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arXiv:1501.04021 · Physical Review Letters

Carrier-Wave Rabi-Flopping Signatures in High-Order Harmonic Generation for Alkali Atoms

Marcelo F. Ciappina, José Antonio Pérez-Hernández, Alexandra S. Landsman, Tomáš Zimmermann, Maciej Lewenstein, L. Roso, Ferenc Krausz

Published Apr 8, 2015• 31 citations
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Abstract

We present a theoretical investigation of carrier-wave Rabi flopping in real atoms by employing numerical simulations of high-order harmonic generation (HHG) in alkali species. Given the short HHG cutoff, related to the low saturation intensity, we concentrate on the features of the third harmonic of sodium (Na) and potassium (K) atoms. For pulse areas of 2π and Na atoms, a characteristic unique peak appears, which, after analyzing the ground state population, we correlate with the conventional Rabi flopping. On the other hand, for larger pulse areas, carrier-wave Rabi flopping occurs, and is associated with a more complex structure in the third harmonic. These characteristics observed in K atoms indicate the breakdown of the area theorem, as was already demonstrated under similar circumstances in narrow band gap semiconductors.

DOI
10.1103/physrevlett.114.143902

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arXiv:2304.14617•Physical Review A•Aug 25, 2023•2 citations
We present a theoretical investigation of carrier-wave Rabi flopping in real atoms by employing numerical simulations of high-order harmonic generation (HHG) in alkali species. Given the short HHG cutoff, related to the low saturation intensity, we concentrate on the features of the third harmonic of sodium (Na) and potassium (K) atoms. For pulse areas of 2π and Na atoms, a characteristic unique peak appears, which, after analyzing the ground state population, we correlate with the conventional Rabi flopping. On the other hand, for larger pulse areas, carrier-wave Rabi flopping occurs, and is associated with a more complex structure in the third harmonic. These characteristics observed in K atoms indicate the breakdown of the area theorem, as was already demonstrated under similar circumstances in narrow band gap semiconductors.
We present theoretical investigations of carrier-wave Rabi flopping (CWRF) in real atoms by studying high-order harmonic generation in alkali species. We concentrate on the features of the third harmonic of Na and K atoms. For pulse areas of 2 π and Na atoms, a characteristic unique peak appears, which, after analyzing the ground state population, we correlate it with the conventional Rabi flopping. On the other hand, for larger pulse areas and K atoms, CWRF occurs, and it is associated with a more complex structure in the third harmonic. These new characteristics indicate the breakdown of the area theorem, as was already demonstrated in narrow band gap semiconductors.
Summary form only given. Illuminating a semiconductor with a constant light intensity can lead to a periodic oscillation of the inversion, a phenomenon which is known as Rabi flopping. Using pulsed excitation, Rabi flopping has been observed on semiconductors and exhibited periods in the range from 100 fs to 1 ps. Hughes (Phys. Rev. Lett. vol. 81, p. 3363, 1998) theoretically investigated the question of what happens when the light intensity becomes so high that the period of one Rabi oscillation becomes comparable with that of only one cycle of light, 2.7 fs for the band edge of GaAs, and predicted a new phenomenon: carrier-wave Rabi flopping. During a carrier-wave Rabi oscillation, the optical polarization becomes strongly distorted, which can lead to a double-peak structure (the Fourier-transform of the Rabi oscillation) in the third-harmonic (3/spl omega/) spectra. This characteristic shape is quite different from the well-known off-resonant third-harmonic generation. Importantly, resonant effects contain information on the dynamics of electronic resonances-potentially on the timescale of a single optical cycle. It is clear that, under these conditions, the usual envelope approximation breaks down, i.e. both the rotating wave approximation (RWA) as well as the slowly varying envelope approximation (SVEA) must not be used. This paper investigates carrier-wave Rabi flopping experimentally.
By solving Maxwell's curl equations coupled to a two-level atom, a theoretical study of carrier-wave Rabi flopping of femtosecond optical pulses of only several carrier-cycles time duration is reported. For pulse areas of $2\ensuremath{\pi}$, the usual self-induced transparency regime is essentially recovered. However, for larger pulse areas, carrier-wave Rabi flopping occurs that manifests in local carrier reshaping and subsequently to the production of significantly higher spectral components on the propagating pulse. These new features are not predicted by employing the area theorem or a slowly-varying-envelope approximation for the amplitude and phase terms---which is the usual approach.
We present a comprehensive theoretical and computational study on harmonic generation (HG) of Li atoms in one- and two-photon Rabi-flopping regimes where the population transfer from the ground 2s2s2s state to the excited 2p2p2p, 3s3s3s, and 3d3d3d states is substantial. Our all-electron approach is based on the time-dependent density-functional theory and takes into account the polarization of the core and the dynamic response of the electrons to the laser field. We show that the population oscillations in the time domain with the Rabi frequency $\mathrm{\ensuremath{\Omega}}$ are reflected in the fine structure of the HG spectra in the frequency domain on the scale of $2\mathrm{\ensuremath{\Omega}}$. Our results also manifest that even finer structures of the harmonic peaks on the smaller frequency scale originate from the pulse-shape-related interference effects. These features are clearly seen in one-photon Rabi-flopping regime between the 2s2s2s and 2p2p2p states. The pattern in the HG spectra becomes more complex in the two-photon Rabi-flopping regime involving 3s3s3s and 3d3d3d states. Our findings can be used for developing coherent control methods for HG in the Rabi-flopping regime.
Recently, a dependence of Rabi flopping on the carrier-envelope phase of the exciting laser pulses was predicted theoretically [Phys. Rev. Lett. 89, 127401 (2002)] for excitation of a thin semiconductor film with intense few-cycle pulses. Here, we report corresponding experiments on 50-100-nm thin GaAs films excited with 5-fs pulses. We find a dependence on the carrier-envelope phase arising from the interference of sidebands from the fundamental or the third-harmonic Mollow triplet, respectively, with surface second-harmonic generation.
High-order harmonic generation (HHG) is one of the most commonly studied nonlinear optical phenomena, originating in the ultrafast dynamics of electrons in atomic gases and semiconductors. It has attracted much attention because of its nonperturbative nature and potential for future attosecond laser pulse sources. On the theory side, a semiclassical picture based on tunneling ionization of electrons is successfully used in explaining key characteristics of the HHG. This model assumes that electric fields nonperturbatively excite electrons beyond the ionization potential or the band gap. Thus, intuitively, a larger gap should lead to an exponentially smaller HHG emission. Despite this intuition, the HHG in the Mott insulator Ca2RuO4{\mathrm{Ca}}_{2}{\mathrm{RuO}}_{4}Ca2​RuO4​ has shown an unconventional exponential increase with respect to the gap width. This experiment implies effects beyond the semiclassical theory. However, most theoretical works have focused on the dependence of the HHG on external control parameters, and the gap dependence of the HHG is poorly understood even in noninteracting systems. Thus, it is essential to clarify the gap dependence of the HHG in a fully quantum mechanical approach. Here, we analyze numerically exactly the gap dependence of the HHG in two-level systems. We find an increase in the strength of the HHG when the Rabi frequency is large compared to the gap width. Furthermore, the relaxation and scattering of electrons increase the visibility of this gap dependence. Finally, we find that the enhancement rate follows a universal scaling law regardless of the driving frequency. The existence of this gap dependence in two-level systems suggests that this unconventional gap dependence is a universal behavior that can be found not only in Mott insulators but also in atomic gases and semiconductors.