Many-body correlations govern a variety of important quantum phenomena such as the emergence of superconductivity and magnetism. Understanding quantum many-body systems is thus one of the central goals of modern sciences. Here we demonstrate an experimental approach towards this goal by utilizing an ultracold Rydberg gas generated with a broadband picosecond laser pulse. We follow the ultrafast evolution of its electronic coherence by time-domain Ramsey interferometry with attosecond precision. The observed electronic coherence shows an ultrafast oscillation with a period of 1 femtosecond, whose phase shift on the attosecond timescale is consistent with many-body correlations among Rydberg atoms beyond mean-field approximations. This coherent and ultrafast many-body dynamics is actively controlled by tuning the orbital size and population of the Rydberg state, as well as the mean atomic distance. Our approach will offer a versatile platform to observe and manipulate non-equilibrium dynamics of quantum many-body systems on the ultrafast timescale.

Molecules are expected to be promising information devices 1-8. Theoretical proposals have been made for logic gates with a molecular wave packet modulated by a strong femtosecond laser pulse 9-15. However, it has not yet been observed how this changes the population of each eigenstate within the wave packet. Here we demonstrate direct observation of the population beating clearly as a function of the delay of the strong laser pulse. The period is close to the recurrence period of the wave packet, even though a single eigenstate should have no information on the wave-packet motion. This unusual beat arises from quantum interference among multiple eigenstates combined on a single eigenstate. This new concept, which we refer to as 'strong-laser-induced interference', is not specific to molecular eigenstates, but universal to the superposition of any eigenstates in a variety of quantum systems, being a new tool for quantum logic gates, and providing a new method to manipulate wave packets with femtosecond laser pulses in general applications of coherent control 16-20. The wavefunctions of electrically neutral systems can replace electric charges of the present Si-based circuits, whose further downsizing will soon reach its limit where current leakage will cause heat and errors with insulators thinned to atomic levels 21. Atoms and molecules are promising candidates for these neutral systems, in which the population and phase of each eigenstate serve as carriers of information 1,2,22,23. A shaped ultrashort laser pulse can access many eigenstates simultaneously within a single atom or molecule, manipulating the amplitude and phase of each eigenstate individually to write more than one million distinct binary codes in the angstrom space 1,2. Molecules in particular are now expected to be promising components to develop scalable quantum computers 5-8. The development of I /O and logic gates with molecules should be meaningful for us to be prepared for such a future scalable system. It is therefore important to study information processing with molecular eigenstates for both high-density classical information processing and quantum information processing. This background has motivated us to propose molecular eigenstate-based information processing (MEIP), and to demonstrate the ultrafast Fourier transform based on the temporal evolution of a molecular wave packet 2-4. For more universal computing in MEIP, however, one should consider another class of logic gates with a strong femtosecond laser pulse whose broad bandwidth and high intensity allow for multiple transitions among different eigenstates within a wave packet simultaneously. This scheme has been employed in a number of theoretical studies on MEIP logic gates 9-15 , and also in a few experimental studies 24 , but it has not yet been observed experimentally how each eigenstate changes its population with those multiple transitions within a wave packet. Here, we report the direct observation of the population of each vibrational eigenstate within a wave packet mod...