Direct sampling of electric-field vacuum fluctuations

Abstract

The ground state of quantum systems is characterized by zero-point motion. This motion, in the form of vacuum fluctuations, is generally considered to be an elusive phenomenon that manifests itself only indirectly. Here, we report direct detection of the vacuum fl uctuations of electromagnetic radiation in free space. The ground·state electric-field variance is inversely proportional to the four-dimensional space·time volume, which we sampled electro-optically with tightly focused laser pulses lasting a few femtoseconds. Subcycle temporal readout and nonlinear coupling far from resonance provide signals from purely virtual photons without amplification. Our findings enable an extreme time-domain approach to quantum physics, with nondestructive access to the quantum state of light. Operating at multiterahertz frequencies, such techniques might also allow time-resolved studies of intrinsic fluctuations of elementarY excitations in condensed matter. The quantum properties of light (10) are typi calJy analyzed either by phcton oorrelation (11 14), bomodyning (15 18), or hybrid measurements (19). In those approaches, information is averaged over multiple cycles, and aocessing the vacuum state requires amplification. Femtnsecond studies still rely on pulse envelopes that vary slowly relative tn the carrier frequency (20 23). In our work, we directly probed the varuum noise of the electric field on a subcycle time scale using laser pulses lasting a few femtnseoonds. In ultrabroad band electro optic sampling (24 27), a horizon tally polarized electric field waveform (red in Fig. lA) propagates through an electro optic crystal (EOX), inducing a change Lln of the linear re fractive index 11.o that is proportional to its local amplitude Em:. (Fig. lA and fig. SI). The geometty is adjusted so that a new index ellipsoid emerges under46°tothe polarization of Ern., with nv and nr = 11.o :1:: !!:.n. An ultrashort optical probe pulse at a much higher carrier frequency vp (green in Fig. 1A; intensity, I p, electric field, E.J coprop~ with Em~ at a variable delay time td. The envelope ·of!Pbastn be on theorderofhalfacycle oflightat the highest frequencies il/2rt of En~ that are detected. We used probe pulses as short as tp = 5.8 fs, oorresponding tn Jess than L5 optical cycles at vp = 255 1Hz ( fig. 82). Upon passage through the EOX, the a! andy' components of Ep acquire a relative phase delay proportional to Lln and Eml.,td). The final polarizatim state of the probe is analyzed with ellipsometry. The differential photn rurrent 111/I is proportional tn the electric field Eml.,t,V. We used a radio frequency lock in ampli tier (R.FLA) for readout.We a<ljusted for optimal conditions tn measure the vacuum signal by studying classical multi ·terabertz transients, which were synchronized tn the probe (8). In Konstanzer Online-Publikations-System (KOPS)

Subcycle quantum electrodynamics

“…1(c)). Note that only 4% of the total fluctuation amplitude in our setup result from a bare multi-terahertz vacuum input while the rest is due to the noise-equivalent field of the detector E SN caused by the quantized flux of near-infrared probe photons 15,21 . Therefore, a RDN of -0.04 would correspond to a complete removal of the vacuum fluctuations in the space-time segment sampled in the DX.…”

“…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.…”

“…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 24 m thickness 15 . It samples the electric field in the copropagating space-time volume via the electro-optic effect 15,20 and as a function of time delay t D .…”

“…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 24 m thickness 15 . It samples the electric field in the copropagating space-time volume via the electro-optic effect 15,20 and as a function of time delay t D . We gain two different types of information: the coherent ("classical") electric field amplitude E THz (t D ) of the squeezing mid-infrared transient is recorded in the conventional way 20 .…”

“…We gain two different types of information: the coherent ("classical") electric field amplitude E THz (t D ) of the squeezing mid-infrared transient is recorded in the conventional way 20 . In addition, the quantum distribution of the multi-terahertz electric field is accessed via statistical readout 15 . Especially, our technique allows us to directly reference the local noise level E rms in a squeezed transient (blue and red distributions in Fig.…”