Historical research guide · 0501 · 2023

Back action in quantum electro-optic sampling of electromagnetic vacuum fluctuations

T. L. M. Guedes · I. Vakulchyk · D. V. Seletskiy · A. Leitenstorfer · A. S. Moskalenko · Guido Burkard

In one minute

Electro-optic sampling is how the mid-infrared vacuum gets measured directly: a laser pulse shorter than one cycle of the field it probes crosses a nonlinear crystal, and the vacuum’s own electric field tilts the pulse’s polarisation by an amount you can read. Thiago Guedes, Alfred Leitenstorfer, Andrey Moskalenko, Guido Burkard and their colleagues ask the question every such measurement owes an answer to — how much does the probe disturb the thing it is probing? They follow the cascade of extra fields the probe builds inside the crystal, for setups using one probe beam and two. The answer is a window. Use too few photons per pulse and shot noise buries the signal; use too many, past roughly a hundred billion, and the probe starts manufacturing the mid-infrared photons it is meant to be listening to. Between the two lies a regime the authors call effectively back-action free. In the two-beam correlation experiment the base shot noise drops out of the averaged signal completely, and at the photon numbers actually used the disturbance is negligible.

Connection

Chapter 2 rests on the claim that the vacuum is a real, measurable medium rather than a bookkeeping device, and this paper is the discipline behind that claim: it works out precisely where the reading is the vacuum and where it is the instrument’s own echo. That is chapter 1’s evidence ladder applied to the most delicate measurement on the site — and it hands experimenters a number, an upper limit on probe intensity, to design to.

From the source

Electro-optic sampling of the electromagnetic ground state works by imprinting information about a multimode quantum state onto the ellipticity of a subcycle coherent pulse at a higher frequency, and because the nonlinear interaction couples optical modes both between and within channels — each an infinite, continuous set of modes — the back action can diverge considerably from the optomechanical-cavity case.Section I, Introduction, paragraphs 3 and 4
Back action on the mid-infrared states is inherent to the electro-optic measurement, yet the detected mid-infrared signal variance can be considered effectively back-action free — a weak measurement — provided the perturbation of those states stays small.Section VI, Conclusions
There is an upper limit to usable probe intensity. Back action begins to dominate roughly where the main electro-optic signal variance becomes comparable to the base shot noise — near 1.6 hundred billion photons per pulse for the first parameter set and 6.4 hundred billion for the second — and past that point raising the probe intensity is detrimental rather than helpful, because base shot noise and main signal are both rapidly overtaken by cascaded effects.Section III, Single-channel results; Figure 2a and 2b
In the two-channel setup the vacuum fluctuations entering at the beam splitter leave the shot noise of the two probe pulses uncorrelated, so the base shot noise does not contribute to the correlation signal at all once many readout events are averaged — although further contributions from nonlinear shot-noise enhancement remain.Abstract; Section IV, Two-channel model
At the probe photon numbers actually used in the reported experiments — around a hundred million per pulse — higher-order contributions to the two-channel correlation function are negligible; they only become comparable to the second-order contribution near a hundred billion photons per pulse.Section V, Two-channel results
Because the measurement itself creates mid-infrared photons, electro-optic sampling is not straightforwardly a quantum nondemolition measurement: a postselection scheme is needed to filter the components of the sample in which no photons were generated, and further back-action evasion by postselection is the authors’ named next step.Section VI, Conclusions, closing sentences

The way in

https://doi.org/10.1103/PhysRevResearch.5.013151

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

Licence confirmed from the statement printed on page 1 of the published article: ‘Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.’ Reproduced from the version of record. The abstract, introduction, results sections and conclusions are given in full; the operator algebra of Section II and Appendices A to G is omitted for length, and equations that do not survive plain text are stated as named results in the authors’ own terms. Figures are described in the authors’ own captions rather than reproduced.

How to cite it

T. L. M. Guedes, I. Vakulchyk, D. V. Seletskiy, A. Leitenstorfer, A. S. Moskalenko, Guido Burkard (2023) Back action in quantum electro-optic sampling of electromagnetic vacuum fluctuations doi:10.1103/PhysRevResearch.5.013151

Where it sits in the curriculum

What the vacuum is