Strongly interacting quantum many-body systems are fundamentally compelling and ubiquitous in science. However, their complexity generally prevents exact solutions of their dynamics. Precisely engineered ultracold atomic gases are emerging as a powerful tool to unravel these challenging physical problems. Here we present a new laboratory for the study of many-body effects: strongly interacting two-level systems formed by the clock states in 87 Sr, which are used to realize a neutral atom optical clock that performs at the highest level of optical-atomic coherence and with precision near the limit set by quantum fluctuations. Our measurements of the collective spin evolution reveal signatures of many-body dynamics, including beyond-mean-field effects. We derive a many-body Hamiltonian that describes the experimental observation of severely distorted lineshapes, atomic spin coherence decay, density-dependent frequency shifts, and correlated quantum spin noise. These investigations open the door to exploring quantum many-body effects and entanglement in quantum systems with optical energy splittings, using highly coherent and precisely controlled optical lattice clocks.
Experimental set-up-angular streaking spectroscopy. Previous streaking measurements of XFEL pulses 37-39 used a linearly polarized streaking field to encode their temporal profile onto the kinetic energy of photoelectrons. Depending on the amplitude and phase of
Laser-driven high-order harmonic generation 1,2 (HHG) provides tabletop sources of broadband extreme-ultraviolet (XUV) light with excellent spatial 3 and temporal 4 coherence. These sources are typically operated at low repetition rates, f rep 100 kHz, where phase-matched frequency conversion into the XUV is readily achieved 5,6 . However, there are many applications that demand the improved counting statistics or frequency-comb precision afforded by operation at high repetition rates, f rep > 10 MHz. Unfortunately, at such high f rep , phase matching is prevented by the accumulated steady-state plasma in the generation volume 7-11 , setting stringent limitations on the XUV average power. Here, we use gas mixtures at high temperatures as the generation medium to increase the translational velocity of the gas, thereby reducing the steady-state plasma in the laser focus. This allows phase-matched XUV emission inside a femtosecond enhancement cavity at a repetition rate of 77 MHz, enabling a record generated power of ∼2 mW in a single harmonic order. This power scaling opens up many demanding applications, including XUV frequency-comb spectroscopy 12,13 of few-electron atoms and ions for precision tests of fundamental physical laws and constants 14-20 .The highly-nonlinear HHG process requires peak laser intensities around 10 14 W/cm 2 , which necessitates large laser pulse energies 10 µJ, and short pulse durations 100 fs, as typically reached with low repetition rate, chirped-pulse amplified 21 laser systems. However, high repetition rates are desirable for applications such as photoelectron spectroscopy 22-24 and microscopy 25 as well as electron-ion coincidence spectroscopy 26,27 , which are limited by counting detection or space-charge effects to few XUV ionization events per shot. Most notably, precision frequency-comb spectroscopy 12,13 requires f rep 10 MHz in order to stabilize the comb. Recent efforts allowed HHG to be directly driven at f rep 1 MHz, using either the direct output of a high-power oscillator 22,28 or the coherent combination of several fibre amplifiers 29,30 . Achieving the necessary intensity for HHG with f rep 10 MHz requires lasers with average power in the kW range. Apart from one demonstration at 20 MHz, where the measured XUV power was extremely low 31 , higher repetition rates up to 250 MHz 32 have been facilitated only by using passive enhancement cavities, which store ∼10 kW of laser power, where a gas jet is introduced at an intracavity focus 7,10-12,33-35 .In a macroscopic extended medium, efficient HHG requires matching the phase velocities of the generating laser and the generated fields. This can be achieved by balancing neutral and plasma dispersion, the geometric phase shift due to focusing (the Gouy phase), and the HHG intrinsic dipole phase 5,36 . Achieving this balance becomes increasingly challenging as the repetition rate increases above ∼10 MHz. The reason for this difficulty is that the plasma generated by one pulse does not have time to clear the focal volume before t...
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