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Physical Review A

Model for describing resonance-enhanced strong-field ionization with shaped ultrafast laser pulses

William D. M. Lunden, Péter Sándor, Thomas C. Weinacht, Tamás Rozgonyi

Published May 7, 2014• 18 citations
Publisher

Abstract

We present a simple model for calculating strong-field atomic and molecular ionization dominated by Freeman resonances. Our model combines multiphoton coupling between bound states, including dynamic Stark shifts, with coupling to a discretized continuum. The simplicity of the model allows us to interpret pulse-shape-dependent strong-field ionization yields and to demonstrate the relevance of strong-field atomic or molecular phase matching to ionization, as well as bound-state population transfer. Comparison with experimental measurements demonstrates that the calculations capture the essence of the pulse-shape-dependent ionization yields.

DOI
10.1103/physreva.89.053403

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We present a simple model for calculating strong-field atomic and molecular ionization dominated by Freeman resonances. Our model combines multiphoton coupling between bound states, including dynamic Stark shifts, with coupling to a discretized continuum. The simplicity of the model allows us to interpret pulse-shape-dependent strong-field ionization yields and to demonstrate the relevance of strong-field atomic or molecular phase matching to ionization, as well as bound-state population transfer. Comparison with experimental measurements demonstrates that the calculations capture the essence of the pulse-shape-dependent ionization yields.
We present results from a time-dependent two-level-plus-continuum model of multiphoton ionization in order to better understand the short-pulse photoelectron spectrum resulting from multiphoton ionization and the role of intermediate states. Both resonant and nonresonant population transfer to the upper state are found to play an important role in the multiphonon ionization process. The dynamic modeling reveals the potential for broadening and shifting peaks in the photoelectron spectrum. However, we conclude that despite the complex dynamics of the excitation, short-pulse photoelectron spectra can be used to measure ac Stark shifts of both ponderomotively and nonponderomotively shifted states in strong laser fields.
The energy levels of atoms and molecules exposed to intense, short, high-frequency laser pulses undergo time-dependent distortion known as dynamic Stark shift (DSS). These level shifts are induced by the coupling with nonresonant (nonessential) states and follow the temporal intensity profile of the laser pulse. Owing to the different DSSs of the individual atomic levels, transient resonance suppressions and enhancements significantly modify the multiphoton ionization pathway, leaving clear fingerprints (asymmetry, splitting, and shifting) in the energy spectrum of emitted photoelectrons. Here we investigate this phenomenon by solving the time-dependent Schr\"odinger equation of the valence electron of Na and Li in increasing levels of complexity: (i) developing minimal models for two-photon transition and (2+12+12+1)-photon ionization, (ii) applying a spectral method without continuum-continuum couplings, and (iii) propagating the electron wave packet on a large spatial grid accounting for all possible couplings. We show that appropriately detuned transform limited pulses provide a high level of control in strong-field excitation, when the atomic levels are dynamically shifted. Furthermore, we demonstrate the role of DSSs in the multipeak structure of the Autler-Townes doublet, found when several Rabi oscillations are induced during the strong-field resonant ionization.
We show that coherent control of multiphoton transitions is possible in the strong field limit, even in the presence of large dynamic Stark shifts. By tailoring the phase of an ultrafast laser pulse, one can compensate for the dynamic Stark shift during the atom-field interaction to achieve efficient population transfer in two-photon absorption. Numerical simulations for atomic sodium reveal efficient population transfer from the $\ensuremath{\mid}3s⟩$ ground state to the $\ensuremath{\mid}4s⟩$ excited state using an appropriately shaped ultrafast laser pulse. The theory and simulations provide insight into coherent control of more complicated multiphoton processes.
The coherent control of atomic energy level population is important for several areas physics and engineering including fluorescent spectroscopy, resonantly enhanced multiphoton ionization, harmonic generation, remote sensing and lasing. At low intensities where the Stark shift can be neglected, coherent control mechanisms usually exploit resonances created from stationary energy states dressed by integer multiples of the photon energy. However, in the strong field limit where large laser pulse intensities lead to significant Stark shifts, the resonant conditions are dynamic both in time and space and will likely not be satisfied for the entire laser pulse or beam.\n\nIn this research, we experimentally and theoretically demonstrate coherent control of atomic energy level population in sodium vapor as well as the selective excitation of sodium Rydberg levels using high intensity laser pulses. We also make a direct measurement of the ponderomotive shift of the continuum. While techniques based on resonance interferences and rapid adiabatic passage have been introduced for selective excitation, the conditions that must be satisfied for these phenomena can be hampered by short femtosecond pulse durations and large Stark shifts. In contrast, a technique referred to here as Resonance Sampling, uses the AC Stark shifts to selectively induce Freeman resonances and is resilient to changes in the spectral phase. Freeman resonances established in this way can result in population inversion of the excited state, and may lead to new lasing mediums and remote sensing applications.\n\n\nIn this research, we experimentally and theoretically demonstrate coherent control of atomic energy level population in sodium vapor as well as the selective excitation of sodium Rydberg levels using high intensity laser pulses. While techniques based on resonance interferences and rapid adiabatic passage have been introduced for selective excitation, the conditions that must be satisfied for these phenomena can be hampered by short femtosecond pulse durations and large Stark shifts. In contrast, a technique referred to here as Resonance Sampling, uses the AC Stark shifts to selectively induce Freeman resonances and is resilient to changes in the spectral phase. Freeman resonances established in this way can result in population inversion of the excited state, and may lead to new lasing mediums and remote sensing applications.
We present an exactly solvable two-level model with smoothly varying coupling, detuning, and loss functions. Whenever the common temporal profile of these parameter functions is analytically integrable, the complex population amplitudes are found for all times in simple analytic forms. This makes the model suitable for studying the population and phase dynamics of resonance-enhanced ionization processes. Incorporating two-photon Rabi frequency, dynamical Stark shifts, and one-photon ionization rate into this model, the 2 + 1 photon ionization of atomic lithium is studied as a showcase example. Finally, when the intensity profile of the laser pulse has the sine-squared shape, we find the exact analytic expression of the photoelectron spectrum, allowing additional insight into the structure of the Autler-Townes doublet.