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arXiv:1411.1545 · Physical Review Letters

Interferometric phase detection at x-ray energies via Fano resonance control

Kilian P. Heeg, Christian Ott, D. Schumacher, Hans‐Christian Wille, Ralf Röhlsberger, Thomas Pfeifer, Jörg Evers

Published May 18, 2015• 85 citations
arXivHTMLPDF

Abstract

Modern x-ray light sources promise access to structure and dynamics of matter in largely unexplored spectral regions. However, the desired information is encoded in the light intensity and phase, whereas detectors register only the intensity. This phase problem is ubiquitous in crystallography and imaging and impedes the exploration of quantum effects at x-ray energies. Here, we demonstrate phase-sensitive measurements characterizing the quantum state of a nuclear two-level system at hard x-ray energies. The nuclei are initially prepared in a superposition state. Subsequently, the relative phase of this superposition is interferometrically reconstructed from the emitted x rays. Our results form a first step towards x-ray quantum state tomography and provide new avenues for structure determination and precision metrology via x-ray Fano interference.

DOI
10.1103/physrevlett.114.207401

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Modern x-ray light sources promise access to structure and dynamics of matter in largely unexplored spectral regions. However, the desired information is encoded in the light intensity and phase, whereas detectors register only the intensity. This phase problem is ubiquitous in crystallography and imaging and impedes the exploration of quantum effects at x-ray energies. Here, we demonstrate phase-sensitive measurements characterizing the quantum state of a nuclear two-level system at hard x-ray energies. The nuclei are initially prepared in a superposition state. Subsequently, the relative phase of this superposition is interferometrically reconstructed from the emitted x rays. Our results form a first step towards x-ray quantum state tomography and provide new avenues for structure determination and precision metrology via x-ray Fano interference.
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Double-slit interference experiments using monochromatic hard X-rays with the energy of 25 keV are presented. The experiments were performed at a synchrotron source with a distance of 110 m between the interferometer and the detector to produce an interference pattern with a sufficiently broad period that could be adequately sampled by a photon-counting detector with 75 micrometre pixels. In the single-particle version of the experiment, over one million image frames with a single registered photon in each one were collected. The sum of these frames showed a clear presence of the interference pattern with the expected period. Subsequent analysis provided an objective estimation of the minimal number of detected photons required to determine, in accordance with the Rose criterion, the presence of the photon interference. Apart from a general theoretical interest, these investigations were aimed at exploring the possibility of medical X-ray phase-contrast imaging in photon-counting regime at minimal radiation doses.
The field of quantum optics describes the interaction of electromagnetic radiation with matter whereby both are described quantum mechanically. So far the used frequencies of the radiation, were restricted to the operation range of lasers, which is between microwave to ultraviolet radiation. With the availability of new radiation sources such as sychrotrons, the field of X-ray quantum optics could be established. The high energy of the X-rays offer new possibilities, such as the examination of the interaction of radiation the nuclei of atoms. Unfortunately, X-ray source limitations still prohibit the direct transfer of control or detection schemes. One approach to overcome such limitations are mechanical motions of resonant absorber, which induces an additional phase at nuclear forward scattering. In this thesis the use of oscillating resonant absorber is examined theoretically. The phase offset of the oscillation offers an additional and controllable degree of freedom, which in uences the time and energy spectrum of a scattered wave packet. One problem occurring due to the high energy, is the lack of methods to measure the energy spectrum. To solve this problem, a new approach is developed, using the phase offset to measure the energy spectrum and the complex phase in the energy domain.
We propose a model for the quantum-state measurement via phase-sensitive amplification. The basic idea is to amplify the quantum state through a two-photon correlated-emission laser, such that there is no noise in the quadrature of interest and all the noise is fed into the conjugate quadrature. The noise-free quadrature is prepared in different phases and then corresponding quadrature distribution is measured. The Wigner function of the initial quantum state is then reconstructed by carrying out inverse Radon transformation familiar in tomographic imaging. This scheme allows us to avoid the deterioration of homodyne detection measurement due to the problem of detector efficiency.
Interferometric methods form the basis of highly sensitive measurement techniques from astronomy to bioimaging. Interferometry typically requires high stability between the measured and reference beams. The presence of rapid phase fluctuations washes out interference fringes, making phase profile recovery impossible. This challenge can be addressed by shortening the measurement time. However, such an approach reduces photon-counting rates, precluding applications in low-intensity imaging. We introduce a phase imaging technique which is immune to time-dependent phase fluctuations. Our technique, relying on intensity correlation instead of direct intensity measurements, allows one to obtain high interference visibility for arbitrarily long acquisition times. We prove the optimality of our method using the Cramér-Rao bound in the extreme case when no more than two photons are detected within the time window of phase stability. Our technique will broaden prospects in phase measurements, including emerging applications such as in infrared and x-ray imaging and quantum and matter-wave interferometry.