Stabilizing an optical cavity containing a bulk diamond crystal at millikelvin temperatures in a cryogen-free dilution refrigerator

TL;DR

This work tackles the challenge of stabilizing optical cavities inside a cryogen-free dilution refrigerator by locking the cavity to a laser and employing a top-platform breadboard to enforce common-mode vibrations. The authors demonstrate stable locking for both a bare cavity and a diamond-integrated cavity at millikelvin temperatures, achieving cavity-length fluctuations on the tens-of-picometers scale and inferring finesses up to F ≈ 1.2e4 (bare) and F ≈ 5.8e3 (diamond). They identify absorption within the bulk diamond (α ≈ 0.15 cm⁻¹) as the primary loss source in the diamond cavity and discuss mitigation strategies such as using lower-defect diamonds or thinner crystals. This work enables practical microwave-optical transduction using diamond spin ensembles in cryogenic environments and paves the way for robust, vibration-tolerant quantum photonics in cryogen-free platforms.

Abstract

We successfully stabilized a Fabry-Pérot optical cavity incorporating a bulk diamond crystal at millikelvin temperatures in a cryogen-free dilution refrigerator with the pulse-tube cryocooler running. In stark contrast to previous demonstrations where lasers were locked to the cavities, our setup locks the cavity to a laser. Our measurements of cavity length fluctuation suggest that the setup could stabilize a cavity up to a finesse of $1.2\times 10^4$ without the diamond and $5.8 \times10^3$ with the diamond crystal. The finesse with a diamond crystal of approximately 90 is primarily limited by the absorption loss inside the diamond.

Figures (14)

• Figure 1: The custom dilution refrigerator setup and vibration measurement. (a) Schematic of the custom dilution refrigerator. An active damping (AD) system supports an aluminum plate, on which both an optical breadboard and the main body of the refrigerator are mounted, suppressing the common-mode vibrations. A laser beam is directed inside via a 45-degree mirror. Different colored arrows indicate the propagation directions of the input, reflected, and transmitted light. The cavity is thermalized to the mixing chamber (MXC) plate through a cylindrical copper shroud. (b) Absolute vibrations measured on the MXC plate with a vibration sensor under three conditions: PT on with AD off, PT on with AD on, and PT off with AD on.
• Figure 2: Relative vibration measurement between the device on the MXC plate and the top optical breadboard. (a) Interferometer measurement setup. The reflected laser beam is directed to a fiber beam splitter (BS) through an optical circulator, combined with a local oscillator (LO), and detected by a photodetector (PD). (b) Relative displacement measurements at $15\,\mathrm{mK}$, comparing PT off with AD on (orange), PT on with AD on (blue), and PT on with AD off (black). (c) Amplitude spectral density (ASD) derived from the fast Fourier transform (FFT) of the data in (b). The black dashed line represents the universal $\mathcal{O} (f^{-2})$ behavior (see main text).
• Figure 3: Optical cavity device. (a) Cross-sectional view and (b) CAD rendering of the optical cavity housed in a gold-plated copper enclosure. The input mirror, an AR-HR coated mirror on a piezo actuator, is mounted on an invar ring [gray, photograph in (c)] and fixed to a threaded copper support for caivty length adjustment. The bottom mirror used for the 'bare-cavity' demonstration (Subsection \ref{['subsec:bareCavLocking']}) is also mounted on an invar ring and fixed to the bottom cavity housing. For the 'diamond-integrated cavity' demonstration (Subsection \ref{['subsec:DiaCavLock']}), the AR-HR coated diamond itself acts as the bottom mirror, mounted on a sapphire disk for thermalization and alignment using a small amount of vacuum grease [photograph in (d)]. Note that the bulk bottom mirror is unmounted in the 'diamond-integrated cavity'.
• Figure 4: PDH locking setup for the cavity. A frequency-stabilized laser is phase modulated by an electro optic modulator (EOM) and is directed into the fridge. Reflected light from the cavity is separated by an optical circulator and detected by an avalanche photodiode (APD). The detected signal generates an error signal through a mixer, fed into a digital PID controller, which provides feedback to the piezo actuator. The frequency response of the locked cavity is measured using a RedPitaya in Bode analyzer mode. All the optics are aligned on the fridge-top breadboard to maintain common-mode vibration.
• Figure 5: Cavity stability measurement at $15\,\mathrm{mK}$ for (a) the bare cavity and (b) the diamond-integrated cavity. The upper panels show the scanning (dark) and locking (light) results for the error signal (orange) and transmitted signal (blue). The scanning plots are stretched along the x-axis. The bottom panels display the cavity length fluctuations derived from the error signals, with root mean square (rms) values of $\approx 30\,\mathrm{pm}$ for the bare cavity and $\approx 63\,\mathrm{pm}$ for the diamond-integrated cavity. The higher finesse of the bare cavity corresponds to better sensitivity, resulting in larger error signal amplitudes in (a) compared to (b).