Historical research guide · 0444 · 2015

Direct sampling of electric-field vacuum fluctuations

C. Riek · D. V. Seletskiy · A. S. Moskalenko · J. F. Schmidt · P. Krauspe · S. Eckart · S. Eggert · G. Burkard · A. Leitenstorfer

In one minute

For most of a century the zero-point motion of the electromagnetic field was something you inferred — from spontaneous emission, from the Lamb shift, from the Casimir force. Claudius Riek, Denis Seletskiy, Alfred Leitenstorfer and their colleagues at Konstanz went and looked at it. Their instrument is electro-optic sampling. A laser pulse lasting 5.8 femtoseconds, less than one and a half cycles of its own light, crosses a nonlinear crystal, and whatever electric field is present at that instant twists its polarisation very slightly. Made short enough, the pulse resolves the field inside a single cycle of the infrared vacuum, and the vacuum’s own fluctuations appear as extra noise riding on the laser’s shot noise. Because the fluctuation amplitude grows as the sampled patch of spacetime shrinks, the team could turn the effect up and down at will by stretching the pulse or widening the focus. The measured vacuum field came out at 18 volts per centimetre against a prediction of 20.2, with no amplifier anywhere in the chain.

Connection

Chapter 2 argues that the vacuum is a structured medium rather than an absence, and this is the measurement that puts a number on it in free space: an electric field of roughly 18 volts per centimetre in the ground state, read directly. For chapter 1 it sits high on the ladder — a laboratory instrument, a predicted magnitude, two independent ways of switching the signal on and off, and follow-up work in other laboratories.

From the source

The ground-state variance of the electric field is inversely proportional to the four-dimensional space-time volume over which it is sampled. Shrink the volume and the fluctuation amplitude rises; that scaling is what the whole experiment turns on, and it is stated in the paper’s opening sentence.Abstract; Equation 5
Probe pulses as short as 5.8 femtoseconds, under 1.5 optical cycles at a carrier frequency of 255 terahertz, give an effective sampling bandwidth of 66 terahertz centred on 67.5 terahertz — a free-space wavelength of 4.4 micrometres. Subcycle temporal readout combined with nonlinear coupling far from resonance is what allows signals from purely virtual photons to be recorded without amplification.Text following Equation 3; Fig. 1B and Fig. 1C
Deconvolving the measured probability distribution recovers the ground-state wave function of the electric field in the sampled polarisation and space-time volume, from which the root-mean-square vacuum amplitude is 18 volts per centimetre — in good agreement with the value of 20.2 volts per centimetre predicted from the mode-counting argument.Fig. 2B; Equation 5
Two independent controls confirm the signal is the vacuum and not the instrument. Stretching the probe from 5.8 to 100 femtoseconds averages over the field along the beam and reduces the excess noise; translating the crystal out of the confocal plane to widen the spot radius from 4.25 up to 85 micrometres averages over it across the beam and does the same. Both follow the predicted dependence, and the total change in normalised noise amplitude of about 4 percent matches the 4.7 percent expected from adding shot noise and vacuum noise in quadrature.Fig. 2A and Fig. 2B; Fig. 3B; Fig. 4; Equations 6 and 7
Only the term ordered with the creation operator survives in the field variance, which the authors read as vacuum fluctuations corresponding to photons that spontaneously arise and vanish in the ground state. Because the readout uses a second-order nonlinearity far from resonance rather than a resonant two-level system, it avoids the decoherence problems of detection schemes in quantum optics and circuit quantum electrodynamics.Closing discussion, first paragraph; Equation 4
Sum-frequency and difference-frequency mixing occur simultaneously in the crystal, so the measurement needs no net transfer of energy, momentum or angular momentum and should leave the multiterahertz ground state essentially undisturbed. Back action is predicted to appear only at third order: with a strong enough probe, the vacuum amplitude in the sampled space-time volume would be depleted and fluctuations in an adjacent interval enhanced. That is the effect to watch for next.Closing discussion, final paragraph

The way in

https://doi.org/10.1126/science.aac9788

Historical source-access record. This guide links to the original; it does not reproduce the paper text.

Published as Science 350, issue 6259, pages 420 to 423, 23 October 2015, under the AAAS journal licence, which is not a Creative Commons licence, so no text of the paper is reproduced here. SOURCE REACHED. The version of record is deposited in KOPS, the Konstanz Online Publication System of the University of Konstanz, and was read in full for this sheet; the summary, the claims and the locators come from that reading and use the paper’s own equation and figure numbers. All authors write from the Department of Physics and the Center for Applied Photonics, University of Konstanz. The work was supported by European Research Council Advanced Grant 290076 ’UltraPhase’, by the Deutsche Forschungsgemeinschaft SFB767, and by an NSF postdoctoral fellowship for D. V. Seletskiy. The skeleton for this sheet dropped the ninth author, Alfred Leitenstorfer, who is the corresponding author; the full list is restored above from the article itself.

How to cite it

C. Riek, D. V. Seletskiy, A. S. Moskalenko, J. F. Schmidt, P. Krauspe, S. Eckart, S. Eggert, G. Burkard, A. Leitenstorfer (2015) Direct sampling of electric-field vacuum fluctuations doi:10.1126/science.aac9788

Where it sits in the curriculum

What the vacuum is