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New Journal of Physics

Photoionization of resonantly driven atomic states by an extreme ultraviolet-free-electron laser: intensity dependence and renormalization of Rabi frequencies

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

Published Sep 12, 2013• 9 citations
Publisher

Abstract

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.

DOI
10.1088/1367-2630/15/9/093016

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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 influence of ultrashort low-frequency laser pulses of different intensities and pulse lengths on the dynamics of a resonantly driven atomic system is investigated theoretically. We demonstrate the periodical dependence of the total ionization rate on the appearance time of a strong few-cycle laser pulse. By depleting the excited state, the intense short pulse not only resets the Rabi oscillations, but also introduces a time shift that is proportional to the pulse length. This time shift can be employed to determine the ultrashort pulse length. In the case of ultrashort pulses with lower intensities, we observe side-bands in the two-photon ionization spectrum, whose intensities vary periodically with the appearance time of the pulse. This can be utilized to measure the period of Rabi oscillations. We have developed an S-matrix theory of two-colour ionization which can explain some of the observations of our numerical calculations. Furthermore, we have studied the high harmonic generation spectra as well as the attosecond pulses generated from the high harmonics. We show that the Rabi oscillation can be used to alter the ionization rate within laser sub-cycles and therefore select different quantum trajectories in the high harmonics generation.
When an atom is driven by a laser field with a photon energy that is nearly resonant with an atomic transition, it can undergo periodic population transfers between the ground and excited state, known as Rabi oscillations [1], [2]. The aim of this work is to study photoionization from atoms for parameters accessible to a free-electron laser (FEL) [3]. Using time dependent perturbation theory to model photoionization from a Rabi oscillating atom, we have shown that in addition to the expected pathway of ionization from the excited state, non-resonant two-photon ionization will have a comparable amplitude at intensities on the order of 1013W/cm2[3].
The two-photon resonance ionization probability of atoms in strong extreme-ultraviolet free-electron laser (EUV FEL) pulses has been investigated by the model of time-dependent wave packet propagation of a light-coupled multilevel atom. Under the simulation within the model assuming single-mode FEL pulses, the ionization probability Pion{P}_{\mathrm{ion}}Pion​ has shown characteristic dependences on the scaled coupling parameter Ugi{U}_{gi}Ugi​ between two levels of the ground (ggg) and intermediate (iii) resonance states, namely, ${P}_{\mathrm{ion}}\ensuremath{\propto}{({U}_{gi})}^{n}$, with nnn being equal to \ensuremath{\sim}2, less than 1, and \ensuremath{\sim}1 for the small, medium, and large Ugi{U}_{gi}Ugi​ regimes, respectively. This power dependence of the ionization probability has been interpreted due to Rabi oscillations between ggg and iii states. To compare with recent experimental results on the same condition, the multimode nature of self-amplitude spontaneous emission (SASE) FEL pulses has been managed in the simulation. Then, the recent experimental laser-power dependence of the two-photon resonance ionization of He [Sato et al., J. Phys. B 44, 161001 (2011)] has been well described by that for the large Ugi{U}_{gi}Ugi​ regime of the simulation, i.e., nnn \ensuremath{\sim} 1. Thus, the observed linear laser-power dependence has been rationalized as being caused by the strong Rabi oscillations between the (2ppp)--(1sss) states.
Abstract Rabi oscillations are periodic modulations of populations in two-level systems interacting with a time-varying field1. They are ubiquitous in physics with applications in different areas such as photonics2, nano-electronics3, electron microscopy4 and quantum information5. 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 interactions within the rotating-wave approximation6. Although intense nanometre-wavelength light sources have been available for more than a decade7–9, Rabi dynamics at such short wavelengths has not been directly observed. Here we show that femtosecond extreme-ultraviolet pulses from a seeded free-electron laser10 can drive Rabi dynamics between the ground state and an excited state in helium atoms. The measured photoelectron signal reveals an Autler–Townes doublet and an avoided crossing, phenomena that are both fundamental to coherent atom–field interactions11. Using an analytical model derived from perturbation theory on top of the Rabi model, we find that the ultrafast build-up of the doublet structure carries the signature of a quantum interference effect between resonant and non-resonant photoionization pathways. Given the recent availability of intense attosecond12 and few-femtosecond13 extreme-ultraviolet pulses, our results unfold opportunities to carry out ultrafast manipulation of coherent processes at short wavelengths using free-electron lasers.
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.
We demonstrate Rabi oscillations in nonlinear ionization of argon by an intense femtosecond extreme ultraviolet (XUV) laser field produced by high-harmonic generation. We monitor the formation of Ar2+\mathrm{A}{\mathrm{r}}^{2+}Ar2+ as a function of the time delay between the XUV pulse and an additional near-infrared (NIR) femtosecond laser pulse, and show that the population of an Ar+∗\mathrm{A}{\mathrm{r}}^{+*}Ar+∗ intermediate resonance exhibits strong modulations both due to an NIR laser-induced Stark shift and XUV-induced Rabi cycling between the ground state of Ar+\mathrm{A}{\mathrm{r}}^{+}Ar+ and the Ar+∗\mathrm{A}{\mathrm{r}}^{+*}Ar+∗ excited state. Our experiment represents a direct experimental observation of a Rabi-cycling process in the XUV regime.