A Lower Tunnel Among the peculiarities inherent in quantum mechanics is the ability of particles to tunnel through barriers that they lack the energy to surmount classically, as happens during radioactive decay. Strong laser fields can liberate electrons in this way from atoms and molecules. Akagi et al. (p. 1364 ) elegantly confirm that tunneling is not limited to the highest-energy electrons in a system by mapping the energy and momentum of both the ejected electron and positive ion produced when an intense laser pulse impinges on hydrogen chloride. When the molecule adopts specific orientations relative to the laser field, tunneling occurs from lower-lying states, as well as the highest-energy occupied orbital. This raises the possibility of tunneling microscopy capable of imaging the electronic structure of single molecules.

We apply the coupled dynamics of time-dependent density functional theory and Maxwell equations to the interaction of intense laser pulses with crystalline silicon. As a function of electromagnetic field intensity, we see several regions in the response. At the lowest intensities, the pulse is reflected and transmitted in accord with the dielectric response, and the characteristics of the energy deposition is consistent with two-photon absorption. The absorption process begins to deviate from that at laser intensities ∼ 10 13 W/cm 2 , where the energy deposited is of the order of 1 eV per atom. Changes in the reflectivity are seen as a function of intensity. When it passes a threshold of about 3 × 10 12 W/cm 2 , there is a small decrease. At higher intensities, above 2 × 10 13 W/cm 2 , the reflectivity increases strongly. This behavior can be understood qualitatively in a model treating the excited electron-hole pairs as a plasma.

We present a first-principles calculation for an optical dielectric breakdown in a diamond, which is induced by an intense laser field. We employ the time-dependent density-functional theory by solving the timedependent Kohn-Sham equation in real time and real space. For low intensities, the ionization agrees well with the Keldysh formula. The calculation shows a qualitative change of electron dynamics as the laser intensity increases, from dielectric screening at low intensities to optical breakdown at and above 7 ϫ 10 14 W / cm 2. Following the pulse, the electrons excited into the conduction band exhibit a coherent plasma oscillation that persists for tens of femtoseconds.

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We theoretically investigate the dynamical Franz-Keldysh effect in femtosecond time resolution, that is, the time-dependent modulation of a dielectric function at around the band gap under an irradiation of an intense laser field. We develop a pump-probe formalism in two distinct approaches: first-principles simulation based on real-time time-dependent density functional theory and analytic consideration of a simple two-band model. We find that, while time-average modulation can be reasonably described by the static Franz-Keldysh theory, a remarkable phase shift is found to appear between the dielectric response and the applied electric field.