A quantitative comparison of amplitude versus intensity interferometry for astronomy - Bojer, Manuel; Huang, Zixin; Karl, Sebastian; Richter, Stefan; Kok, Pieter; von Zanthier, Joachim (New Journal of Physics, 2022)
Astronomical imaging can be broadly classified into two types. The first type is amplitude interferometry, which includes conventional optical telescopes and very large baseline interferometry (VLBI). The second type is intensity interferometry, which relies on Hanbury Brown and Twiss-type measurements. At optical frequencies, where direct phase measurements are impossible, amplitude interferometry has an effective numerical aperture that is limited by the distance from which photons can coherently interfere. Intensity interferometry, on the other hand, correlates only photon fluxes and can thus support much larger numerical apertures, but suffers from a reduced signal due to the low average photon number per mode in thermal light. It has hitherto not been clear which method is superior under realistic conditions. Here, we give a comparative analysis of the performance of amplitude and intensity interferometry, and we relate this to the fundamental resolution limit that can be achieved in any physical measurement. Using the benchmark problem of determining the separation between two distant thermal point sources, e.g., two adjacent stars, we give a short tutorial on optimal estimation theory and apply it to stellar interferometry. We find that for very small angular separations the large baseline achievable in intensity interferometry can more than compensate for the reduced signal strength. We also explore options for practical implementations of very large baseline intensity interferometry (VLBII).
CRIS-Team WoS Importer:2022-04-29

Collective photon emission of two correlated atoms in free space - Richter, Stefan; Wolf, Sebastian; von Zanthier, Joachim; Schmidt-Kaler, Ferdinand (Physical Review Research, 2023)
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.
CRIS-Team WoS Importer:2023-04-07

Comparing different approaches for stellar intensity interferometry - Karl, Sebastian; Zmija, Andreas; Richter, Stefan; Vogel, Naomi; Malyshev, Dmitry; Zink, Adrian; Michel, Thilo; Anton, Gisela; von Zanthier, Joachim; Funk, Stefan (Monthly Notices of the Royal Astronomical Society, 2022)
Stellar intensity interferometers correlate photons within their coherence time and could overcome the baseline limitations of existing amplitude interferometers. Intensity interferometers do not rely on phase coherence of the optical elements and thus function without high-grade optics and light combining delay lines. However, the coherence time of starlight observed with realistic optical filter bandwidths (> 0.1 nm) is usually much smaller than the time resolution of the detection system (> 10 ps), resulting in a greatly reduced correlation signal. Reaching high signal-to-noise ratio in a reasonably short measurement time can be achieved in different ways: either by increasing the time resolution, which increases the correlation signal height, or by increasing the photon rate, which decreases statistical uncertainties of the measurement. We present laboratory measurements employing both approaches and directly compare them in terms of signal-to-noise ratio. A high-time-resolution interferometry setup designed for small-to-intermediate-sized optical telescopes and thus lower photon rates (diameters < some metres) is compared to a setup capable of measuring high photon rates, which is planned to be installed at Cherenkov telescopes with dish diameters of > 10 m. We use a xenon lamp as a common light source simulating starlight. Both setups measure the expected correlation signal and work at the expected shot-noise limit of statistical uncertainties for measurement times between 10 min and 23 h. We discuss the quantitative differences in the measurement results and give an overview of suitable operation regimes for each of the interferometer concepts.
CRIS-Team WoS Importer:2022-04-08
Keywords: instrumentation: high angular resolution; instrumentation: interferometers; telescopes; stars: imaging

Imaging Trapped Ion Structures via Fluorescence Cross-Correlation Detection - Richter, Stefan; Wolf, Sebastian; von Zanthier, Joachim; Schmidt-Kaler, Ferdinand (Physical Review Letters, 2021)
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 fspatial=1490±2stat±8syst 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.<br

Imaging via Correlation of X-Ray Fluorescence Photons - Trost, Fabian; Ayyer, Kartik; Prasciolu, Mauro; Fleckenstein, Holger; Barthelmess, Miriam; Yefanov, Oleksandr; Dresselhaus, J. Lukas; Li, Chufeng; Bait, Sasa; Carnis, Jerome; Wollweber, Tamme; Mall, Abhishek; et al. (Physical Review Letters, 2023)
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.
CRIS-Team Scopus Importer:2023-05-26

Light of Two Atoms in Free Space: Bunching or Antibunching? - Wolf, Sebastian; Richter, Stefan; von Zanthier, Joachim; Schmidt-Kaler, Ferdinand (Physical Review Letters, 2020)
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))(tau) 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.
CRIS-Team WoS Importer:2020-02-28

Phase retrieval in incoherent diffractive imaging using higher-order photon correlation functions - Bojer, Manuel; Eckert, J.; Karl, Sebastian; Richter, Stefan; von Zanthier, Joachim (New Journal of Physics, 2024)
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.
CRIS-Team Scopus Importer:2024-06-21
Keywords: higher-order photon correlation functions; incoherent diffractive imaging; phase retrieval problem; x-ray structure analysis