Reaching the quantum noise limit for interferometric measurement of optical nonlinearity in vacuum

Quantum Electrodynamics predicts that the vacuum must behave as a nonlinear optical medium:the vacuum optical index should increase when vacuum is stressed by intense electromagnetic fields.The DeLLight (Deflection of Light by Light) project aims to measure it by using intense and ultra-short laser pulses delivered by the LASERIX facility at IJCLab (Paris-Saclay University). Theprinciple is to measure by interferometry the deflection of a low-intensity probe pulse when crossingthe vacuum optical index gradient produced by an external high-intensity pump pulse. The detectionof the expected signal requires measuring the position of the interference intensity profile with a highspatial resolution, limited by the ultimate quantum noise. However, the spatial resolution is highlydegraded by the phase noise induced by the mechanical vibrations of the interferometer. In order tosuppress this interferometric phase noise, we have developed a new method, named High-FrequencyPhase Noise Suppression (HFPNS) method, based on the use of a delayed reference signal to correctany noise-related signal appearing in the probe beam. In this work, we present the experimentalvalidation of this novel method. The results demonstrate a robust path toward picometer-scalesensitivity and provide a key step toward the observation of QED-induced vacuum refraction.

💡 Research Summary

The paper reports on the experimental progress of the DeLLight project, which aims to observe the QED‑predicted nonlinear optical response of the vacuum. In QED, virtual electron‑positron pairs render the vacuum a medium whose refractive index increases under intense electromagnetic fields. To detect this tiny effect, the authors use ultra‑intense femtosecond pump pulses (2.5 J, 30 fs, focused to a 5 µm waist) from the LASERIX facility to create a peak electric field of order 2 × 10²⁰ W cm⁻². A low‑intensity probe pulse co‑propagates through the same interaction region. The probe is injected into a Sagnac interferometer, where the two counter‑propagating beams interfere destructively at the dark output. Because the beamsplitter is not perfectly balanced, a residual interference signal remains; its intensity relative to the input defines the extinction factor F. The smaller F, the larger the amplification factor A ≈ F⁻¹/², which magnifies the probe’s transverse shift caused by the vacuum index gradient. With an experimentally achieved F ≈ 4 × 10⁻⁶, the expected QED‑induced shift of about 15 pm is amplified to roughly 3.8 nm, making it in principle detectable.

In practice, however, the spatial resolution is dominated not by quantum shot noise (≈15 nm for the best CCD) but by phase noise arising from mechanical vibrations of the interferometer. These vibrations produce a relative lateral displacement Δy_Φ between the probe and reference beams, which, after amplification, overwhelms the signal by three orders of magnitude. Conventional passive isolation would need to improve vibration levels by two orders of magnitude, an impractical engineering challenge.

To overcome this, the authors introduce the High‑Frequency Phase Noise Suppression (HFPNS) technique. The incoming probe pulse is split into two identical copies; one copy is delayed by ≈5 ns using a pair of beamsplitters and mirrors. Because the delay is much shorter than the vibration period, both copies experience the same instantaneous interferometric phase noise. The delayed copy, however, does not overlap temporally with the pump pulse and therefore does not acquire the QED‑induced deflection Δy_QED. By recording the interference patterns of both the prompt and delayed pulses on the same CCD (the delayed pulse’s polarization is switched with a high‑speed electro‑optic modulator and separated with a polarizing beamsplitter), the authors obtain two intensity profiles:

I_P(y) = F · I_in(y + Δy_BP + Δy_Φ + Δy_QED)
I_D(y) = F · I_in(y + Δy_BP + Δy_Φ),

where Δy_BP denotes beam‑pointing fluctuations. Subtracting the barycenters of these two profiles removes both Δy_BP and Δy_Φ, leaving only the pure QED signal Δy_QED. The experimental implementation includes a spatial filter (telescope + 300 µm pinhole) to enforce a near‑Gaussian beam, a set of 100 mm and 200 mm focal length lenses for focusing, and a CCD (Basler acA3088‑16gm) with 5.84 µm pixels. The extinction factor is tuned to F ≈ 4 × 10⁻⁴ by rotating the beamsplitter by ~1°, balancing the need for sufficient signal intensity against CCD saturation due to back‑reflections.

Measurements demonstrate that the delayed and prompt interferograms share identical phase‑noise‑induced shifts, and after offline subtraction the residual spatial jitter falls to the shot‑noise limit (σ_y ≈ 15 nm). With a 10 Hz laser repetition rate, a four‑day data acquisition yields a 1σ sensitivity sufficient to resolve the predicted Δy_QED ≈ 15 pm. Thus, the HFPNS method successfully suppresses vibration‑induced phase noise without requiring extreme mechanical isolation, achieving picometer‑scale position sensitivity.

The work constitutes a crucial step toward the first direct observation of vacuum optical nonlinearity. Future improvements—higher pump energies, better extinction (F ≈ 10⁻⁶), and longer integration times—should enable a statistically significant detection of the QED‑predicted refractive‑index increase, opening new experimental avenues in quantum electrodynamics, high‑field physics, and precision metrology.