Subcycle quantum electrodynamics

Abstract

2Coherent states represent the closest counterpart to a classical electromagnetic wave that exists in quantum electrodynamics. The quantum noise amplitudes of their electric and magnetic fields coincide precisely with those of the vacuum state 19 . Recently, we have succeeded to directly detect the bare vacuum fluctuations of the mid-infrared electric field with highly sensitive electro-optic sampling based on ultrashort laser pulses 15,16 . One key aspect of this technique is that it operates out of a time-domain perspective. Therefore, it should provide a resolution substantially below the duration of an oscillation period of any quantum field under study. Naturally, it is tempting to think about an experiment that synchronously couples a nonclassical state of light into the space-time volume which is probed, thus providing a quantum noise amplitude that deviates from pure vacuum fluctuations. Especially, it would be an attractive manifestation of quantum physics if less noise as compared to the quantum vacuum could be localized in time and space. In conventional homodyning studies, the carrier wave of a local oscillator needs to be phaselocked to a quantum state 11,16 . Instead, we have to prepare a squeezed electromagnetic transient with a noise pattern that is synchronized with the intensity envelope of an ultrashort probe pulse. This tightly focussed few-femtosecond optical wave packet then defines a subcycle space-time segment in which the quantum statistics of a mid-infrared nonclassical signal is sampled. Our scheme to implement such an experiment is sketched in Fig. 1(a). We send an intense near-infrared pump pulse (red-yellow envelope) with duration of 12 fs and centre frequency of 200 THz into a thin generation crystal (GX). In a first step, a carrier-envelope phase-locked electric field transient 20 is generated by optical rectification (red line). Once built up, it starts to locally phase shift the co-propagating multi-terahertz vacuum fluctuations (green shaded band) by means of the electro-optic effect in the GX which establishes a change in refractive index n(t) proportional to the mid-infrared electric field amplitude E THz (t). In a simplified picture, the resulting local anomalies in the speed of light might induce depletion of vacuum amplitude at certain space-time regions (blue shaded sections), piling it up in others (stained in red). A high efficiency for this two-step mechanism to squeeze the mid-infrared vacuum is 3 ensured by the large second-order nonlinearity of the 16-m-thick exfoliated piece of GaSe we employ as GX 20 . Tight focussing of the pump to a paraxial spot radius w pump of 3.6 m also defines the transverse spatial mode for the nonclassical electric field pattern. After the GX, the squeezed vacuum is collimated and residual pump is removed by a 70-m-thick GaSb filter inserted under Brewster's angle. A mode-matched 5.8 fs probe pulse (blue envelope) is then superimposed onto the multi-terahertz field and focussed to w probe = 3.6 m in a AgGaS 2 detector crystal (DX) of...

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