Self-consistent Bohmian description of strong field-driven electron dynamics

Drawing from the Bohmian formulation of the time-dependent Schrödinger equation, we present a self-consistent hydrodynamical method to describe electron dynamics in strong field light-matter interactions. Prototypical implementation is made for one-dimensional H atom embedded in short and intense laser pulses. The method provides very accurate electron densities and yields quantum trajectories that shed light on the electron dynamics, beyond the strong-field approximation.

Figure 1

Bohmian trajectory flow associated to 1D-H atom embedded in a laser field $F(t)$ with $I=3\hspace{0.5em}{10}^{14}$ W/cm${}^2$ and $\lambda =400$ nm, superposed on a contour map corresponding to the total potential $V_c+V_F+V_Q$ (see text). Time $t$ is expressed in units of the laser period $T$ and the nucleus is located at $x=0$. The trajectories are painted in red (light gray) when their energy $E_i(t)$ is negative and in black when $E_i(t)>0$. The right quadrant contains the temporal evolution of $F(t)$. In the upper quadrant, the electron densities issued from Bohmian and TDSE calculations are compared at the end of the interaction.

Figure 2

Bohmian trajectory flows associated to 1D-H atom embedded in sin${}^2$-laser fields $F(t)$ with $I=3\hspace{0.5em}{10}^{14}$ W/cm${}^2$ and (a) $\lambda =200$ and (b) $\lambda =800$ nm. Figures 2a and 2b are organized as in Fig. 1, except that time $t$ is expressed in fs and the trajectories are in black corresponding to their energy $E_i(t)$. Figures 2c and 2d emphasize the birth of ionizing trajectories in Figs. 2a and 2b, respectively.

Figure 3

Short and long trajectories issued from SFA (QOM) calculations (dashed lines), CTMC simulations (dark red lines), and present Bohmian trajectory flow (light orange lines) for HHG emission of harmonics below ($3\omega$), around ($5\omega$), and above ($9\omega$) threshold. Both the target and field conditions are the same as those of Fig. 1.