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Quantum control of x-ray spectra

Stefano M. Cavaletto

Published Jan 1, 2013• 1 citation
Publisher

Abstract

The direct and optical control of x-ray transitions is studied theoretically by investigating the spectra of resonance fluorescence and absorption. The work is motivated by the rapid advances in x-ray science, enabling the application of quantum-control schemes at short wavelengths. In a two-level system we study Rabi oscillations of atomic inner-shell electrons, induced by intense x-ray pulses and competing with Auger decay, and their signature in the spectrum of resonance fluorescence. Subsequently, optical manipulation of x-ray transitions is examined, by employing an optical frequency comb coupling nearby excited levels to control their spontaneous decay. First, narrow-bandwidth x rays are adopted, giving rise to the periodic shaping of the atomic dynamic variables and the imprinting of a comb onto the x-ray resonance fluorescence spectrum. A more realistic model for an immediate experimental implementation is then provided, by developing a scheme to imprint a comb onto the absorption spectrum of an ultrashort x-ray pulse. An experimental realization of the predicted comb structures is anticipated to transfer the accuracy of optical frequency combs into the x-ray regime

DOI
10.11588/heidok.00015982

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The direct and optical control of x-ray transitions is studied theoretically by investigating the spectra of resonance fluorescence and absorption. The work is motivated by the rapid advances in x-ray science, enabling the application of quantum-control schemes at short wavelengths. In a two-level system we study Rabi oscillations of atomic inner-shell electrons, induced by intense x-ray pulses and competing with Auger decay, and their signature in the spectrum of resonance fluorescence. Subsequently, optical manipulation of x-ray transitions is examined, by employing an optical frequency comb coupling nearby excited levels to control their spontaneous decay. First, narrow-bandwidth x rays are adopted, giving rise to the periodic shaping of the atomic dynamic variables and the imprinting of a comb onto the x-ray resonance fluorescence spectrum. A more realistic model for an immediate experimental implementation is then provided, by developing a scheme to imprint a comb onto the absorption spectrum of an ultrashort x-ray pulse. An experimental realization of the predicted comb structures is anticipated to transfer the accuracy of optical frequency combs into the x-ray regime
An x-ray pulse-shaping scheme is put forward for imprinting an optical frequency comb onto the radiation emitted on a driven x-ray transition, thus producing an x-ray frequency comb. A four-level system is used to describe the level structure of NNN ions driven by narrow-bandwidth x rays, an optical auxiliary laser, and an optical frequency comb. By including many-particle enhancement of the emitted resonance fluorescence, a spectrum is predicted consisting of equally spaced narrow lines which are centered on an x-ray transition energy and separated by the same tooth spacing as the driving optical frequency comb. Given an x-ray reference frequency, our comb could be employed to determine an unknown x-ray frequency. While relying on the quality of the light fields used to drive the ensemble of ions, the model has validity at energies from the 100 eV to the keV range.
The spectrum of resonance fluorescence is calculated for a two-level system excited by an intense, ultrashort x-ray pulse made available, for instance, by free-electron lasers such as the Linac Coherent Light Source. We allow for inner-shell hole decay widths and destruction of the system by further photoionization. This two-level description is employed to model neon cations strongly driven by x rays tuned to the $1s2{p}^{\ensuremath{-}1}\ensuremath{\rightarrow}1{s}^{\ensuremath{-}1}2p$ transition at 848eV848\phantom{\rule{0.28em}{0ex}}\phantom{\rule{0.16em}{0ex}}\mathrm{eV}848eV; the x rays induce Rabi oscillations which are so fast that they compete with Ne 1s1s1s-hole decay. We predict resonance fluorescence spectra for two different scenarios: first, chaotic pulses based on the self-amplified spontaneous emission principle, like those presently generated at x-ray free-electron-laser facilities and, second, Gaussian pulses which will become available in the foreseeable future with self-seeding techniques. As an example of the exciting opportunities derived from the use of seeding methods, we predict, in spite of the above obstacles, the possibility to distinguish at x-ray frequencies a clear signature of Rabi flopping in the spectrum of resonance fluorescence.
This thesis investigates quantum dynamics induced in atoms by ultrashort pulses of light. The work is motivated by recent developments in free-electron lasers, which generate ultrashort pulses of intense, coherent light and enable coherent control of quantum dynamics. We develop theoretical models to study the processes of absorption and emission in laser-atom interactions. Additionally, we study photoionisation, which creates an ion and an electron, and the entanglement that can be generated between these particles. Finally, we have investigated how the spontaneous decay of the ion induces entanglement transfer from the ion-electron pair to the electron-photon pair.This thesis compiles seven papers. Paper I investigates the absorption of light from an attosecond pulse by an atom in a prepared coherent superposition of states. We show how the evolution of the phase of the superposition wave packet influences the attosecond transient absorption spectra. Paper II predicts the existence of Mollow-like triplets in the absorption spectra of strongly coupled atoms. We establish the conditions for the pulse envelope under which this triplet pattern can be supported.Paper III studies two-photon Rabi oscillations, establishing which systems can sustain such dynamics. We find that a two-photon