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Practical Criterion for Single-Photon Entanglement at X-Ray Energies

Fabian Lauble

Published Aug 1, 2017• 0 citations
OpenAlex

Abstract

The generation and verification of entanglement is one of the big remaining challenges in x-ray quantum optics. We generalize a criterion for two-mode entanglement based on a Bell inequality, which was put forward by Johansen. We show that the experimentally simple criterion detects entanglement even for arbitrary losses behind the source. Furthermore, a beamsplitter of arbitrary reflectivity can be used to generate two-mode entanglement from a single-photon input. We investigate a range of other interesting input states and find that states similar to the single-photon state produce entanglement as well. The criterion thus provides a robust and practical benchmark for both theoretical and experimental work on single-photon entanglement. By applying a post-selection scheme, we demonstrate the importance of two-photon events in experiments, even for very low event rates. The criterion’s possible experimental implementation at x-ray energies, requiring only an interferometer and photodetectors, is discussed. We investigate Mössbauer nuclei in a thin-film cavity as an interferometer and derive a scheme to extract the first-order coherence g(1) from its Fano spectrum. Analyzing experimental data, we show that thin-film cavity systems are capable of sufficiently high coherence for the interferometry part of the criterion.

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•Jan 1, 2014•0 citations
The generation and verification of entanglement is one of the big remaining challenges in x-ray quantum optics. We generalize a criterion for two-mode entanglement based on a Bell inequality, which was put forward by Johansen. We show that the experimentally simple criterion detects entanglement even for arbitrary losses behind the source. Furthermore, a beamsplitter of arbitrary reflectivity can be used to generate two-mode entanglement from a single-photon input. We investigate a range of other interesting input states and find that states similar to the single-photon state produce entanglement as well. The criterion thus provides a robust and practical benchmark for both theoretical and experimental work on single-photon entanglement. By applying a post-selection scheme, we demonstrate the importance of two-photon events in experiments, even for very low event rates. The criterion’s possible experimental implementation at x-ray energies, requiring only an interferometer and photodetectors, is discussed. We investigate Mössbauer nuclei in a thin-film cavity as an interferometer and derive a scheme to extract the first-order coherence g(1) from its Fano spectrum. Analyzing experimental data, we show that thin-film cavity systems are capable of sufficiently high coherence for the interferometry part of the criterion.
A promising approach for direct detection of quantum entanglement in solid state materials is probing with entangled particles. X-rays are ideal for characterization of many materials but have not been generated as entangled pairs in useful numbers, even at the most powerful synchrotron sources. This proposal describes how x-rays in fully entangled N00N states (with N = 2) can be produced by applying Hong-Ou-Mandel interferometry at an x-ray synchrotron source. The technical requirements for indistinguishable photons, x-ray beamsplitters, and interferometer design are met with existing resources. The entangled x-ray biphotons can be filtered from the unavoidable single photon background by simple diffraction from an analyzer crystal, resulting in intense beams suitable for characterizing quantum materials.
Resonant inelastic X-ray scattering (RIXS) is conventionally used to probe elementary excitations and correlations in quantum materials. Here, we propose an interferometric RIXS protocol that instead creates entanglement between spatially separated regions of a solid-state material. An incident X-ray photon is coherently split by a beam splitter into two arms illuminating opposite ends of a sample. Recombining the scattered photons at a second beam splitter and detecting an energy-selected photon then projects the material into a coherent superposition of excitations at the two ends. This protocol is the X-ray, solid-state analogue of the Duan-Lukin-Cirac-Zoller (DLCZ) heralding scheme. Using a Kramers-Heisenberg formalism with quantized photon modes, we show that orthogonal and degenerate end excitations yield maximally entangled states. We illustrate this mechanism in three models: (1) two decoupled sites yield a heralded Bell state. (2) An open tight-binding chain exhibits reflection-parity-dependent interference, providing a benchmark for the interferometer's coherence. (3) A spin-1 Haldane (AKLT) chain yields an entangled pair of fractionalized edge spins. We also discuss practical considerations and challenges for realizing the protocol in X-ray experiments.
