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Journal of Physics B Atomic Molecular and Optical Physics

Scaling properties of field ionization of Rydberg atoms in single-cycle THz pulses: 1D considerations

Hicham Agueny, M Chovancova, J. P. Hansen, L Kocbach

Published Nov 25, 2016• 8 citations
Publisher

Abstract

Abstract In recent experiments of single-cycle field ionization of excited Na( nd ) atoms with principal quantum number n ∈ [ 6 , 15 ] (Li and Jones 2014 Phys. Rev. Lett. 112 143006 ) it was shown that the maximum field intensity necessary to ionize 10% of the atoms decreases with increasing n according to an n − 3 power law dependence. This scaling property at the same ionization probability was confirmed in classical trajectory Monte Carlo calculations. In this work we note that the scaling relation in the experiment is much more general, it is in fact valid for all ionization probabilities. When applied to the emitted electron energies it places a very wide distribution of electron momenta from different initial states onto a narrow range. These aspects are investigated in a one-dimensional model with a 3D hydrogen-like spectrum. Calculations confirm the general n − 3 scaling relation for the ionization probability and that this particular scaling of the kinetic emission spectrum puts the ejected electron momenta on a narrow common scale. The ionization mechanism itself is identified as quantum mechanical tunneling and the nature of the tunneling process is the direct origin of the scaling law.

DOI
10.1088/0953-4075/49/24/245002

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Abstract In recent experiments of single-cycle field ionization of excited Na( nd ) atoms with principal quantum number n ∈ [ 6 , 15 ] (Li and Jones 2014 Phys. Rev. Lett. 112 143006 ) it was shown that the maximum field intensity necessary to ionize 10% of the atoms decreases with increasing n according to an n − 3 power law dependence. This scaling property at the same ionization probability was confirmed in classical trajectory Monte Carlo calculations. In this work we note that the scaling relation in the experiment is much more general, it is in fact valid for all ionization probabilities. When applied to the emitted electron energies it places a very wide distribution of electron momenta from different initial states onto a narrow range. These aspects are investigated in a one-dimensional model with a 3D hydrogen-like spectrum. Calculations confirm the general n − 3 scaling relation for the ionization probability and that this particular scaling of the kinetic emission spectrum puts the ejected electron momenta on a narrow common scale. The ionization mechanism itself is identified as quantum mechanical tunneling and the nature of the tunneling process is the direct origin of the scaling law.
We study the ionization of Rydberg atoms in a single-cycle-pulse electric field based on both classical and quantum calculations. The ionization-probability curve exhibits a ``ripple'' structure as a function of the pulse duration and the field amplitude. These ripple structures are found to be dependent on the angular distribution of the initial state. A large electron-emission asymmetry is observed, and the ionized electron is almost completely emitted to one side of the atom except when the pulse length is roughly one Rydberg period. In both the long-pulse and the short-pulse regimes, larger electron energy can be expected from the ionization of lower-lying Rydberg states, matching the observation in a recent experiment [S. Li and R. R. Jones, Phys. Rev. Lett. 112, 143006 (2014)]. This trend is closely related to the electron-emission asymmetry associated with the field-direction change in a single-cycle pulse. The possible implications of the different energy transfer in a single-cycle pulse from that in a multicycle pulse are also discussed briefly for the strong-field ionization of the ground atomic state.
We study the field-ionization threshold behavior when a Rydberg atom is ionized by a short single-cycle pulse field. Both hydrogen and sodium atoms are considered. The required threshold field amplitude is found to scale inversely with the binding energy when the pulse duration becomes shorter than the classical Rydberg period, and, thus, more weakly bound electrons require larger fields for ionization. This threshold scaling behavior is confirmed by both three-dimensional classical trajectory Monte Carlo simulations and numerically solving the time-dependent Schr\"odinger equation. More surprisingly, the same scaling behavior in the short pulse limit is also followed by the ionization thresholds for much lower bound states, including the hydrogen ground state. An empirical formula is obtained from a simple model, and the dominant ionization mechanism is identified as a nonzero spatial displacement of the electron. This displacement ionization should be another important mechanism beyond the tunneling ionization and the multiphoton ionization. In addition, an ``ionization window'' is shown to exist for the ionization of Rydberg states, which may have potential applications to selectively modify and control the Rydberg-state population of atoms and molecules.
ization of Rydberg atoms by a single-cycle pulse, and also its implications for the strong field ionization of ground state. The required threshold field amplitude (for 10% ionization probability) scales inversely with the binding energy of initial states and also the pulse-duration square when the pulse duration becomes much shorter than the classical Rydberg period. A simple model is introduced to understand this threshold behavior, where the nonzero displacement induced by a single-cycle pulse plays a critical role. By combining with the adiabatic-ionization threshold in the low-frequency limit, an ionization window is expected for the ionization of different states. The ionization-probability curve exhibits a “ripple” structure as a function of the pulse duration and the field amplitude, which is sensitive to the angular distribution of initial states. The observation of larger emitted-electron energy for the ionization of lower-lying Rydberg states in a recent experiment [S Li and R. R. Jones, Phys. Rev. Lett. 112, 143006 (2014)] is confirmed in our calculations for both sodium and hydrogen atoms. The differences between the ionization dynamics in a single-cycle pulse and that in a multi-cycle pulse are also discussed and presented.
Recent attoclock experiments and theoretical studies regarding the strong-field ionization of atoms by few-cycle infrared pulses revealed features that have attracted much attention. Here we investigate tunneling ionization and the dynamics of the electron probability using Bohmian mechanics. We consider a one-dimensional problem to illustrate the underlying mechanisms of the ionization process. It is revealed that in the major part of the below-the-barrier ionization regime, in an intense and short infrared pulse, the electron does not tunnel through the entire barrier, but rather starts already from the classically forbidden region. Moreover, we highlight the correspondence between the probability of locating the electron at a particular initial position and its asymptotic momentum. Bohmian mechanics also provides a natural definition of mean tunneling time and exit position, taking account of the time dependence of the barrier. Finally, we find that the electron can exit the barrier with significant kinetic energy, thereby corroborating the results of a recent study [N. Camus et al., Phys. Rev. Lett. 119, 023201 (2017)].
Fully quantum and classical trajectory Monte Carlo calculations are performed for a Rydberg alkali-metal atom that is kicked by a pulsed electric field. The two calculations are compared to recent experimental results through the ionization probability versus peak field strength. The energy distributions of the final electrons are compared between the two calculations. There is a qualitative difference between the classical and quantum momentum distributions which is measurable in principle. An experiment to detect the time-dependent precession of the orbital angular momentum in Cs is also proposed.
The ionization of potassium np Rydberg atoms with n∼388n\sim388n∼388 by pulsed unidirectional electric fields, termed half-cycle pulses (HCPs), with various well-characterized shapes (rectangular, triangular, and sawtooth) and durations $T\sb{p}$ comparable to the classical electron orbital period $T\sb{n}$ is investigated. The experimental results are compared to classical trajectory Monte Carlo (CTMC) simulations and the classically-scaled results of quantum calculations undertaken at n=5.n=5.n=5. The data show that in the intermediate regime, $T\sb{p}\sim T\sb{n},$ the threshold field for ionization becomes sensitive to the shape and rise time of the HCP, increasing with increasing rise time. For each pulse shape, the agreement between the experimental measurements and both the CTMC and quantum calculations is very good.