Demonstration of an interferometric technique for measuring vacuum magnetic birefringence with an optical cavity

TL;DR

This paper proposes and validates a three-resonance interferometric technique to measure vacuum magnetic birefringence (VMB) by tracking frequency shifts of lasers stabilized to a high-finesse optical cavity, leveraging a string of ALPS II magnets. The method decouples cavity-length noise from the birefringence signal by using three resonances and a heterodyne readout, enabling extraction of the VMB-induced differential refractive index change from beatnote fluctuations. A 19 m prototype demonstrates the feasibility, achieving low-frequency differential-length sensitivities and measuring the cavity’s static birefringence ($\Delta\theta \approx 3.38\times10^{-6}$ rad) through controlled polarization rotation. Extrapolations indicate that, with RAM suppression and other upgrades, the approach could reach the $\sim10^{-17}$ m/√Hz differential length sensitivity required to detect the QED-predicted VMB signal of $\Delta L_{\rm VMB} \approx 2.37\times10^{-20}$ m in the 245 m ALPS II magnet string, enabling a potential macroscopic test of QED and probes of beyond-Standard-Model physics.

Abstract

The vacuum magnetic birefringence effect is a prediction of quantum electrodynamics, that in the presence of a magnetic field vacuum behaves as a non-linear medium, exhibiting a birefringence. In this work, an experiment is proposed to measure this effect for the first time, by sensing the changes in the frequencies of laser fields stabilized to the resonances of a 245 m long optical cavity whose eigenmode propagates through a string of 24 superconducting magnets arranged for the ALPS II experiment. Results from a prototype setup using a 19 m test cavity without a magnetic field are presented and projected in terms of the sensitivity of the proposed full-scale experiment.

Figures (7)

• Figure 1: (a) Plot of the magnetic field while modulating the ALPS II magnetic string. (b) Projected signal in terms of the changes in the differential cavity length for orthogonal polarization states $\delta L_{_{\rm VMB}}$.
• Figure 2: The diagram in (a) shows the frequencies of the all fields in the birefringence measurement scheme, at the detection port of the cavity. The fields $E_{p_-}$, $E_{s_0}$, and $E_{p_+}$ are all stabilized to different cavity resonance separated by a fixed number of FSRs, while the local oscillator field $E_{h}$ is phase locked looped to $E_{s_0}$ at a frequency $f_{\rm PLL}$ such that it is not resonant with the cavity. In (b) an exaggerated diagram of the sources of fluctuations in the frequency of the cavity resonance probed by $E_{s_0}$ are shown, including the dynamic birefringence noise of the cavity $\delta\nu_{_{\theta}}$, and the birefringence signal generated by the VMB effect $\delta\nu_{_{\rm VMB}}$.
• Figure 3: A diagram of the layout of the optical system for the measurement. The fields $E_{p_-}$ and $E_{p_+}$ are generated by frequency shifting laser L1 using AOMs in a double pass configuration (not shown). The field $E_{s_0}$ is provided by laser L2. All three fields are frequency stabilized to a different resonance of a 19 m optical cavity. The interference beatnotes for the birefringence measurement are sensed using the photodetector $\rm PD_t$ and their frequencies are readout using digital phasemeter 1.
• Figure 4: A diagram of the frequencies of the fields present at the photodetector $\rm PD_t$ for the actual experimental setup that was used in the measurement. To perform the three resonant measurement of the birefringence effects in the cavity, the interference beatnotes at $f_+$ and $f_2$ where measured.
• Figure 5: Shown above are a time series (a), Allan deviation (b), and amplitude spectral density (c) of the measurement of the frequency drifts of the interference beatnotes. Here the $\delta f_+$ is shown in blue, $\delta f_2$ is shown in green, and the normal measurement of $2\,\delta f_+-\delta f_2$ is shown in red-orange and a separate null measurement of $2\,\delta f_+-\delta f_2$ is shown in yellow. The calibrated feedback control signal sent to the laser temperature is shown in purple. The out-of-loop noise of measured in the $E_{p_+}$PDH frequency stabilization loop is shown in light blue.