Effects of the Carrier-Envelope Phase in the Multiphoton Ionization Regime

We theoretically investigate the effects of the carrier-envelope phase of few-cycle laser pulses in the multiphoton ionization regime. For atoms with low ionization potential, total ionization yield barely exhibits phase dependence, as expected. However, population of some bound states clearly shows phase dependence. This implies that the measurement of the carrier-envelope phase would be possible through the photoemission between bound states without energy-and-angle-resolved photoelectron detection. The considered scheme could be particularly useful to measure the carrier-envelope phase for a light source without an amplifier, such as a laser oscillator, which cannot provide sufficient pulse energy to induce tunneling ionization.

Figure 1

Level scheme of Cs.

Figure 2

Depth of modulation, $M$, for Cs as a function of the number of cycles, $N$, for the photon energy of 1.55 eV (solid line) at the peak intensity of ${10}^{11}\mathrm{W}/{\mathrm{cm}}^2$, and for the photon energy of 1.0 eV (dashed line) at the peak intensity of $4.2\times {10}^{10}\mathrm{W}/{\mathrm{cm}}^2$. Note that both curves correspond to the same Keldysh parameter, $\gamma =18$. For the definition of $M$, see Eq. (5).

Figure 3

Total ionization yield and the population of some bound states of Cs as a function of carrier-envelope phase for 1.55 eV photon and the peak intensity of ${10}^{11}\mathrm{W}/{\mathrm{cm}}^2$ with $N=1$. The calculated result without ionization are shown by the dashed line in each panel. The calculated result with ionization but using a different pseudopotential [Ref. 16 ] is shown by the dot-dashed line in each panel.

Figure 4

Change of modulation for $5d$, $8p$, and $4f$ states (a) at slightly different intensities, $I=0.9\times {10}^{11}\mathrm{W}/{\mathrm{cm}}^2$ (dashed line), ${10}^{11}\mathrm{W}/{\mathrm{cm}}^2$ (solid line), and $1.1\times {10}^{11}\mathrm{W}/{\mathrm{cm}}^2$ (dot-dashed line) with $N=1$, and (b) with slightly different number of cycles, $N=0.9$ (dashed line), 1.0 (solid line), and 1.1 (dot-dashed line) at the intensity of ${10}^{11}\mathrm{W}/{\mathrm{cm}}^2$. Photon energy is taken to be 1.55 eV for all graphs.