Three-Dimensional Momentum Imaging of Electron Wave Packet Interference in Few-Cycle Laser Pulses

Using a reaction microscope, three-dimensional (3D) electron (and ion) momentum ($\mathbf{P}$) spectra have been recorded for carrier-envelope-phase (CEP) stabilized few-cycle ($\sim 5\mathrm{fs}$), intense ($\sim 4\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$) laser pulses (740 nm) impinging on He. Preferential emission of low-energy electrons ($E_e<15\mathrm{eV}$) to either hemisphere is observed as a function of the CEP. Clear interference patterns emerge in $\mathbf{P}$ space at CEPs with maximum asymmetry, interpreted as attosecond interferences of rescattered and directly emitted electron wave packets by means of a simple model.

Figure 1

Electron trajectories in an ultrashort pulse, with ${\varphi }_{\mathrm{CEP}}=\pi /2$. Electrons born at times $t_s$ ($s=1$, 2) end up with the same momentum $p(t_s)$ following the trajectories given by the red and blue curves, respectively: $p(t_s)=-{\int }_{t_s}^{\infty }E(t)dt$, in atomic units. The right-hand axis is the displacement of the electron from $z=0$.

Figure 2

(a) Recoil-ion (${\mathrm{He}}^{+}$) momentum distributions along the laser polarization axis for CEP with maximum asymmetry towards positive momenta and (b) at ${\varphi }_{\mathrm{CEP}}=\pi /2$. Shaded curve: ion momentum distribution at a similar intensity but for longer, 25 fs pulses normalized to the integral under the blue line. The thin blue curve in (b) is a mirror image of the blue curve in (a). Inset: asymmetry parameter $a({\varphi }_{\mathrm{CEP}})$ as a function of the relative CE phase (see text).

Figure 3

Positions of peaks in the parallel momentum $p_{\parallel }$ for 5 fs, $0.4\mathrm{PW}/{\mathrm{cm}}^2$ pulses at a phase of maximum asymmetry as extracted from Fig. 2 (red full circles). Blue open circles are from previous results for 25 fs, $0.6\mathrm{PW}/{\mathrm{cm}}^2$ (shaded area in Fig. 2) [12]. The black curve simulates a square-root ATI-like behavior. Green triangles: SFA model calculation (see text).

Figure 4

2D electron-momentum distribution (linear scale) for a CE phase with maximum asymmetry. The $x$ axis is the longitudinal momentum, the $y$ axis is the momentum transverse to the polarization direction. The red line indicates the position of $p_{\parallel }=0$. The projection onto the $p_{\parallel }$ axis is indicated as white dotted line. Events below the gray bar have been cut out since here the electron TOF is equal to an integer multiple of the cyclotron frequency of the electrons in the magnetic field of the reaction microscope and, accordingly, the transverse resolution diverges [8]. Inset : TDSE calculations for the ionization of He, with a Gaussian pulse, $I_0=0.3\mathrm{PW}/{\mathrm{cm}}^2$, at 740 nm and FWHM $\sim 2.7\mathrm{fs}$.