Entanglement, or quantum inseparability, is a crucial resource in quantum information applications, and therefore the experimental generation of separated yet entangled systems is of paramount importance. Experimental demonstrations of inseparability with light are not uncommon, but such demonstrations in physically well-separated massive systems, such as distinct gases of atoms, are new and present significant challenges and opportunities. Rigorous theoretical criteria are needed for demonstrating that given data are sufficient to confirm entanglement. Such criteria for experimental data have been derived for the case of continuous-variable systems obeying the Heisenberg-Weyl (position-momentum) commutator. To address the question of experimental verification more generally, we develop a sufficiency criterion for arbitrary states of two arbitrary systems. When applied to the recent study by Julsgaard, Kozhekin, and Polzik [Nature 413, 400 (2001)] of spin-state entanglement of two separate, macroscopic samples of atoms, our criterion confirms the presence of spin entanglement.
The problem of on-demand generation of entanglement between single-atom qubits via a common photonic channel is examined within the framework of optical interferometry. As expected, for a Mach-Zehnder interferometer with coherent laser beam as input, a high-finesse optical cavity is required to overcome sensitivity to spontaneous emission. We show, however, that with a twin-Fock input, useful entanglement can in principle be created without cavity enhancement. Both approaches require single-photon resolving detectors, and best results would be obtained by combining both cavity feedback and twin-Fock inputs. Such an approach may allow a fidelity of 0.99 using a two-photon input and currently available mirror and detector technology. In addition, we study interferometers based on NOON states, i.e., maximally entangled NNN-particle states, and show that they perform similarly to the twin-Fock states, yet without the need for high-precision photodetectors. The present interferometrical approach can serve as a universal, scalable circuit element for quantum information processing, from which fast quantum gates, deterministic teleportation, entanglement swapping, etc., can be realized with the aid of single-qubit operations.
Single photon sources can be used to generate and control highly non-classical states of light. Here, we consider the possibility of generating bi-partite entanglement between two separate multi-photon states by splitting the input modes of the single photon sources into a mode distributed to AAA and a mode distributed to BBB. If multiple photons are combined at AAA and at BBB, the large variety of photon patterns observed after linear optics transformations of the local multi-mode systems can be used to characterize the non-classical correlation of this entangled state. However, the transformation between different photon number states in linear optics is a complicated problem, and further analysis is needed to understand the possible applications of this scalable quantum system. To obtain maximal complementarity between two measurements, we consider the unbiased interference of all input modes represented by a discrete Fourier transform of the multi-mode field. We identify characteristic patterns that can be used to identify non-classical correlations between the two multi-photon systems at AAA and BBB and derive a quantitative criterion for entanglement verification. Our results indicate that the large scale quantum operations can be achieved by a comparatively simple quantum network interfering the outputs of multiple single photons, where the size of the system mainly depends on the number of available single photon sources.
In this thesis thin-film cavities with embedded Mössbauer nuclei probed by near-resonant x-ray light are studied from a quantum optical perspective. A theoretical framework is developed and compact expressions for the observables are derived for the linear excitation regime, which is encountered in current experiments. Even advanced cavity layouts can be modeled in excellent agreement with the results of previous experiments and semi-classical approaches. In the absence of magnetic hyperfine splitting, the spectral response of the system is found to be formed by tunable Fano profiles. An experimental implementation of this line shape control allows to extract spectroscopic signatures with high precision and to reconstruct the phase of the nuclear transition in good agreement with the theoretical predictions. The alignment of medium magnetization and polarization control of the x-rays enable to engineer advanced quantum optical level schemes, in which vacuum induced coherence effects are predicted and successfully demonstrated in an experiment. Furthermore, it is shown that group velocity control for x-ray pulses can be achieved in the cavity. A scheme for its observation is proposed and then employed to experimentally confirm sub-luminal x-ray propagation. Finally, non-linear effects, which could become accessible with future light sources, are explored and a non-linear line shape control mechanism is discussed.