Rabi oscillating system can induce giant counter-rotating oscillations in the population dynamics, enabling investigations of physical effects beyond the rotating-wave approximation.Paper IV studies ionisation from an atom strongly coupled by a dichromatic field, where interference between the two frequency components shapes the temporal symmetry of the atomic dynamics, allowing for coherent control of the photoelectron distribution.Paper V considers an experiment performed at a Free-Electron Laser facility where a helium atom is ionised and the resulting ion is subsequently strongly coupled. The photoelectron spectra are theoretically reproduced and the entanglement between the ion and photoelectron is studied. Paper VI investigates how the entanglement in the ion--electron pair, generated via photoionisation followed by strong coupling, can be coherently controlled by harnessing the time symmetry of the pulse. We find that the observable manifestation of the entanglement can be altered in such a way that the electron energy becomes associated with the ionic state, allowing the entanglement to be detected via coincidence measurements. Paper VII investigates how quantum correlations between the ion and the electron can be coherently controlled by sequential strong coupling of the ion. We find that both the build-up of entanglement and its manifestation can be controlled, and we establish a quantitative measure of the amplitude entanglement that explains the dynamics in an intuitive way. Paper VIII studies the process of entanglement transfer induced by the spontaneous decay of the ion. We find that the ion--electron entanglement generated during the ultrashort interaction with the laser field is transferred to the electron--photon system over the much longer timescale of fluorescence.
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.
New generations of ultrashort and intense laser pulses as well ashigh power synchrotron radiation sources and x-ray free electronlasers have promoted fast developments in nonlinear optics andx-ray spectroscopy.The new experimental achievements and the appearance of varieties of novelnonlinear phenomena call for further development of theories. The objective of this thesis is to develop and apply thetheories to explain existing experimental data and to suggest new experiments. The first part of the thesis is devoted to nonlinear propagation of optical pulses. It is shown that the vibrational levels can be selectively populated by varying the duration, shape and intensity of the pump pulse. We obtained a strict analytical solution for the resonant two-photon interaction in a multilevel system beyond rotating wave approximation. Simulations show that the polarization anisotropy of the two-photon excitation affects strongly the anisotropy of photobleaching.The two-photon area theorem is reformulated with taking into account the dynamical Stark shift and the contribution from the permanent dipole moments. In general the dynamical Stark shift does not allow complete population of the excited state, but it can be compensated by detunings in atoms. A dynamical theory of the sequential two-photon absorption of microsecond pulses is developed to explore the role of transverse inhomogeneity of the light beam on optical limiting properties. The propagation of ultrashort laser pulses in nondipolar and dipolar media is investigated with special attention to the generation of superfluorescence and supercontinuum and the formation of attosecond pulses. The second part of the thesis addresses the interaction of molecules with x-ray radiation. We explore here the role of nuclear dynamics in resonant Auger scattering. Multimode simulations of the Auger spectra of ethylene molecule explain the main spectral features of the experimental spectra and show that the spectral profiles are formed mainly due to six vibrational modes. We predict the Doppler splitting of the atomic peak in resonant Auger scattering from SF6 molecule for circularly polarized x-rays. This effect is confirmed by the recent experiment. A new scheme of x-ray pump-probe spectroscopy, namely, resonant inelastic x-ray scattering accompanied by core-hole hopping induced by strong laser fields is suggested. The laser-induced promotion of core holes opens the symmetry forbidden scattering channels and gives rise to new spectral lines in the x-ray scattering spectrum. The strength of the symmetry forbidden lines becomes strong when the time of Rabi flopping is shorter than the lifetime of the core-excited state. We study the role of propagation of femtosecond x-ray free-electron pulses on the Auger process. Simulations show that there exists a strong competition between Auger decay and stimulated emission. The Auger yield and Auger branching ratio are strongly suppressed in the course of pulse propagation.
Direct frequency-comb spectroscopy is a technique that employs a train of well-stabilized ultrashort pulses to study the spectral properties of atomic or molecular systems. In this way, it opens the possibility of incorporating various coherent-control techniques for such spectral investigations. Here we introduce a theory for the interaction of a multilevel atom with such pulse trains, which is general enough to take into account an arbitrarily shaped frequency comb. We illustrate its application by studying the interaction of 87Rb^{87}\text{R}\text{b}87Rb atoms with trains of pulses of various shapes, resonant with the $5S\text{\ensuremath{-}}5D$ two-photon transition of rubidium. More specifically, we treat the interaction with hyperbolic-secant pulses, chirped pulses, and 0-$\ensuremath{\pi}$ pulses, respectively. The theory is designed to work at an arbitrary perturbation order. For the results presented here, we mostly used a 12th-order perturbation series at the pulse's electric field. Due to the large number of levels involved, such modeling may be quite complex computationally, and an important point of the present work is then to introduce the required numerical approach to treat this problem efficiently.