions. For the case of two ions we obtain from the cross-correlations a spatial frequency f_{spatial}=1490±2_{stat}±8_{syst} rad^{-1}, where the statistical uncertainty improves with the integrated number of correlation events as N^{-0.51±0.06}. We independently determine the spatial frequency to be 1494±11 rad^{-1}, proving excellent agreement. Expanding our method to the case of three ions, we demonstrate its functionality for two-dimensional arrays of emitters of indistinguishable photons, serving as a model system to yield structural information where direct imaging techniques fail.

Testing Higher-Order Quantum Interference with Many-Particle States.

Quantum theory permits interference between indistinguishable paths but, at the same time, restricts its order. Single-particle interference, for instance, is limited to the second order, that is, to pairs of single-particle paths. To date, all experimental efforts to search for higher-order interferences beyond those compatible with quantum mechanics have been based on such single-particle schemes. However, quantum physics is not bound to single-particle interference. We here experimentally study many-particle higher-order interference using a two-photon-five-slit setup. We observe nonzero two-particle interference up to fourth order, corresponding to the interference of two distinct two-particle paths. We further show that fifth-order interference is restricted to 10^{-3} in the intensity-correlation regime and to 10^{-2} in the photon-correlation regime, thus providing novel bounds on higher-order quantum interference.

Light of Two Atoms in Free Space: Bunching or Antibunching?

Photon statistics divides light sources into three different categories, characterized by bunched, antibunched, or uncorrelated photon arrival times. Single atoms, ions, molecules, or solid state emitters display antibunching of photons, while classical thermal sources exhibit photon bunching. Here we demonstrate a light source in free space, where the photon statistics depends on the direction of observation, undergoing a continuous crossover between photon bunching and antibunching. We employ two trapped ions, observe their fluorescence under continuous laser light excitation, and record spatially resolved the autocorrelation function g^{(2)}(τ) with a movable Hanbury Brown and Twiss detector. Varying the detector position we find a minimum value for antibunching, g^{(2)}(0)=0.60(5) and a maximum of g^{(2)}(0)=1.46(8) for bunching, demonstrating that this source radiates fundamentally different types of light alike. The observed variation of the autocorrelation function is understood in the Dicke model from which the observed maximum and minimum values can be modeled, taking independently measured experimental parameters into account.

Prime number decomposition using the Talbot effect.

We report on prime number decomposition by use of the Talbot effect, a well-known phenomenon in classical near field optics whose description is closely related to Gauss sums. The latter are a mathematical tool from number theory used to analyze the properties of prime numbers as well as to decompose composite numbers into their prime factors. We employ the well-established connection between the Talbot effect and Gauss sums to implement prime number decompositions with a novel approach, making use of the longitudinal intensity profile of the Talbot carpet. The new algorithm is experimentally verified and the limits of the approach are discussed.

Analysis of super-resolution via 3D structured illumination intensity correlation microscopy.

Intensity correlation microscopy (ICM), which is prominently known through antibunching microscopy or super-resolution optical fluctuation imaging (SOFI), provides super-resolution through a correlation analysis of antibunching of independent quantum emitters or temporal fluctuations of blinking fluorophores. For correlation order m the PSF in the signal is effectively taken to the mth power, and is thus directly shrunk by the factor m. Combined with deconvolution, a close to linear resolution improvement of factor m can be obtained. Yet, analysis of high correlation orders is challenging, which limits the achievable resolutions. Here we propose to use three dimensional structured illumination along with mth-order correlation analysis to obtain an enhanced scaling of up to m + m = 2m. Including the stokes shift or plasmonic sub-wavelength illumination enhancements beyond 2m can be achieved. Hence, resolutions far below the diffraction limit in full 3D imaging and with already low correlation orders, can potentially be achieved. Since ICM operates in the linear regime our approach may be particularly promising for enhancing the resolution in biological imaging at low illumination levels.

Photon statistics as an interference phenomenon.

Interference of light fields, first postulated by Young, is one of the fundamental pillars of physics. Dirac extended this observation to the quantum world by stating that each photon interferes only with itself. A precondition for interference to occur is that no welcher-weg information labels the paths the photon takes; otherwise, the interference vanishes. This remains true, even if two-photon interference is considered, e.g., in the Hong-Ou-Mandel-experiment. Here, the two photons interfere only if they are indistinguishable, e.g., in frequency, momentum, polarization, and time. Less known is the fact that two-photon interference and photon indistinguishability also determine the photon statistics in the overlapping light fields of two independent sources. As a consequence, measuring the photon statistics in the far field of two independent sources reveals the degree of indistinguishability of the emitted photons. In this Letter, we prove this statement in theory using a quantum mechanical treatment. We also demonstrate the outcome experimentally with a simple setup consisting of two statistically independent thermal light sources with adjustable polarizations. We find that the photon statistics vary indeed as a function of the polarization settings, the latter determining the degree of welcher-weg information of the photons emanating from the two sources.

Directional Dicke Subradiance with Nonclassical and Classical Light Sources.

We investigate Dicke subradiance of N≥2 distant quantum sources in free space, i.e., the spatial emission patterns of spontaneously radiating noninteracting multilevel atoms or multiphoton sources, prepared in totally antisymmetric states. We find that the radiated intensity is marked by a full suppression of spontaneous emission in particular directions. In resemblance to the analogous, yet inverted, superradiant emission profiles of N distant two-level atoms prepared in symmetric Dicke states, we call the corresponding emission patterns directional Dicke subradiance. We further derive that higher-order intensity correlations of the light emitted by statistically independent thermal light sources display the same directional Dicke subradiant behavior and show that it stems from the same interference phenomenon as in the case of quantum sources. We finally present measurements of directional Dicke subradiance for N=2,…,5 distant thermal light sources corroborating the theoretical findings.

