The sub-cycle interaction of light and matter is one of the key frontiers of inquiry made accessible by attosecond science. Here, we show that when light excites a pair of charge carriers inside of a solid, the transition probability is strongly localized to instants slightly after the extrema of the electric field. The extreme temporal localization is utilized in a simple electronic circuit to record the waveforms of infrared to ultraviolet light fields. This form of petahertz-bandwidth field metrology gives access to both the modulated transition probability and its temporal offset from the laser field, providing sub-fs temporal precision in reconstructing the sub-cycle electronic response of a solid state structure.
The electric field of a laser pulse can be described as Here we report the first method permitting absolute CEP detection with a solid-state detector applicable in ambient conditions. Recently, we have shown that the strong electric field of an intense, linearly-polarized, visible/near-infrared (VIS/NIR), few-cycle laser pulse can rapidly increase the (ac) conductivity of a solid insulator, allowing electric currents to be induced and switched with the field of visible light [22]. In these experiments, we exposed amorphous silicon dioxide (bandgap g 9 eV E ≈ ) to a strong, controlled electric field ( ) F t of a few-cycle pulse with a carrier photon energy of ∆ is a consequence of dispersive pulse broadening inside the glass wedges. However, in our experiments P ( ) Q l ∆ was still detectable above the noise level for values of 400 µm l ∆ > , corresponding to a pulse duration of more than 9 fs (FWHM of the time-dependent cycle-averaged intensity). Subsequently, PQ was calibrated with respect to the absolute CEP of the laser pulse via stereo-ATI measurements performed with identical pulses [4]. After the measurement of P ( ) Q l ∆ with the solid-state device, a mirror was inserted into the beam path, deflecting the 5 pulses into a stereo-ATI apparatus located -together with the solid-state detector -in the same vacuum chamber (Fig. 1). Here, the CEP of the incident laser pulse was detected by analyzing the kinetic energy distribution of electrons that are photoemitted from Xe atoms, see Methods Summary. An uncertainty due to a Gouy phase shift in both foci can be neglected since in both experiments, the sample was placed exactly in the region of the highest laser intensity.We set 17 different propagation lengths l ∆ , ranging from 21.5 µm − to 27.5 µm +. For each of them, 500 single-shot stereo-ATI measurements were performed. Because consecutive laser pulses had a CEP-shift of π , which is only required for the accurate detection of P ( ) Q l ∆ , only spectra from odd-numbered pulses were considered for the stereo-ATI measurements. As shown in [4], CEϕ can then be reconstructed by calculating two asymmetry parameters ( , ) X Y by integrating the averaged time-of-flight spectra L,R TOF ( ) n t of the electrons photoemitted from Xe atoms by the intense few-cycle VIS/NIR pulses in two different regions. The parametric plot of ( , ) X Y in Fig. 2(a) was obtained by calculating, for each. The photoelectron spectra L,R TOF ( ) n twere measured with the left (L) and right (R) micro-channel plates (MCPs) of the set-up in Fig. 1 We have compared the results of the solid-state-based phase retrieval with the predictions of two quantum mechanical models. The first model, which was earlier employed in Ref.[24] to describe the ultrafast increase in conductivity of SiO 2 nanojunctions, is based on the nearestneighbor tight-binding approximation. The second model, presented in detail in Ref.[25], describes quantum dynamics in a one-dimensional pseudopotential (see the Methods Summary for details). In both models, the electric fi...
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