Time-resolved multimode heterodyne detection for dissecting coherent states of matter

Unveiling and controlling the time evolution of the momentum and position of low energy excitations such as phonons, magnons, and electronic excitation is the key to attain coherently driven new functionalities of materials. Here we report the implementation of femtosecond time- and frequency-resolved multimode heterodyne detection and show that it allows for independent measurement of the time evolution of the position and momentum of the atoms in coherent vibrational states in α-quartz. The time dependence of the probe field quadratures reveals that their amplitude is maximally changed when the atoms have maximum momentum, while their phase encodes a different information and evolves proportionally to the instantaneous atomic positon. We stress that this methodology, providing the mean to map both momentum and position in one optical observable, may be of relevance for both quantum information technologies and time-domain studies on complex materials.