Creation and detection of squeezed phonons in pump and probe experiments: a fully quantum treatment
Abstract
Femtosecond pump and probe techniques are standard experimental methodologies used for studying ultrafast dynamics in solids, in particular phonon oscillations in target materials. So far, only semiclassical methods have been employed in order to theoretically interpret the experimental data. In contrast, a fully quantum treatment will be presented here taking into account the quantum features of the generation mechanism of excited phonons by pump laser pulses, and of the process of accessing their behaviour by probe laser pulses. A single effective Hamiltonian will be used to model the interaction between photons and phonons both for the pumping and probing processes. In addition, as they interact with their environment, mainly electrons in the target, the excited phonons cannot be considered an isolated system. Their dynamics is then that typical of open quantum systems and generated by a master equation of Lindblad form, that takes into account the dissipative and noisy effects due to the environment. In this formalism, phonon oscillations can be analysed through suitable probe photon observables. Specifically, unlike in the existing literature, we will not focus only upon the scattered probe pulse intensity, namely on the probe photon number, but also on the number variance. Through the latter some quantum features of the phonon state can be accessed; in particular, specific signals of the presence of squeezed phonons can thus be identified.
