In recent years, light detection and ranging (LIDAR) has seen a steep rise in the sensitivity of measuring the distances of remote objects. Here, we propose to enhance the sensitivity of LIDAR even further by exploiting Dicke's concept of superradiance, i.e., the collective light emission of statistically independent light sources. By using N thermal light sources (TLS) and measuring intensity correlations of order m ≥ 2 instead of m=1, i.e., the intensity, we show that the Cramér-Rao bound on the measurement of the distance of a remote object undercuts that of traditional LIDAR by a factor of N, and can be reduced further with increasing correlation order m. Our numerical calculations are supported by analytical expressions for the special cases of two and three TLS and a general approximate expression for any number of TLS.

In this proceeding we present a high throughput single photon counting system able to detect at high photon count rates with the potential to enhance the effectiveness of stellar intensity interferometry (SII) measurements. The system consists of a photon detection module, PhotonPix (TM), and a time-tagging acquisition unit, LINTag, and enables nearly dead time free photon acquisition. PhotonPix (TM) is a sensor with an active area of 8 mm diameter, based on a microchannel plate (MCP) photomultiplier tube (PMT) supported by fast integrated electronics. A quantum efficiency (QE) of over 30% in the UV and visible is reachable at the desired wavelength by choosing a matching photocathode. Here we report temporal resolution measurements of the system at various count rates. We observe a resolution better than 40 ps full width at half maximum (FWHM) at count rates of up to 10 MHz with a marginal degradation down to 50 ps FWHM at 97 MHz detected rate. This combination of high temporal resolution, fast acquisition and large sensitive area, enables SII measurements with higher significance and/or on dimmer stars.

The axioms of quantum mechanics provide limited information regarding the structure of the Hilbert space, such as the underlying number system. The latter is generally regarded as complex, but generalizations of complex numbers, so-called hyper-complex numbers, cannot be ruled out in theory. Therefore, specialized experiments to test for hyper-complex quantum mechanics are needed. To date, experimental tests are limited to single-particle interference exploiting a closed phase relation in a three-path interferometer called the Peres test. The latter distinguishes complex quantum mechanics from quaternionic quantum mechanics. Here, we propose a general matrix formalism putting the Peres test on a solid mathematical ground. On this basis, we introduce multi-path and multi-particle interference tests, which provide a direct probe for any dimension of the number system of quantum mechanics.

We study collective light scattering from linear crystals with up to twelve $^{40}\text{Ca}^+$ ions, acting as coherent single photon emitters. Light-scattering is induced by two-photon laser excitation, starting from the S$_{1/2}$ to D$_{5/2}$ quadrupole transition at 729~nm in combination with laser excitation of the D$_{5/2}$ to P$_{3/2}$ dipole transition at 854~nm, followed by a decay back to S$_{1/2}$ via a single photon emission near 393~nm. The scattered intensity is recorded in the far field, featuring the interference of emitted light fields of the entire crystal. Furthermore, we demonstrate spin-dependent coherent scattering and unveil the time evolution of a previously encoded spin texture in a crystal employing the recorded dynamics of the spatial frequency components of the fringe pattern.

We investigate the photon statistics of an ensemble of coherently driven non-interacting two-level atoms in the weak driving regime. As it turns out, the system displays unique emission characteristics that are strongly in contrast to the emission of classical oscillating dipoles. By deriving the second-order autocorrelation function, we show that extraordinary two-photon correlations are obtained, ranging from strong antibunching to superbunching. These features are enhanced by disorder in the emitter positions, and the control parameter is the number of excitations in the system. We observe the appearance of bunching and antibunching when the light is scattered by the atoms predominantly coherently, i.e., mimicking classical Rayleigh scattering, whereas thermal photon statistics is obtained when the light is scattered via spontaneous decay, a well-known quantum effect. The underlying mechanism is the interplay between coherent scattering, which exhibits spatial fluctuations due to interference, and dissipation in the form of isotropic spontaneous decay.

