Time dependence of Bragg forward scattering and self-seeding of hard x-ray free-electron lasers

Free-electron lasers (FELs) can now generate temporally short, high power x-ray pulses of unprecedented brightness, even though their longitudinal coherence is relatively poor. The longitudinal coherence can be potentially improved by employing narrow bandwidth x-ray crystal optics, in which case one must also understand how the crystal affects the field profile in time and space. We frame the dynamical theory of x-ray diffraction as a set of coupled waves in order to derive analytic expressions for the spatiotemporal response of Bragg scattering from temporally short incident pulses. We compute the profiles of both the reflected and forward scattered x-ray pulses, showing that the time delay of the wave $\tau$ is linked to its transverse spatial shift $\Delta x$ through the simple relationship $\Delta x = c\tau \cot\theta$, where $\theta$ is the grazing angle of incidence to the diffracting planes. Finally, we apply our findings to obtain an analytic description of Bragg forward scattering relevant to monochromatically seed hard x-ray FELs.Comment: 11 pages, 6 figure

Single-Photon Entanglement in the keV Regime via Coherent Control of Nuclear Forward Scattering

Generation of single-photon entanglement is discussed in nuclear forward scattering. Using successive switchings of the direction of the nuclear hyperfine magnetic field, the coherent scattering of photons on nuclei is controlled such that two signal pulses are generated out of one initial pump pulse. The two time-resolved correlated signal pulses have different polarizations and energy in the keV regime. Spatial separation of the entangled field modes and extraction of the signal from the background can be achieved with the help of state-of-the-art x-ray polarizers and piezoelectric fast steering mirrors.Comment: minor changes, updated to the final version; 4 pages, 2 figure

Coherent storage and phase modulation of single hard x-ray photons using nuclear excitons

Coherent storage and phase modulation of x-ray single-photon wave packets in resonant scattering of light off nuclei is investigated theoretically. We show that by switching off and on again the magnetic field in the nuclear sample, phase-sensitive storage of photons in the keV regime can be achieved. Corresponding $\pi$ phase modulation of the stored photon can be accomplished if the retrieving magnetic field is rotated by $180^{\circ}$. The development of such x-ray single-photon control techniques is a first step towards forwarding quantum optics and quantum information to shorter wavelengths and more compact photonic devices.Comment: 12 pages, 6 figures; v2 modified to match the published version, condensed to 4 figures, results unchange

Charge excitations associated with charge stripe order in the 214-type nickelate and superconducting cuprate

Charge excitations were studied for stipe-ordered 214 compounds, La$_{5/3}$Sr$_{1/3}$NiO$_{4}$ and 1/8-doped La$_{2}$(Ba, Sr)$_{x}$CuO$_{4}$ using resonant inelastic x-ray scattering in hard x-ray regime. We have observed charge excitations at the energy transfer of 1 eV with the momentum transfer corresponding to the charge stripe spatial period both for the diagonal (nikelate) and parallel (cuprates) stripes. These new excitations can be interpreted as a collective stripe excitation or charge excitonic mode to a stripe-related in-gap state.Comment: 5 pages, 4 figure

Nuclear forward scattering in particulate matter: dependence of lineshape on particle size distribution

In synchrotron Moessbauer spectroscopy, the nuclear exciton polariton manifests itself in the lineshape of the spectra of nuclear forward scattering (NFS) Fourier-transformed from time domain to frequency domain. This lineshape is generally described by the convolution of two intensity factors. One of them is Lorentzian related to free decay. We derived the expressions for the second factor related to Frenkel exciton polariton effects at propagation of synchrotron radiation in Moessbauer media. Parameters of this Frenkelian shape depend on the spatial configuration of Moessbauer media. In a layer of uniform thickness, this factor is found to be a simple hypergeometric function. Next, we consider the particles spread over a 2D surface or diluted in non-Moessbauer media to exclude an overlap of ray shadows by different particles. Deconvolving the purely polaritonic component of linewidths is suggested as a simple procedure sharpening the experimental NFS spectra in frequency domain. The lineshapes in these sharpened spectra are theoretically expressed via the parameters of the particle size distributions (PSD). Then, these parameters are determined through least-squares fitting of the line shapes.Comment: 13 pages, 12 figure