Conventional spectroscopy uses classical light to detect matter properties through the variation of its response with frequencies or time delays. Quantum light opens up new avenues for spectroscopy by utilizing parameters of the quantum state of light as novel control knobs and through the variation of photon statistics by coupling to matter. This Roadmap article focuses on using quantum light as a powerful sensing and spectroscopic tool to reveal novel information about complex molecules that is not accessible by classical light. It aims at bridging the quantum optics and spectroscopy communities which normally have opposite goals: manipulating complex light states with simple matter e.g. qubits versus studying complex molecules with simple classical light, respectively. Articles cover advances in the generation and manipulation of state-of-the-art quantum light sources along with applications to sensing, spectroscopy, imaging and interferometry.

Measurements of the spatial and temporal coherence of single, femtosecond x-ray pulses generated by the first hard x-ray free-electron laser, the Linac Coherent Light Source, are presented. Single-shot measurements were performed at 780 eV x-ray photon energy using apertures containing double pinholes in “diffract-and-destroy” mode. We determined a coherence length of $17\mu \mathrm{m}$ in the vertical direction, which is approximately the size of the focused Linac Coherent Light Source beam in the same direction. The analysis of the diffraction patterns produced by the pinholes with the largest separation yields an estimate of the temporal coherence time of 0.55 fs. We find that the total degree of transverse coherence is 56% and that the x-ray pulses are adequately described by two transverse coherent modes in each direction. This leads us to the conclusion that 78% of the total power is contained in the dominant mode.

In a recent paper [P. Wochner et al., Proc. Natl. Acad. Sci. U.S.A. 106, 11511 (2009)] x-ray scattering intensity correlations around a ring, in the speckle diffraction pattern of a colloidal glass, were shown to display a remarkable $\sim${}cos(n$\varphi${}) dependence on the angular coordinate $\varphi${} around the ring, with integer index n depending on the magnitude of the scattering wave vector. With an analytical derivation that preserves full generality in the Fraunhofer diffraction limit, we clarify the relationship between this result and previous x-ray studies of bond-orientation order, and provide a sound basis to the statement that the angular intensity correlations deliver information on local bond arrangements in a disordered (or partially ordered) system. We present a detailed analysis of the angular cross-correlation function and show its applicability for studies of a wide range of structural properties of disordered systems, from local structure to spatial correlations between distant structural elements.

The emergence of high repetition-rate X-ray free-electron lasers (XFELs) powered by superconducting accelerator technology enables the measurement of significantly more experimental data per day than was previously possible. The European XFEL is expected to provide 27,000 pulses per second, over two orders of magnitude more than any other XFEL. The increased pulse rate is a key enabling factor for single-particle X-ray diffractive imaging, which relies on averaging the weak diffraction signal from single biological particles. Taking full advantage of this new capability requires that all experimental steps, from sample preparation and delivery to the acquisition of diffraction patterns, are compatible with the increased pulse repetition rate. Here, we show that single-particle imaging can be performed using X-ray pulses at megahertz repetition rates. The results obtained pave the way towards exploiting high repetition-rate X-ray free-electron lasers for single-particle imaging at their full repetition rate.

The experimental characterization of the spatial and temporal coherence properties of the free-electron laser in Hamburg (FLASH) at a wavelength of 8.0 nm is presented. Double pinhole diffraction patterns of single femtosecond pulses focused to a size of about 10×10 μm² were measured. A transverse coherence length of 6.2 ± 0.9 μm in the horizontal and 8.7 ± 1.0 μm in the vertical direction was determined from the most coherent pulses. Using a split and delay unit the coherence time of the pulses produced in the same operation conditions of FLASH was measured to be 1.75 ± 0.01 fs. From our experiment we estimated the degeneracy parameter of the FLASH beam to be on the order of 10¹⁰ to 10¹¹, which exceeds the values of this parameter at any other source in the same energy range by many orders of magnitude.

A general theoretical approach based on the decomposition of statistical fields into a sum of independently propagating transverse modes was used for the analysis of the coherence properties of the new free-electron laser source FLASH operated at 13.7 nm wavelength. The analysis shows that several transverse modes are contributing to the total radiation field of FLASH. The results of theoretical calculations are compared with measurements using Young’s double-slit experiment. The coherence lengths in the horizontal and in the vertical directions 20 m downstream from the source are estimated at 300 and $250\mu \mathrm{m}$, respectively.