Ultrafast quantum-path interferometry revealing the generation process of coherent phonons

Optical dual-pulse pumping actively creates quantum-mechanical superposition of the electronic and phononic states in a bulk solid. We here made transient reflectivity measurements in an $n$-GaAs using a pair of relative-phase-locked femtosecond pulses and found characteristic interference fringes. This is a result of quantum-path interference peculiar to the dual-pulse excitation as indicated by theoretical calculation. Our observation reveals that the pathway of coherent phonon generation in the $n$-GaAs is impulsive stimulated Raman scattering at the displaced potential due to the surface-charge field, even though the photon energy lies in the opaque region.

Figure 1

Two-dimensional image map of the change in reflection intensity with the pump-probe delay ($t_{13}$) and pump-pump delay ($t_{12}$).

Figure 2

Two-dimensional image map of the Fourier spectra at various pump-probe delays ($t_{13}$).

Figure 3

Interference fringe of LO phonon (a) and LOPC (b) and optical interference (c).

Figure 4

Double-sided Feynman diagrams for the density matrices corresponding to (a) the ISRS process and (b) the IA process. The thin and thick solid lines respectively represent the ground and excited states. The dashed curves represent the one-LO-phonon state. The red and blue Gaussian curves represent the pulse envelope of the first and the second pulses, respectively, with the wavy lines their photon propagators.

Figure 5

(a) Theoretical curve for the interference fringe in the oscillation amplitude of transient reflectivity due to the ISRS process at the LO phonon frequency plotted against the pump-pump delay ($t_{12}$). (b) Same as (a) but for the IA process.