Revealing the time evolution of different vibrations by noise correlation spectroscopy

The word “noise” in experimental physics has a negative connotation and is associated to a useless phenomenon which overcomes the interesting information, or, at least, compromises its comprehension. Usually our aim as experimentalists is to reduce its contribution in the measurements by maximizing the stability of the set-up and averaging several results, in order to obtain the cleanest data possible. However, this approach hides several pieces of information, which are actually contained in the fluctuation of the physical variable chosen to study the system.
We used this interpretation to develop and propose a new experimental method in the field of non-linear optics, that is the class of techniques which study the phenomena occurring when intense light pulses interact with a material. The main problem of these experiments is that they provide extremely weak signals, thus requiring long integrations in time, in order to get defined response. In order to bypass this inconvenience, we used tailored light pulse, whose features can be finely tuned, in order to maximize the experimental response.
In particular, we combined optical pump-probe measurements with femtosecond covariance spectroscopy. In the former technique the sample is excited by an intense light pulse named pump and its optical properties are probed by a second pulse, whose intensity variation is measured after the interaction with the sample. The time delay between the pump and the probe is tuned to study the complete de-excitation process and to separate the relaxation of different degrees of freedom in complex materials. The latter technique exploits the fluctuations of broadband light pulses which have interacted with the sample, in order to get its Raman spectrum. In particular, this experimental method is able to detect the correlation between the pulse spectral components, whose difference in frequency matches the Raman modes of the sample. Because of the weakness of the signal, the original pulse should be characterized by very low internal correlation, which otherwise would overcome the information about the sample Raman modes. For this reason, a random noise between the spectral components of the pulse is introduced from the beginning, in order to minimize the internal correlation between the spectral components of the light pulse (Fig.1 a). This goal can be achieved through a spatial light modulator, that allows to control and tune continuously the main features of light pulses.
When the two methods are combined, the sample is excited by an intense almost monochromatic pump, whereas a broadband randomized pulse acts as probe and its intensity fluctuations for each spectral component are detected in a single pulse acquisition scheme.
The experiment was performed on quartz, a paradigmatic example for the generation of coherent phonons via Impulsive Stimulated Raman Scattering (Fig 1b): for this reason, it represents the ideal playground to test the coupling of the two techniques described above.
The measurement outcomes provide the energies of the Raman modes of quartz (Fig. 1c). The sign of the correlation at these frequencies varies in time, mirroring the alternating Stokes and anti-Stokes shifts (Fig. 1d).

 figure 1

Figure 1.  a) Example of spectral content of the probe pulse after the introduction of the random noise. b) Scheme of the interaction process taking place at a positive pump – probe time delay Δt for a phonon with frequency Ω. c) map of the correlation coefficient at fixed time delay between the pump and the probe. d) integration of the correlation map (c) along the diagonal axis, as a function of the frequency distance from the diagonal for several Δt values.

Both the clearness of the measurements and the spectral resolution depend on the noise added to the stochastic probe pulse: an optimal correlation length would be chosen by balancing these two factors based on the need of the experiment. 
This alternative approach to 2D Raman spectroscopy has several advantages: it reduces the experimental complexity, the number of required pulses and acquisition times, providing additional information with respect to a standard average intensity measurement. In particular, it allows to identify a specific sample response even when the pump excites more modes simultaneously and it is intrinsically sensitive to weak signals and it is able to resolve both energy and phase of each pulse mode. Moreover, it enables measurements of population signals, which is not possible in current mean-value based techniques, demonstrating the importance of higher modes beyond the mean-value in non-linear optics.

The measurements were performed in the Q4Q labs at Elettra-Sincrotrone Trieste, within the European Research Council project INCEPT (GA#677488) and the Scientific Independent Research Grant from the MIUR (GA#RBSI14ZIY2).


This research was conducted by the following research team:

G. Sparapassi1,2, S. Cavaletto3, J. Tollerud4, A. Montanaro1,2, F. Glerean1,2, A. Marciniak1,2, F. Giusti1,2, S. Mukamel3, D. Fausti1,2

Physics Department, University of Trieste, Trieste, Italy
Elettra-Sincrotrone Trieste S.C.p.A., Trieste, Italy
Chemistry Department, University of California, Irvine
Optical Sciences Centre, Swinburne University, Melbourne, Australia

Contact persons:

Daniele Fausti:
Francesca Giusti:



G. Sparapassi, S. Cavaletto, J. Tollerud, A. Montanaro, F. Glerean, A. Marciniak, F. Giusti, S. Mukamel and D. Fausti "Transient measurement of phononic states with covariance-based stochastic spectroscopy", Nature Light Science & Applications  11, 44 (2022)  DOI: 10.1038/s41377-022-00727-6

Last Updated on Thursday, 17 March 2022 14:54