Quantum imaging with incoherently scattered light from a free-electron laser

Abstract

The advent of accelerator-driven free-electron lasers (FEL) has opened new avenues for high-resolution structure determination via di raction methods that go far beyond conventional X-ray crystallography methods 1-10 . These techniques rely on coherent scattering processes that require the maintenance of first-order coherence of the radiation field throughout the imaging procedure. Here we show that higher-order degrees of coherence, displayed in the intensity correlations of incoherently scattered X-rays from an FEL, can be used to image two-dimensional objects with a spatial resolution close to or even below the Abbe limit. This constitutes a new approach towards structure determination based on incoherent processes 11,12 , including fluorescence emission or wavefront distortions, generally considered detrimental for imaging applications. Our method is an extension of the landmark intensity correlation measurements of Hanbury Brown and Twiss 13 to higher than second order, paving the way towards determination of structure and dynamics of matter in regimes where coherent imaging methods have intrinsic limitations 14 .The discovery by Hanbury Brown and Twiss of photon bunching of thermal light 15 and its application in astronomy to determine the angular diameter of stars by measuring spatial photon correlations 13 was a hallmark experiment for the development of modern quantum optics 16 . The subsequent quantum mechanical description of photon correlations by Glauber paved the way for a generalized concept of optical coherence 17 that is founded on the analysis of correlation functions of order m rather than the first-order coherence. For example, the spatial second-order photon correlation function g (2) (r 1 , r 2 ) expresses the probability to detect a photon at position r 1 given that a photon is recorded at position r 2 . In the case of two incoherent sources, g (2) (r 1 , r 2 ) displays a cosine modulation which oscillates at a spatial frequency depending on the source separation 18,19 . In this way interference fringes show up even in the complete absence of first-order coherence, allowing the extraction of structural information from incoherently emitting objects. This has been applied in Earth-bound stellar interferometry to measure the angular diameter of stars with 100-fold increased resolution 13 or to reveal the spatial and statistical properties of pulsed FEL sources 20,21 .Extending this concept to arbitrary arrangements of incoherently scattering emitters enables one to use intensity correlations for imaging applications. This has been demonstrated recently for one-dimensional arrays of emitters in the visible range of the spectrum [22][23][24] , where a spatial resolution even below the canonical Abbe limit has been achieved. Here we go still further and employ the method to image arbitrary two-dimensional incoherently scattering objects radiating in the vacuum ultraviolet. The extension from one dimension 24 to two dimensions is non-trivial and even unexpected in view of the tremendously enlarg...

Statistical properties of a free-electron laser revealed by Hanbury Brown–Twiss interferometry

“…This could lead to quantum optics experiments such as the exploration of nonclassical states of light [57], superresolution and quantum imaging experiments [58,59], or ghost imaging experiments [60,61] at the FEL sources. As it was shown in our work, by sufficient monochromatization, a single longitudinal mode of FEL radiation or Fourier limited pulses with high photon flux can be achieved.…”

Many-particle interference to test Born's rule

“…Recently, two groups have independently observed genuine three-photon interference that does not originate from two-or single-photon interference [24,25]. Many-particle interference is not only of interest from a fundamental point of view [21][22][23][24][25][26], but has also been exploited in imaging [27][28][29], metrology [30,31] and for quantum information processing [32,33]. Multi-boson interference in unitary networks has for instance been shown to be computationally hard, yielding the promising model of boson sampling [32].…”

Optimal Imaging of Remote Bodies Using Quantum Detectors

“…However, the retention of the spatial information seems to be restricted to highly symmetric sources [19], and it is an open question how we can optimally extract the spatial characteristics of arbitrary sources. Possible candidates include conventional telescopes, Hanbury Brown and Twiss interferometry [20,21], or estimating higher-order correlations in the far field [22][23][24].…”