Intensity interferometry is a reemerging astronomical technique for performing high angular resolution studies at visible wavelengths, benefiting immensely from the recent improvements in (single) photon detection instrumentation. We developed an ultra-fast, single photon counting and highly stable intensity interferometry instrument for 1 m class optical telescopes. The instrument records on sky the expected stellar photon rates and reaches the temporal coherence times as measured in the laboratory. In addition, all components, especially the photon detection hardware, of the instrument are easily upgradeable with custom hardware currently being developed. The collimated telescope output is spectrally filtered via an ultra narrow band pass of 2 nm at a central wavelength of 405 nm. We use hybrid photon detectors (HPDs) for single photon detection and a constant fraction discriminator (CFD) for signal conditioning. A time to digital converter (TDC) is used for time stamping. The combination of HPDs and CFDs is optimized for large active area and high timing resolution. We successfully measured photon bunching of three bright A-type stars - Vega, Altair and Deneb at the 1.04 m Omicron telescope of C2PU at the Calern Observatory in the south of France. In all cases the observed coherence time fits well to both the pre-calculated expectations as well as the values measured in preceding laboratory tests. We obtained the previously estimated photon count rates at the telescope and achieved highly stable coupling of the star light to the detectors. Utilizing a new class of large area single photon detectors based on multichannel plate amplification, high resolution spatial intensity interferometry experiments are within reach at 1 m diameter class telescopes within one night of observation time for bright stars.

We investigate two-electron interference in free space using two laser-triggered needle tips as independent electron sources, a fermionic realisation of the landmark Hanbury Brown and Twiss interferometer. We calculate the two-electron interference pattern in a quantum path formalism taking into account the fermionic nature and the spin configuration of the electrons. We also estimate the Coulomb repulsion in the setup in a semiclassical approach. We find that antibunching resulting from Pauli's exclusion principle and repulsion stemming from the Coulomb interaction can be clearly distinguished.

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.

Intensity interferometry is a re-emerging interferometry tool that alleviates some of the challenges of amplitude interferometry at the cost of reduced sensitivity. We demonstrate the feasibility of intensity interferometry with fast single photon counting detectors at small telescopes by utilising a telescope of diameter of merely $0.5$\,m. The entire measurement setup, including collimation, optical filtering, and two single photon detectors, is attached directly to the telescope without the use of optical fibres, facilitated by the large area of our single photon detectors. For digitisation and timing, we utilise a Time-To-Amplitude-Converter. Observing $\alpha$ Lyrae (Vega) for a total exposure time of $32.4$\,h over the course of six nights, an auto-correlation signal with a contrast of $(9.5 \pm 2.7) \times 10^-3$ and a coherence time of $(0.34 \pm 0.12)$ ps at a SNR of 2.8 is measured. The result fits well to preceding laboratory tests as well as expectations calculated from the optical and electronic characteristics of our measurement setup. This measurement, to our knowledge, constitutes the first time that a bunching signal with starlight was measured in the B band with single photon counting detectors. Simultaneously, this is to date the stellar intensity interferometry measurement utilising the smallest telescope. Our successful measurement shows that intensity interferometry can be adopted not only at large scale facilities, but also at readily available and inexpensive smaller telescopes.

We propose a quantum error mitigation scheme for single-qubit measurement errors, particularly suited for one-way quantum computation. Contrary to well established error mitigation methods for circuit-based quantum computation, that require to run the circuits several times, our method is capable of mitigating measurement errors in real-time, during the processing measurements of the one-way computation. For that, an ancillary qubit register is entangled with the to-be-measured qubit and additionally measured afterwards. By using a voting protocol on all measurement outcomes, occurring measurement errors can be mitigated in real-time while the one-way computation continues. We provide an analytical expression for the probability to detect a measurement error in dependency of the error rate and the number of ancilla qubits. From this, we derive an estimate of the ancilla register size for a given measurement error rate and a required success probability to detect a measurement error. Additionally, we also consider the CNOT gate error in our mitigation method and investigate how this influences the probability to detect a measurement error. Finally, we show in proof-of-principle simulations, also considering a hardware noise model, that our method is capable of reducing the measurement errors significantly in a one-way quantum computation with only a small number of ancilla qubits.

To obtain spatial information about an arbitrary atomic distribution in x-ray structure analysis, e.g., in molecules or proteins, the standard method is to measure the intensity in the far field, i.e., the first-order photon correlation function of the coherently scattered x-ray photons (coherent diffractive imaging). Recently, it was suggested to record alternatively the incoherently scattered photons and measure the second-order photon correlation function to reconstruct the geometry of the unknown atomic distribution (incoherent diffractive imaging). Yet, besides various advantages of the latter method, both techniques suffer from the so-called phase retrieval problem. Lately, an ab-initio phase retrieval algorithm to reconstruct the phase of the so-called structure factor of the scattering objects based on the third-order photon correlation function was reported. The algorithm makes use of the closure phase, which contains important, yet incomplete phase information, well-known from triple correlations and their bispectrum in speckle masking and astronomy applications. Here, we provide a detailed analysis of the underlying scheme and quantities in the context of x-ray structure analysis. In particular, we explicitly calculate for the first time the third-order photon correlation function for single photon emitters in a full quantum mechanical treatment and discuss the uniqueness of the closure phase equations constructed from. In this context, we recapitulate the sign problem of the closure phase and how it can be lifted using redundant information. We further show how the algorithm can be improved using even higher-order photon correlation functions produced by single photon emitters, e.g., the fourth-order correlation function, delivering new phase relations appearing in the four-point correlations.

