Attosecond Double-Slit Experiment

A new scheme for a double-slit experiment in the time domain is presented. Phase-stabilized few-cycle laser pulses open one to two windows (slits) of attosecond duration for photoionization. Fringes in the angle-resolved energy spectrum of varying visibility depending on the degree of which-way information are measured. A situation in which one and the same electron encounters a single and a double slit at the same time is observed. The investigation of the fringes makes possible interferometry on the attosecond time scale. From the number of visible fringes, for example, one derives that the slits are extended over about 500 as.

Figure 1

Temporal variation of the electric field $\mathcal{E}(t)={\mathcal{E}}_0(t)\cos (\omega t+\phi )$ of few-cycle laser pulses with phase $\phi =0$ (“cos-like”) and $\phi =3\pi /2$ (“sin-like”). In addition, the field ionization probability $R(t)$, calculated at the experimental parameters, is indicated. Note that an electron ionized at $t=t_0$ will not necessarily be detected in the opposite direction of the field $\mathcal{E}$ at time $t_0$ due to deflection in the oscillating field.

Figure 2

Photoelectron spectra of argon measured with 6 fs laser pulses for intensity $1\times {10}^{14}\mathrm{W}/{\mathrm{cm}}^2$ as a function of the phase. Panel (a) displays the spectra for $\pm \sin $- and $\pm \cos $-like laser fields. The red curves are spectra recorded with the left detector (negative direction), while the black curves relate to the positive direction. For $\phi =\pi /2$ the fringes exhibit maximum visibility for electron emission to the right, while in the opposite direction minimum fringe visibility is observed. In addition, the fringe positions are shifted. Panel (b) displays the entire measurement where the fringe visibility is coded in false colors. The fringe positions vary as the phase $\phi$ of the pulse is changed. This causes the wavelike bending of the stripes in these figures. Both panels, in principle, show the same information because a phase shift of $\pi$ mirrors the pulse field in space and thus reverses the role of positive and negative direction. However, the data shown were recorded simultaneously but independently as the phase $\phi$ was varied between 0 and $2\pi$.

Figure 3

The result of a numerical solution of the time-dependent Schrödinger equation, as described in the text. This figure should be compared with the right panel of Fig. 2b.

Figure 4

Vector potential of a $-\sin $-like few-cycle pulse. The temporal slits are given by the condition $p-eA(t_0)=0$. For a $-\sin $-like pulse, this leads to a double slit in the negative (since $e=-|e|$) direction and a single slit in the opposite direction. Each slit can be resolved into a pair of slits.