Ultrafast quantum path interferometry to determine the electronic decoherence time of the electron-phonon coupled system in n -type gallium arsenide

Quantum coherence is the key to new quantum technologies, although the details of decoherence processes and times are still not well understood in solids. We demonstrate how to measure the decoherence time of electronic excited states in $n$-type gallium arsenide ($n$-GaAs) crystals using a relative-phase locked double pulse excitation method and quantitatively evaluate with a simple model including temperature dependence. The interference patterns of both electronic and phonon coherence are observed in $n$-GaAs using ultrafast quantum path interferometry with $\ensuremath{\pi}/4$ polarized femtosecond pulses, via the amplitude of longitudinal optical phonons as a function of pump-pump delay. The electronic coherence shows uplifting and splitting in the collapse and revival of the electronic interference, which is sensitive to temperature, and these features are well reproduced using a simple quantum mechanical model. The decoherence time is determined using quantum calculations, from the splitting and uplifting in the interference shape, to be $27.8\ifmmode\pm\else\textpm\fi{}0.5, 23.0\ifmmode\pm\else\textpm\fi{}0.3$, and $12.9\ifmmode\pm\else\textpm\fi{}0.3$ fs at 10, 90, and 290 K, respectively. The temperature dependence of the decoherence time is well reproduced by the density of electrons in the conduction band with the group velocity of the photoinduced electrons.