We present a theoretical model for describing the interaction of an electron, weakly bound in a short-range potential, with an intense, few-cycle laser pulse. General definitions for the differential probability of above-threshold ionization and for the yield of high-order-harmonic generation (HHG) are presented. For HHG we then derive detailed analytic expressions for the spectral density of generated radiation in terms of the key laser parameters, including the number $N$ of optical cycles in the pulse and the carrier-envelope phase (CEP). In particular, in the tunneling approximation, we provide detailed derivations of the closed-form formulas presented briefly by M. V. Frolov et al. [ Phys. Rev. A 83, 021405(R) (2011)], which were used to describe key features of HHG by both H and Xe atom targets in an intense, few-cycle laser pulse. We then provide a complete analysis of the dependence of the HHG spectrum on both $N$ and the CEP $\phi$ of an $N$-cycle laser pulse. Most importantly, we show analytically that the structure of the HHG spectrum stems from interference between electron wave packets originating from electron ionization from neighboring half-cycles near the peak of the intensity envelope of the few-cycle laser pulse. Such interference is shown to be very sensitive to the CEP. The usual HHG spectrum for a monochromatic driving laser field (comprising harmonic peaks at odd multiples of the carrier frequency and spaced by twice the carrier frequency) is shown analytically to occur only in the limit of very large $N$, and begins to form, as $N$ increases, in the energy region beyond the HHG plateau cutoff.

We study control of high-order harmonic generation (HHG) driven by time-delayed, few-cycle $\omega$ and $2\omega$ counterrotating mid-IR pulses. Our numerical and analytical study shows that the time delay between the two-color pulses allows control of the harmonic positions, both those allowed by angular momentum conservation and those seemingly forbidden by it. Moreover, the helicity of any particular harmonic is tunable from left to right circular without changing the driving pulse helicity. The highest HHG yield occurs for a time delay comparable to the fundamental period $T=2\pi /\omega$.

The time-dependent effective-range (TDER) theory introduced by Frolov et al. [Phys. Rev. Lett. 91, 053003 (2003)] and used in numerous applications for processes involving a linearly polarized intense laser field is presented in detail for the general problem of an electron, initially bound in a short-range potential, interacting with a laser field of arbitrary polarization. The TDER theory combines the well-known effective-range theory for a weakly bound electron in a short-range potential with the quasistationary, quasienergy state (QQES) or Floquet formulation for an electron interacting with a harmonic, time-dependent field, such as a monochromatic laser field. We present the basic underlying assumptions, the relevant boundary conditions, and the key equations for both the quasienergy $ϵ$ of the system and its associated, three-dimensional, time-dependent wave function ${\Phi }_{ϵ}(\mathbf{r},t)$. The specific equations appropriate for two initial state symmetries (i.e., $s$- or $p$-valence electrons) and for three cases of laser field polarization (linear, circular, and elliptical) are derived and discussed. Results of the formulation are presented for the specific case of the Stark shift (and level splitting, in the case of an initially degenerate $p$ state) and detachment rates for ${\mathrm{H}}^{-}$, ${\mathrm{O}}^{-}$, the negative alkali-metal ions, and the negative halogen ions.

We present exact ab initio quantum results for harmonic generation (HG) by a weakly bound electron interacting with a strong monochromatic laser field. The analytic structure of the HG amplitude resulting from the multiphoton detachment thresholds is demonstrated. Our numerical results show that the HG spectrum is sensitive primarily to the distance in energy from the thresholds, thereby opening new possibilities for control of HG.

An analytic description for the yield, $\mathcal{P}(\mathbf{p})$, of high-energy electrons ionized from an atom by a short (few-cycle) laser pulse is obtained quantum mechanically. Factorization of $\mathcal{P}(\mathbf{p})$ in terms of an electron wave packet and the cross section for elastic electron scattering (EES) is shown to occur only for an ultrashort pulse, while in general $\mathcal{P}(\mathbf{p})$ involves interference of EES amplitudes with laser-field-dependent momenta. The analytic predictions agree well with accurate numerical results.

An ab initio parametrization of the two-photon double ionization amplitude from an $s^2$ subshell of an atom in a ${}^{1}S$ state is presented and used to predict two light polarization effects on photoelectron angular distributions that do not exist in single-photon double ionization: (i) elliptic dichroism and (ii) circular dichroism at equal energy sharing. Estimates for He show large magnitudes for these effects, which provide a means for polarization control of double ionization by vacuum ultraviolet light.