Preparing attosecond coherences by strong-field ionization

Strong-field ionization (SFI) has been shown to prepare wave packets with few-femtosecond periods. Here, we explore whether this technique can be extended to the attosecond time scale. We introduce an intuitive model, which is based on the Fourier transform of the subcycle SFI rate, for predicting the bandwidth of ionic states that can be coherently prepared by SFI. The coherent bandwidth decreases considerably with increasing central wavelength of the ionizing pulse but it is much less sensitive to its intensity. Many-body calculations based on time-dependent configuration-interaction singles support these results. The influence of channel interactions and laser-induced dynamics within the ion is discussed. Our results further predict that multicycle femtosecond pulses can coherently prepare subfemtosecond wave packets with higher selectivity and versatility compared to single-cycle pulses with an additional sensitivity to the mutual parity of the prepared states.

Figure 1

(a) Electric field of a 6.3 fs pulse centered at 800 nm and nonadiabatic SFI rate for a peak intensity of ${10}^{14} \mathrm{W}/{\mathrm{cm}}^2$, ionization energy of 12.1 eV, and angular momentum quantum numbers $\ell =1$ and $m=0$. (b) Fourier-transform amplitude of the full SFI rate (solid blue line) or the SFI rate restricted to the window shown in (a) (green dashed line). The dotted blue line shows the degree of coherence $C$ between the ground state and an excited state with $I_p=12.1\text{eV}+\mathrm{\Delta }E$ as a function of $\mathrm{\Delta }E$, calculated according to Eqs. (3) and (4).

Figure 2

Level structure of the artificial xenon atom used in the TDCIS calculations to represent the case of initial states of the (a) same parity and (b) opposite parities.

Figure 3

Coherence between two ionic states prepared by SFI with the same (a) or opposite [(b),(c)] parities as a function of their separation $\mathrm{\Delta }E$. The states in (a) are the $5p_{1/2}^{-1}$ and $5p_{3/2}^{-1}$ of ${\mathrm{Xe}}^{+}$ ($m_J=1/2$), and in (b) the states $5s^{-1}$ and $5p_0^{-1}$ with spin-orbit interactions turned off. Results are shown for TDCIS (solid red) and Eq. (4) using nonadiabatic tunneling rates [26] (dotted blue). (c) same as (b) comparing the full TDCIS calculation with the result obtained by setting the $5s^{-1}\leftrightarrow 5p_0^{-1}$ transition dipole moment to zero. In all panels the ionizing pulse is 12.7 fs (FWHM) long, has a peak intensity of ${10}^{14} \mathrm{W}/{\mathrm{cm}}^2$, and a central wavelength of 1900 nm. The vertical dashed lines mark energy splittings corresponding to $2n\omega$ and $(2n+1)\omega$, respectively.

Figure 4

(a) Effect of the intensity on the coherence between the $5p_{1/2}^{-1}$ and $5p_{3/2}^{-1}$ states of ${\mathrm{Xe}}^{+}$ ($m_J=1/2$) as a function of their energy separation from TDCIS calculations. (b) Same as (a) for the $5s^{-1}$ and $5p_0^{-1}$ states. All other pulse parameters are the same as in Fig. 3. (c) Effect of the wavelength on the coherence between $5p_{1/2}^{-1}$ and $5p_{3/2}^{-1}$ using an energy-level separation of 1.3 eV, a peak intensity of ${10}^{14} \mathrm{W}/{\mathrm{cm}}^2$, and a single-cycle pulse at each wavelength.