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.

We propose an ansatz quantum circuit for the variational quantum eigensolver (VQE), suitable for exploring the phase structure of the multi-flavor Schwinger model in the presence of a chemical potential. Our ansatz is capable of incorporating relevant model symmetries via constrains on the parameters, and can be implemented on circuit-based as well as measurement-based quantum devices. We show via classical simulation of the VQE that our ansatz is able to capture the phase structure of the model, and can approximate the ground state to a high level of accuracy. Moreover, we perform proof-of-principle simulations on superconducting, gate-based quantum hardware. Our results show that our approach is suitable for current gate-based quantum devices, and can be readily implemented on measurement-based quantum devices once available.

By preparing two distant emitters in entangled Dicke states via detection of a single photon, the subsequent spatiotemporal photon emission is investigated. Depending on the parity of the established quantum state, emission patterns for the second scattered photon are observed featuring spatial superradiance as well as subradiance. We employ ultrafast single-photon resolving cameras with high spatial resolution disclosing the spatiotemporal emission characteristics. By recording the first photon in one direction and the second photon in another, revealing the spatial two-photon cross-correlation function g(2)(r1, r2), we characterize the collective spontaneous emission behavior of two ions in free space. We explain the observed contrast of g(2)(r1, r2) considering independently derived experimental parameters. Our results show how the detection of a single photon can profoundly modify the collective spontaneous emission dynamics of an atomic ensemble.

We propose a variational quantum eigensolver suitable for exploring the phase structure of the multi-flavor Schwinger model in the presence of a chemical potential. The parametric ansatz circuit we design is capable of incorporating the symmetries of the model, present in certain parameter regimes, which allows for reducing the number of variational parameters substantially. Moreover, the ansatz circuit can be implementated on both measurement-based and circuit-based quantum hardware. We numerically demonstrate that our ansatz circuit is able to capture the phase structure of the model and allows for faithfully approximating the ground state. Our results show that our approach is suitable for current intermediate-scale quantum hardware and can be readily implemented on existing quantum devices.

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.

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 focused X-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.

We give an overview of collective light scattering of trapped ion crystals serving as arrays of correlated emitters of single, indistinguishable photons into free space. The collectively emitted light is recorded in the far field by detectors, which feature high spatial and high temporal resolution. We observe interference in the first- and second-order photon correlation functions as well as bunched and antibunched photon statistics. We analyze theoretically how the observed features of collective light scattering off arrays of correlated single photon emitters result from projective quantum measurements into Dicke states.

Fully-excited two-level atoms separated by less than the transition wavelength cooperatively emit light in a short burst, a phenomenon called superradiance by R. Dicke in 1954. The burst is characterized by a maximum intensity scaling with the square of the number of atoms $N$ and a temporal width reduced by $N$ compared to the single atom spontaneous decay time. Both effects are usually attributed to a synchronization of the electric dipole moments of the atoms occurring during the process of light emission. Contrary to this explanation, it was recently shown by use of a quantum path description that the peak intensity results from the quantum correlations among the atoms when occupying symmetric Dicke states. Here we investigate from this perspective the temporal evolution of the ensemble, starting in the small sample limit, i.e., when the atoms have mutual separations much smaller than the transition wavelength $\lambda$ and pass down the ladder of symmetric Dicke states. In addition, we explore the temporal evolution for the case of non-interacting atoms with mutual separations much larger than $\lambda$. We show that in this case a similar superradiant burst of the emitted radiation is observed if the quantum correlations of the atoms are generated by conditional photon measurements retaining the atomic ensemble within or close to the symmetric subspace.

We study the collective spontaneous emission of three identical two-level atoms initially prepared in the excited states by measuring Glauber's third-order photon correlation function. Assuming two atoms at subwavelength distance from each other such that they are subject to the dipole-dipole interaction while the third one is located several wavelengths away, we observe super- and subradiant decay alike, depending on the direction of observation. Unlike the case where no remote atom is introduced or no conditional measurements are performed, the spontaneous emission behavior of the conditioned three-atom system is strongly modified, i.e., differing from the single-atom and the canonical two-atom configuration. The conditional measurements associated with the three-photon correlation function in combination with the dipole-dipole interaction between the adjacent atoms lead to quantum interference among the different decay channels allowing one to engineer the spontaneous emission in space and time.