Femtosecond covariance spectroscopy.

The success of nonlinear optics relies largely on pulse-to-pulse consistency. In contrast, covariance-based techniques used in photoionization electron spectroscopy and mass spectrometry have shown that a wealth of information can be extracted from noise that is lost when averaging multiple measurements. Here, we apply covariance-based detection to nonlinear optical spectroscopy, and show that noise in a femtosecond laser is not necessarily a liability to be mitigated, but can act as a unique and powerful asset. As a proof of principle we apply this approach to the process of stimulated Raman scattering in α-quartz. Our results demonstrate how nonlinear processes in the sample can encode correlations between the spectral components of ultrashort pulses with uncorrelated stochastic fluctuations. This in turn provides richer information compared with the standard nonlinear optics techniques that are based on averages over many repetitions with well-behaved laser pulses. These proof-of-principle results suggest that covariance-based nonlinear spectroscopy will improve the applicability of fs nonlinear spectroscopy in wavelength ranges where stable, transform-limited pulses are not available, such as X-ray free-electron lasers which naturally have spectrally noisy pulses ideally suited for this approach.

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.