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Physical Review Letters

Multiphoton π Pulses

George N. Gibson

Published Dec 9, 2002• 41 citations
Publisher

Abstract

Multiphoton excitation in a two-level system is exceedingly weak because of small multiphoton coupling strengths, large ac Stark shifts, and ionization. I will discuss a three-level system in which the ac Stark shift is greatly reduced and the multiphoton coupling strength is greatly enhanced over a two-level system, to such an extent that multiphoton pi pulses can be produced. I will also present two-electron calculations in a model potential, including ionization that shows a 12-photon pi pulse driven with 800-nm photons. This three-level configuration may provide the basis for an amplifying medium in the vacuum ultraviolet, as well as multiphoton adiabatic passage and innershell ionization.

DOI
10.1103/physrevlett.89.263001

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Multiphoton excitation in a two-level system is exceedingly weak because of small multiphoton coupling strengths, large ac Stark shifts, and ionization. I will discuss a three-level system in which the ac Stark shift is greatly reduced and the multiphoton coupling strength is greatly enhanced over a two-level system, to such an extent that multiphoton pi pulses can be produced. I will also present two-electron calculations in a model potential, including ionization that shows a 12-photon pi pulse driven with 800-nm photons. This three-level configuration may provide the basis for an amplifying medium in the vacuum ultraviolet, as well as multiphoton adiabatic passage and innershell ionization.
Compared to single-photon rates, multiphoton excitation rates of atoms and molecules are generally quite small, even at high laser intensities, at least in a 2-level system. Small multiphoton coupling strengths, large ac Stark shifts, and ionization all inhibit real population transfer between bound states. However, it has recently been shown that a 3-level system consisting of a ground state and a pair of nearly degenerate strongly coupled upper states greatly enhances the multiphoton coupling with the ground state, while also greatly reducing the ac Stark shift of the ground state. In this paper I will derive an analytic expression for the n-photon Rabi frequency, for this system, in the case of degenerate upper states, as well as an expression for the level shifts induced in the case of nondegenerate upper states. Numerical calculations based on the 3-level system are presented to verify the analytic results and to show that high-order {pi} pulses can be driven at moderate field strengths. To demonstrate the feasibility of this process in a real physical system, I will present fully correlated 2-electron calculations in a model one-dimensional molecular potential, including ionization that show a 12-photon {pi} pulse driven with near-infrared photons. In other words, amore » single excited state 18.6 eV above the ground state can be populated with over 90% efficiency with little ionization while the ground state is almost completely depopulated. Besides the possibility of producing an amplifying medium in the vacuum ultraviolet, this 3-level configuration may open the door to other strong field effects previously restricted to single-photon interactions, such as adiabatic passage and inner-shell ionization.« less
Compared to single-photon rates, multiphoton excitation rates of atoms and molecules are generally quite small, even at high laser intensities, at least in a 2-level system. Small multiphoton coupling strengths, large ac Stark shifts, and ionization all inhibit real population transfer between bound states. However, it has recently been shown that a 3-level system consisting of a ground state and a pair of nearly degenerate strongly coupled upper states greatly enhances the multiphoton coupling with the ground state, while also greatly reducing the ac Stark shift of the ground state. In this paper I will derive an analytic expression for the n-photon Rabi frequency, for this system, in the case of degenerate upper states, as well as an expression for the level shifts induced in the case of nondegenerate upper states. Numerical calculations based on the 3-level system are presented to verify the analytic results and to show that high-order \ensuremath{\pi} pulses can be driven at moderate field strengths. To demonstrate the feasibility of this process in a real physical system, I will present fully correlated 2-electron calculations in a model one-dimensional molecular potential, including ionization that show a 12-photon \ensuremath{\pi} pulse driven with near-infrared photons. In other words, a single excited state 18.6 eV above the ground state can be populated with over 90% efficiency with little ionization while the ground state is almost completely depopulated. Besides the possibility of producing an amplifying medium in the vacuum ultraviolet, this 3-level configuration may open the door to other strong field effects previously restricted to single-photon interactions, such as adiabatic passage and inner-shell ionization.
Coherent interactions between light fields and simple quantum systems, such as $\ensuremath{\pi}$-pulses and adiabatic passage through frequency chirps and stimulated Raman interactions, generally use one- or two-photon processes. This limits the use of such interactions to energy scales close to the photon energy of the control field. However, recent calculations have shown that a 3-level system, generic to ionized diatomic molecules, shows such a strong multiphoton coupling that $\ensuremath{\pi}$-pulses are possible on at least 12-photon transitions. In this paper, we show that adiabatic transfer of population is also possible on such high-order multiphoton transitions. Full one-dimensional quantum mechanical two-electron calculations confirm this effect even in a system with many excited states and an ionization continuum.
Excitation of an atomic system subjected to a slowly varying external electromagnetic field is studied using a two-level model. Time evolution of the system is found using an approach which is nonperturbative in the field strength. There is no constraint to small values of the applied field, that is, the field (in appropriate energy units) need not be small compared to the difference in energies of the two levels. Rather, we use the fact that the situation of interest to us is where the frequency of the exciting field is small compared to the frequency associated with the level difference. Transition probabilities and resonance conditions are found which circumscribe both the large- and small-field limits. In the weak-field limit the previous results of high-order perturbation theory are readily recovered. For a monochromatic field the characteristic features of resonance excitation at high harmonic number of the applied field are (a) extremely narrow resonance widths and (b) shifts in resonance positions which are strong functions of field intensity. Because of this sensitivity, we are able to demonstrate that when slow temporal evolution of the field amplitude is taken into account (e.g., due to finite pulse duration) the appropriate mean excitation rate is that due to the uncorrelated contribution of many resonances. The results of this analysis are used to estimate excitation rates in a specific atomic system, Cd12+{\mathrm{Cd}}^{12+}Cd12+, which are then compared to multiphoton-ionization rates. Our calculations suggest that the ionization rate exceeds the excitation rate by several orders of magnitude.
We have made several different types of measurements of the three-photon ionization of Li produced by 3-ps laser pulses and describe the results using a Floquet picture. Over the photon frequency range 15 000 to 15 800 ${\mathrm{cm}}^{\mathrm{\ensuremath{-}}1}$, Li represents a strongly coupled three-state system with the 2s ground state coupled to the 2p and 3d states by one and two photons, respectively. Energy analysis of the photoelectrons allows the measurement of the intensity dependent shift of the 2s Floquet state during the laser pulse. The shift shows a strong frequency dependence that is not predicted by first-order perturbation theory. We have also measured the total ionization spectrum over several ranges of frequency, as well as the angular distribution of the ionization and the first above-threshold ionization peak for frequencies where the ground state is near resonance with the 4s and 4d excited states. Calculations based on the Floquet Hamiltonian indicate that all of these processes may be understood in terms of a Floquet description.