Simulating the photon stream of a real thermal light source.

We present a computer algorithm capable of simulating the photon stream and the corresponding temporal photon statistics of thermal light sources. The algorithm implements realistic experimental conditions, incorporating the relevant parameters of the source as well as of the detection process. The code is verified by comparing the temporal photon autocorrelation function computed from the simulations to the one measured with a real thermal light source. In view of the renewed interest for intensity interferometry in astronomy and the life sciences, such simulations become increasingly relevant.

Incoherent Diffractive Imaging via Intensity Correlations of Hard X Rays.

Established x-ray diffraction methods allow for high-resolution structure determination of crystals, crystallized protein structures, or even single molecules. While these techniques rely on coherent scattering, incoherent processes like fluorescence emission-often the predominant scattering mechanism-are generally considered detrimental for imaging applications. Here, we show that intensity correlations of incoherently scattered x-ray radiation can be used to image the full 3D arrangement of the scattering atoms with significantly higher resolution compared to conventional coherent diffraction imaging and crystallography, including additional three-dimensional information in Fourier space for a single sample orientation. We present a number of properties of incoherent diffractive imaging that are conceptually superior to those of coherent methods.

Visibility of Young's Interference Fringes: Scattered Light from Small Ion Crystals.

We observe interference in the light scattered from trapped ^{40}Ca^{+} ion crystals. By varying the intensity of the excitation laser, we study the influence of elastic and inelastic scattering on the visibility of the fringe pattern and discriminate its effect from that of the ion temperature and wave-packet localization. In this way we determine the complex degree of coherence and the mutual coherence of light fields produced by individual atoms. We obtain interference fringes from crystals consisting of two, three, and four ions in a harmonic trap. Control of the trapping potential allows for the adjustment of the interatomic distances and thus the formation of linear arrays of atoms serving as a regular grating of microscopic scatterers.

Superresolving Imaging of Arbitrary One-Dimensional Arrays of Thermal Light Sources Using Multiphoton Interference.

We propose to use multiphoton interferences of photons emitted from statistically independent thermal light sources in combination with linear optical detection techniques to reconstruct, i.e., image, arbitrary source geometries in one dimension with subclassical resolution. The scheme is an extension of earlier work [S. Oppel et al., Phys. Rev. Lett. 109, 233603 (2012)], where N regularly spaced sources in one dimension were imaged by use of the Nth-order intensity correlation function. Here, we generalize the scheme to reconstruct any number of independent thermal light sources at arbitrary separations in one dimension, exploiting intensity correlation functions of order m≥3. We present experimental results confirming the imaging protocol and provide a rigorous mathematical proof for the obtained subclassical resolution.

Complete three photon Hong-Ou-Mandel interference at a three port device.

We report the possibility of completely destructive interference of three indistinguishable photons on a three port device providing a generalisation of the well known Hong-Ou-Mandel interference of two indistinguishable photons on a two port device. Our analysis is based on the underlying mathematical framework of SU(3) transformations rather than SU(2) transformations. We show the completely destructive three photon interference for a large range of parameters of the three port device and point out the physical origin of such interference in terms of the contributions from different quantum paths. As each output port can deliver zero to three photons the device generates higher dimensional entanglement. In particular, different forms of entangled states of qudits can be generated depending on the device parameters. Our system is different from a symmetric three port beam splitter which does not exhibit a three photon Hong-Ou-Mandel interference.

An Image-Based Prior Knowledge-Free Approach for a Multi-Material Decomposition in Photon-Counting Computed Tomography.

Photon-counting CT systems generally allow for acquiring multiple spectral datasets and thus for decomposing CT images into multiple materials. We introduce a prior knowledge-free deterministic material decomposition approach for quantifying three material concentrations on a commercial photon-counting CT system based on a single CT scan. We acquired two phantom measurement series: one to calibrate and one to test the algorithm. For evaluation, we used an anthropomorphic abdominal phantom with inserts of either aqueous iodine solution, aqueous tungsten solution, or water. Material CT numbers were predicted based on a polynomial in the following parameters: Water-equivalent object diameter, object center-to-isocenter distance, voxel-to-isocenter distance, voxel-to-object center distance, and X-ray tube current. The material decomposition was performed as a generalized least-squares estimation. The algorithm provided material maps of iodine, tungsten, and water with average estimation errors of 4% in the contrast agent maps and 1% in the water map with respect to the material concentrations in the inserts. The contrast-to-noise ratio in the iodine and tungsten map was 36% and 16% compared to the noise-minimal threshold image. We were able to decompose four spectral images into iodine, tungsten, and water.

Superbunching and Nonclassicality as new Hallmarks of Superradiance.

Superradiance, i.e., spontaneous emission of coherent radiation by an ensemble of two-level atoms in collective states introduced by Dicke in 1954, is one of the enigmatic problems of quantum optics. The startling gist is that even though the atoms have no dipole moment they radiate with increased intensity in particular directions. Following the advances in our understanding of superradiant emission by atoms in entangled W-states we examine the quantum statistical properties of superradiance. Such investigations require the system to have at least two excitations in order to explore the photon-photon correlations of the radiation emitted by such states. We present specifically results for the spatially resolved photon-photon correlations of systems prepared in doubly excited W-states and give conditions when the atomic system emits nonclassial light. Equally, we derive the conditions for the occurrence of bunching and even of superbunching, a rare phenomenon otherwise known only from nonclassical states of light like the squeezed vacuum. We finally investigate the photon-photon cross correlations of the spontaneously scattered light and highlight the nonclassicalty of such correlations. The theoretical findings can be implemented with current technology, e.g., using ions in a linear rf-trap, atoms in an optical lattice or quantum dots in a cavity.