Overcoming fluctuations by correlation: a new way to attosecond resolution at FELs

Having access to how processes evolve in time is a key milestone for understanding the dynamics and correlation of the different elements constituting the physical system under investigation. For phenomena occurring on ultrafast timescales (less than about 1 ns = 10^-9 s), the investigations are usually performed in pump-probe experiments in which the pump (typically a light pulse or an electron wave packet) initiates the dynamics in the system, and the probe interrogates it at a later controllable time. The electronic dynamics evolves on timescales that can be as fast as a few attoseconds (1 as = 10^-18 s), calling for the application of attosecond pulses (in a train, or isolated) to pump-probe experiments. While attosecond waveforms are routinely produced by table-top intense laser sources, only recently the generation of attosecond bursts of light has been achieved at free electron lasers (FELs). These facilities, however, suffer from large fluctuations in the control of the delay between the pump and probe pulses, thus leading to a smearing effect in the temporal resolution of the experiments.

In our work, performed on the Low Density Matter end-station of the seeded FEL FERMI, we demonstrate a novel approach for the application of trains of isolated attosecond pulses for the investigation of electronic dynamics. We use a correlation technique in the analysis of the photoelectron spectra generated by the combination of an extreme ultraviolet comb of frequencies and an infrared pulse. In our experiment the relative delay between these fields changes randomly on a single-shot basis: The idea is then to correlate the intensities of those photoelectron peaks contributed by both fields (usually known as sidebands), which are linked by a characteristic correlation even though their single-shot value changes randomly. A typical correlation map of the sidebands generated between the harmonics H7 and H8 of the FEL, and those generated by H8 and H9 is presented in Fig.1a. In general, the ensemble of experimental points forms an ellipse, whose precise shape can be controlled by changing the relative synchronization of the three harmonics H7, H8, and H9. The angular position of the single experimental point reflects the relative timing between the attosecond pulse train and the infrared field, thus mapping the synchronization onto an angle. This approach offers a straightforward method to reorder in time the ensemble of single-shot experimental points, thus recovering the information about the delay between the two pulses, which was lost due to their residual instability. Supported by extensive simulations, which also consider the residual fluctuations of each harmonic, we demonstrate that the accuracy in the reconstruction of the relative synchronization is as high as one atomic unit of time (24 as), thus paving the way for time-resolved experiments with attosecond resolution at a FEL. We demonstrate the validity of our approach, by reconstructing the variation of the sideband intensities as a function of the relative delay, as shown in Fig.1b. The intensities clearly oscillate as predicted by theoretical models, thus returning a first, direct demonstration of the validity the scheme.

Being able to control the phases of each individual harmonic of FERMI, we take a step further, demonstrating the possibility to control the intensity and timing of the sideband oscillations by manipulating selectively a specific quantum path contributing to the sidebands. In the experiment we focus on the sideband S^(-)_7,8 generated between the harmonics H7 and H8, using as control knob the phase of the neighbor harmonic H6 (see Fig.2a,b).  Apart from the paths contributed by the adjacent harmonics (H7 and H8), a path determined by the absorption of the harmonic H6 and four additional infrared photons, can contribute to that sideband. The sideband oscillations were retrieved using the approach outlined above and then a fitting procedure returned the amplitude and timing of the oscillations. The results are presented in Fig.2c,d and clearly show that the amplitude and phase of the sideband oscillation can be controlled by manipulating the phase of harmonic H6.

These results are the first demonstration of attosecond coherent control of electronic wave packets obtained by addressing a single harmonic. A key element of the experiment is the unique characteristic of FERMI in which different harmonics of the common seed laser can be generated with an adjustable relative phase.

This research was conducted by the following research team:

Praveen Kumar Maroju¹, Michele Di Fraia², Oksana Plekan², Matteo Bonanomi^3,4, Barbara Merzuk¹, David Busto^1,5, Ioannis Makos¹, Marvin Schmoll¹, Ronak Shah¹, Primož Rebernik Ribič², Luca Giannessi^2,6, Giovanni De Ninno^2,7, Carlo Spezzani^2,7, Giuseppe Penco², Alexander Demidovich², Miltcho Danailov², Marcello Coreno^2,6,8, Marco Zangrando², Alberto Simoncig², Michele Manfredda², Richard J. Squibb⁹, Raimund Feifel⁹, Samuel Bengtsson⁵, Emma Rose Simpson⁵, Tamás Csizmadia¹⁰, Mathieu Dumergue¹⁰, Sergei Kühn¹⁰, Kiyoshi Ueda¹¹, Jianxiong Li¹², Kenneth J. Schafer¹², Fabio Frassetto¹³, Luca Poletto¹³, Kevin C. Prince², Johan Mauritsson⁵, Carlo Callegari² & Giuseppe Sansone¹.

¹ Physikalisches Institut, Albert-Ludwigs-Universität Freiburg, Freiburg, Germany.
² Elettra-Sincrotrone Trieste, Basovizza, Trieste, Italy.
³ Dipartimento di Fisica Politecnico, Milan, Italy.
⁴ Istituto di Fotonica e Nanotecnologie CNR-IFN, Milan, Italy.
⁵ Department of Physics, Lund University, Lund, Sweden.
⁶ INFN Laboratori Nazionali di Frascati, Frascati, Italy.
⁷ Laboratory of Quantum Optics, University of Nova Gorica, Nova Gorica, Slovenia.
⁸ ISM-CNR, Istituto Struttura della Materia, Trieste, Italy.
⁹ Department of Physics, University of Gothenburg, Gothenburg, Sweden.
¹⁰ ELI ALPS, ELI-HU Non-Profit, Szeged, Hungary.
¹¹ Institute of Multidisciplinary Research for Advanced Materials, Tohoku University, Sendai, Japan.
¹² Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA, USA.
¹³ Istituto di Fotonica e Nanotecnologie, CNR, Padova, Italy.

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