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Physical Review A

Non-Markovian behavior of ultrafast coherent ionization dynamics in a crystal exposed to a seeded free-electron-laser pulse

A. Brand, Benjamin Kaiser, Alexei Vagov, V. M. Axt, U. Pietsch

Published Jun 5, 2014• 1 citation
Publisher

Abstract

We investigate the ionization dynamics of a crystal structure driven by ultrafast coherent x-ray pulses of moderate to high intensities for excitations where dipole-allowed, single-photon ionization dominates. Using a simple model of the crystal, we demonstrate that quantum coherences may already play an important role at moderate pulse intensities, leading to qualitatively novel features which cannot be described by rate equations. In particular, the ionization may exhibit a minimum as a function of the pulse duration, where the ionization drops to almost zero, although during the pulse a noticeable fraction of the electrons is promoted to unbound states. For higher intensities, the qualitative deviations between the coherent quantum-mechanical treatment and the rate description is even more pronounced. In particular, due to the presence of quantum-mechanical coherences, the full theory predicts, even for the single-photon transitions to a continuum of free-electron states, a Rabi-type behavior similar to what is known for two-level systems.

DOI
10.1103/physreva.89.063404

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We investigate the ionization dynamics of a crystal structure driven by ultrafast coherent x-ray pulses of moderate to high intensities for excitations where dipole-allowed, single-photon ionization dominates. Using a simple model of the crystal, we demonstrate that quantum coherences may already play an important role at moderate pulse intensities, leading to qualitatively novel features which cannot be described by rate equations. In particular, the ionization may exhibit a minimum as a function of the pulse duration, where the ionization drops to almost zero, although during the pulse a noticeable fraction of the electrons is promoted to unbound states. For higher intensities, the qualitative deviations between the coherent quantum-mechanical treatment and the rate description is even more pronounced. In particular, due to the presence of quantum-mechanical coherences, the full theory predicts, even for the single-photon transitions to a continuum of free-electron states, a Rabi-type behavior similar to what is known for two-level systems.
We develop a large scale quantum master equation approach to describe dynamical processes of practical open quantum systems driven by both coherent and stochastic interactions by including more than one thousand true states of the systems, motivated by the development of highly bright and fully coherent lasers in the X-ray wavelength regime. The method combines the processes of coherent dynamics induced by the X-ray laser and incoherent relaxations due to spontaneous emissions, Auger decays, and electronic collisions. As examples, theoretical investigation of {\it real} coherent dynamics of inner-shell electrons of a neon gas, irradiated by a high-intensity X-ray laser with a full temporal coherence, is carried out with the approach. In contrast to the rate equation treatment, we find that coherence can suppress the multiphoton absorptions of a neon gas in the ultra-intense X-ray pulse, due to coherence-induced Rabi oscillations and power broadening effects. We study the influence of coherence on ionization processes of neon, and directly prove that sequential single-photon processes for both outer- and inner-shell electrons dominate the ionizations for the recently typical experiments with a laser intensity of ≈1018\approx10^{18}≈1018 W/cm2{\rm W/cm^2}W/cm2. We discuss possible experimental implementations such as signatures for coherent evolution of inner-shell electrons via resonance fluorescence processes. The approach can also be applied to many different practical open quantum systems in atomic, quantum optical, and cold matter systems, which are treated qualitatively by a few-level master equation model before.
Both coherent pumping and energy relaxation play important roles in understanding physical processes of ultra-intense coherent light-matter interactions. Here, using a large-scale quantum master equation approach, we describe dynamical processes of practical open quantum systems driven by both coherent and stochastic interactions. As examples, two typical cases of light-matter interactions are studied. First, we investigate coherent dynamics of inner-shell electrons of a neon gas irradiated by a high-intensity X-ray laser along with vast number of decaying channels. In these single-photon dominated processes, we find that, due to coherence-induced Rabi oscillations and power broadening effects, the photon absorptions of a neon gas can be suppressed resulting in differences in ionization processes and final ion-stage distributions. Second, we take helium as an example of multiphoton and multichannel interference dominated electron dynamics, by investigating the transient absorption of an isolated attosecond pulse in the presence of a femtosecond infrared laser pulse.
We analyze theoretically the high intensity photoionization dynamics of a system with two atomic states resonantly coupled by coherent extreme ultraviolet laser radiation that also gives rise to the ionization. The ground state occupation of such a system is shown to exhibit damped Rabi oscillations. The corresponding ionization, which is responsible for the damping, scales almost linearly with the field intensity when the pulse length exceeds the Rabi period. For shorter pulses a quadratic scaling is found. The Rabi frequency is shifted compared to its value for an isolated two-level system. The shift increases with excitation intensity and can acquire a high percentage of the unrenormalized frequency at high intensities. Analytical results obtained within a simplified solvable model demonstrate that the damping and the shift both result from the coupling of the discrete states to the ionization continuum and are therefore closely related. Numerical simulations for a two-electron system reveal at high intensities the importance of off-resonant ionization channels.
The dynamics of neighboring states exposed to short intense laser pulses of carrier frequencies well above the ionization threshold of the system is investigated theoretically in the dipole approximation. It is shown that the ionizing pulse induces a time-dependent non-Hermitian coupling between these states determined by the Raman coupling and the direct ionization probability. This coupling induces quantum oscillations between the neighboring states while the strong pulse is on. The phenomenon opens the possibility to achieve a coherent control over the populations of neighboring states by short intense ionizing pulses. The present numerical results suggest exciting applications for free-electron lasers and attosecond experiments.
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.
Rabi oscillations are periodic modulations of populations in two-level systems interacting with a time-varying field. They are ubiquitous in physics with applications in different areas such as photonics, nano-electronics, electron microscopy, and quantum information. While the theory developed by Rabi was intended for fermions in gyrating magnetic fields, Autler and Townes realized that it could also be used to describe coherent light-matter interaction within the rotating wave approximation\cite. Although intense nanometer-wavelength light-sources have been available for more than a decade, Rabi dynamics at such short wavelengths have not been observed directly. Here we show that femtosecond extreme-ultraviolet pulses from a seeded free-electron laser can drive Rabi oscillations between the ground state and an excited state in helium atoms. The measured photoemission signal revealed an Autler-Townes doublet as well as an avoided crossing, phenomena that are both trademarks of quantum optics. Using theoretical analyses that go beyond the strong-field approximation, we found that the ultrafast build-up of the doublet structure follows from a quantum interference effect between resonant and non-resonant photoionization pathways. Given the recent availability of intense attosecond and few-femtosecond extreme-ultraviolet pulses, our results offer opportunities to carry out ultrafast manipulation of coherent processes at short wavelengths using free-electron lasers.