Interferences of Ultrashort Free Electron Wave Packets

Interferences of free electron wave packets generated by a pair of identical, time-delayed, femtosecond laser pulses which ionize excited atomic potassium have been observed. Two different schemes are investigated: threshold electrons produced by one-photon ionization with parallel laser polarization and above threshold ionization electrons produced by a two-photon transition with crossed laser polarization. Our results show that the temporal coherence of light pulses is transferred to free electron wave packets, thus opening the door to a whole variety of exciting experiments.

Figure 1

Principle of the experiment. (a) Intensity of a pair of identical 30 fs Gaussian laser pulses separated by a time delay $\tau$. (b) $P_e({\omega }_e)$ corresponding photoelectron spectrum for threshold electrons. Spatial distribution of the electron wave packets: (c) after creation by the pulse pair, (d) free motion of the wave packets leading to an overlap due to dispersion, and (e) long term evolution of the interference pattern.

Figure 2

Excitation scheme in potassium atoms. With a 405 nm femtosecond laser pulse the atom is prepared in its $5p$ state. After a fixed delay (T) of 3 ns, the pair of two identical pulses generates a coherent double peaked free electron wave packet. The experimental photoelectron spectrum shows the threshold electrons (1) and the first ATI electron peak produced by the 790 nm femtosecond laser pulse (2). The ATI peak (2) overlaps with a strong contribution from the photoionization of the $5p$ state by the 405 nm pulse (3). For frequency labels see text.

Figure 3

Experimental results for threshold electrons with parallel polarizations, for zero (a) and negative (c) delay times $\tau$. For comparison and to enhance the visibility of the observed ellipses, calculated contours are superimposed. (b) A section along the time delay axes at fixed energy indicates oscillatory behavior with varying time delay. (d) Section along the photoelectron energy axes at $\tau =-96\mathrm{f}\mathrm{s}$ showing fringes in the measured photoelectron spectrum (bold). A calculated spectrum convoluted with 25 meV spectrometer resolution is given for comparison.

Figure 4

Fourier transform of photoelectron signal employing a time window from 25–50 fs at threshold energy (0.29 eV, grey) and above threshold ionization (ATI) energy (1.86 eV, black). The photon frequency $\omega$ ($12658\mathrm{c}{\mathrm{m}}^{\mathrm{-}\mathrm{1}}$) and the second harmonic $2\omega$ are indicated with vertical dashed lines. For parallel polarization (a) a dominant peak at $\omega$ is observed but no contribution at $2\omega$. For crossed polarization (b) the frequency spectrum of the threshold electrons does not show discernible features above the noise limit, whereas the ATI spectrum has a distinct maximum at $2\omega$ due to quantum mechanical interferences.