Proof-of-principle demonstration of a Polarization-Circulation Speed Meter

TL;DR

This work addresses the challenge of quantum back-action in precision motion sensing by implementing a polarization-circulation speed meter in a simplified single-cavity setup. The authors stabilize the polarization circulation cavity with a green-locking scheme and demonstrate a lock-acquisition procedure that enables speed-meter operation, validating the concept by injecting a pseudo-displacement and measuring the transfer function $H(f)=\frac{\gamma_{\mathrm{cut}}/2\pi - i f}{\gamma_1/2\pi - i f}$. The results show the observed transfer function exhibits the expected frequency dependence and agree with the theoretical model, with fitted parameters such as a main-cavity loss of $\mathcal{L}_{\mathrm{cav}} \approx 85$ ppm and a spectral behavior consistent with back-action cancellation. This proof-of-principle study confirms the feasibility of polarization-circulation speed meters and suggests the control scheme can be extended to more complex configurations like Michelson interferometers and suspended-mirror systems, offering a practical pathway toward quantum-limited speed measurements in gravitational-wave detectors.

Abstract

We present the first experimental implementation of a polarization-circulation speed meter. In our experiment, the interferometer was reduced to a single-cavity configuration with all mirrors fixed. A green-locking scheme was employed to stabilize the polarization circulation cavity, and a lock-acquisition procedure was demonstrated to realize speed-meter operation. The system was characterized by measuring the transfer function from a pseudo-displacement signal to the photodetector output, confirming that the device measures the speed of mirror motion. These results support the feasibility of polarization-circulation speed meters and suggest that the control scheme could be extended to more complex configurations, such as Michelson interferometers and suspended-mirror systems.

Figures (8)

• Figure 1: Toy models of the (a) position and (b) speed measurement. (c) Schematic of the polarization-circulation speed meter. For the direction of circulation, see the main text. Abbreviations: ITM, input test mass; ETM, end test mass; BS, beam splitter; QWP, quarter-wave plate; PBS, polarization beam splitter; PCM, polarization circulation mirror; HD, homodyne detector.
• Figure 2: Schematic of the experimental setup. Red lines represent the 1064 nm laser beam. The solid red line indicates the main beam used to lock the main cavity, while the dashed red line indicates the signal beam that carried the phase signal. The main beam is injected through the polarization beam splitter (PBS), and the PDH signal is derived from the transmission of the polarization circulation mirror (PCM). The signal beam is picked off from the main beam and injected from the anti-reflective side of the end test mass (ETM) after being modulated by the broadband electro-optic modulator (bEOM). The green (GR) beam is injected from the anti-reflective side of the PCM and resonated inside the polarization circulation cavity (PCC). Gray lines represent electrical signals. The cyan shaded area is where we zoom into in Fig. \ref{['fig:evaluation_schemes']}.
• Figure 3: Phasor diagram. The modulated input sidebands, shown in dashed arrow were denoted as $e_\mathrm{in}$. The first circulation field had a transfer function of $f_\mathrm{pm}$, and the second circulation field had an additional factor $\rho$. The measured transfer function was obtained by taking the beat note between the sideband and the main IR field.
• Figure 4: (a) Path of the main IR beam. The input state was p-pol. The photodetector behind the ETM monitored the transverse mode leaking from the main cavity. Approximately 1% of the light transmitted through the PCM and was used for frequency locking of the main cavity via the PDH method. (b) Path of the signal IR beam. The input, denoted as $e_\mathrm{in}$, was demodulated by the broadband EOM. The QWP converted the input s-pol to r-pol, and the PBS transmitted half of the light (first circulation). The remaining component, which was s-pol, was recycled back into the cavity and transmitted through the PBS at the end. The interference between the first and second circulations was detected as $e_\mathrm{out}$. (c) Path of the GR beam. The wave plate functioned as a half-wave plate (HWP). The input s-pol beam was converted to l-pol by the HWP and then converted back to s-pol. In this way, the GR beam resonated inside the PCC, allowing the PDH method to be employed. The ITM transmissivity at 532 nm was chosen to be sufficiently low so that the GR beam did not simultaneously resonate in the main cavity. (d) Setup for evaluating the out-of-loop noise. The PCC was locked by the GR beam. A polarizer placed inside the cavity selected a linear polarization, forming a Michelson-type interferometer in the polarization domain. By taking the interference between the circulating IR beams, the setup measured the path fluctuation of the PCC.
• Figure 5: Schematic of lock acquisition. Each of the four panels shows the stored power in the cavities as a function of light frequency. The dashed red and solid purple curves indicate the resonances of the main cavity and the PCC for the main IR beam, respectively. The solid green curve shows the resonance of the PCC for the GR beam. In each panel, the translucent shapes indicate the states prior to each procedure.