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X-Ray Quantum Optics With Mössbauer Nuclei In Thin-Film Cavities

Kilian P. Heeg

Published Jan 1, 2014• 0 citations
Publisher

Abstract

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.

DOI
10.11588/heidok.00017869

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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.
A promising platform for the emerging field of x-ray quantum optics consists of M\"ossbauer nuclei embedded in thin-film cavities probed by near-resonant x-ray light, as used in a number of recent experiments. Here we develop a quantum optical framework for the description of experimentally relevant settings involving nuclei embedded in x-ray waveguides. We apply our formalism to two settings of current experimental interest based on the archetype M\"ossbauer isotope 57{}^{57}57Fe. For the present experimental conditions, we derive compact analytical expressions and show that the alignment of medium magnetization, as well as incident and detection polarization, enable the engineering of advanced quantum optical level schemes. The model encompasses nonlinear and quantum effects which could become accessible in future experiments.
This thesis is dedicated to the study of collective effects of nuclei in single xray photon superradiance. To this end we investigate aspects of superradiance in both nuclear forward scattering and in thin-film cavities with an embedded 57Fe nuclear layer. A general theoretical framework is developed to investigate a single-photon cooperative emission from a cloud of resonant systems, atoms or nuclei, in the presence of magnetic hyperfine splitting. In the limit of a thick sample, we present our results for two means to coherently control the collective single x-ray photon emission in nuclear forward scattering. In the limit of a thin sample in a thin-film cavity with embedded resonant nuclei, we find out that unlike the magnetic hyperfine splitting of a single atom or nucleus, interesting collective effects may occur which modify the hyperfine level structure. In addition, for a certain parameter regime a spectrum reminiscent of electromagnetically induced transparency (EIT) can be achieved. Based on this EIT-like effect, a theoretical control mechanism for stopping x-ray pulses in the thin-film x-ray cavity is put forward. Finally, we show theoretically that for the case of two nuclear ensembles in the thin-film cavity, pseudo-Rabi splitting due to the strong coupling between the two layers should occur. The latter findings are confirmed by preliminary experimental data.
Thin-film cavities containing layers of M\"ossbauer nuclei have been demonstrated to be a rich platform for x-ray quantum optics. At low excitation, these systems can be described by effective few-level schemes, thereby providing tunable artificial quantum systems at hard x-ray energies. With the recent advent of an ab initio theory, a numerically efficient description of these systems is now possible. On this basis, we introduce the inverse design and develop a comprehensive optimization for an archetypal system with a single resonant layer, corresponding to an artificial two-level scheme. We discover a number of qualitative insights into x-ray photonic environments for nuclei that will likely impact the design of future x-ray cavities and thereby improve their performance. The methods presented readily generalize beyond the two-level case and thus provide a clear perspective towards the inverse design of more advanced tunable x-ray quantum optical level schemes.
A control mechanism for stopping x-ray pulses in resonant nuclear media is investigated theoretically. We show that narrow-band x-ray pulses can be mapped and stored as nuclear coherence in a thin-film planar x-ray cavity with an embedded ^{57}Fe nuclear layer. The pulse is nearly resonant to the 14.4 keV Mössbauer transition in the ^{57}Fe nuclei. The role of the control field is played here by a hyperfine magnetic field which induces interference effects reminiscent of electromagnetically induced transparency. We show that, by switching off the control magnetic field, a narrow-band x-ray pulse can be completely stored in the cavity for approximately 100 ns. Additional manipulation of the external magnetic field can lead to both group velocity and phase control of the pulse in the x-ray cavity sample.
Abstract Mössbauer nuclei with quadrupole-split levels provide a versatile platform for exploring coherent x-ray light-matter interactions. We theoretically study ensembles of 57 Fe nuclei embedded in thin-film x-ray cavities, explicitly accounting for different orientations of the electric field gradient. By mapping isotropic electric field gradient distributions to an effective equal-weight two-transition model, we derive analytical expressions for the time-dependent reflectivity and reveal the emergence of cavity-mediated quantum beats. The oscillation frequency and temporal profile of these beats can be tuned via the cavity-induced coherent coupling, offering a flexible approach to control collective nuclear dynamics and manipulate nuclear coherence in the x-ray regime.
Ensembles of M\"ossbauer nuclei embedded in thin-film cavities form a promising platform for x-ray quantum optics. A key feature is that the joint nuclei-cavity system can be considered as an artificial x-ray multilevel scheme in the low-excitation regime. Using the cavity environment, the structure and parameters of such level schemes can be tailored beyond those offered by the bare nuclei. However, so far, the direct determination of a cavity structure providing a desired quantum optical functionality has remained an open challenge. Here we address this challenge using an inverse design methodology. As a first qualitative result, we show that the established fitting approach based on scattering observables in general is not unique, since the analysis may lead to different multilevel systems for the same cavity if based on observables in different scattering channels. Motivated by this, we distinguish between scattering signatures and the microscopic level scheme as separate design objectives, with the latter being uniquely determined by an ab initio approach. We find that both design objectives are of practical relevance and that they complement each other regarding potential applications. We demonstrate the inverse design for both objectives using example tasks, such as realizing electromagnetically induced transparency. Our results pave the way for future applications in nuclear quantum optics involving more complex x-ray cavity designs.