Can a diamond-filled optical cavity stay stable at millikelvin in a cryogen-free fridge?

The cavity follows the laser, not the reverse

Most cryogenic cavity work locks a laser onto a cavity resonance. Here the feedback loop runs the other way: a frequency-stabilized laser serves as the reference, and a piezo actuator adjusts the cavity length so its resonance tracks the laser. The authors argue this direction matters for quantum transducers, because locking a laser to a cavity lets the converted photon frequency drift with the cavity, which can degrade fidelity or reduce the generation rate of remote entanglement.

The cavity itself is a Fabry-Pérot resonator: two highly reflective mirrors facing each other, with light bouncing between them so that only certain resonance frequencies pass. The team built two versions, a bare cavity and one with a bulk diamond crystal inside. Both sat on the mixing-chamber plate of a cryogen-free dilution refrigerator, and both were stabilized using a standard Pound-Drever-Hall scheme with a 150 MHz phase modulation and a digital PID controller driving the piezo.

Pulse-tube vibration is the obstacle being tested

A cryogen-free dilution refrigerator reaches millikelvin temperatures without a liquid-helium bath, but its pulse-tube cryocooler introduces mechanical vibration that is hard on an optical cavity. The paper treats this as the central difficulty rather than a side note. The authors report peak-to-peak relative length fluctuations of about 60 nm with the pulse tube on and about 10 nm with it off, measured with an interferometer at the mixing chamber.

Their mitigation is largely mechanical and does not require major cryostat modification. An optical breadboard sits on top of the refrigerator on the same thick aluminum plate that supports the fridge body, so the cavity device and the tabletop optics move together in common mode. The helium compressor was moved about 4 meters away behind a soundproof wall, T-dampers were fitted to the vacuum lines, the pulse-tube motor valve and buffer tanks were anchored to the building frame, and an active damping system cancels displacement between 1 Hz and 200 Hz.

Length stability sets a finesse ceiling

The headline numbers are length fluctuations, not finesse. The authors convert them into an achievable finesse, which is the quantity that tells a reader how lossy a cavity could be while still staying locked. Finesse here means how many times light circulates inside the cavity before leaking out; a higher finesse means a narrower resonance and a smaller tolerable length error.

Using the measured average cavity length fluctuations of 27.6±3 pm for the bare cavity and 69.3±3.6 pm with the diamond, the paper estimates the setup could stabilize a cavity up to a finesse of 1.3×10⁴ without diamond and 5.3×10³ with it. The abstract quotes slightly different rounded values, 1.2×10⁴ and 5.8×10³, so the two sets should be read as the same estimate expressed at different rounding. The diamond roughly halves the tolerable finesse, and the reason is not vibration but optical loss.

Diamond absorption, not vibration, caps the diamond cavity

The diamond-integrated cavity was measured with a finesse of about 90, far below the 310 of the bare cavity. The paper attributes this primarily to absorption loss inside the diamond rather than to the cryostat's motion. That distinction matters: better vibration isolation would not fix a finesse of 90, but a cleaner crystal could.

The sample details support the loss story. It is a chemical-vapor-deposition single crystal measuring 4.5 × 4.5 × 0.5 mm, aligned to the [001] orientation, with substitutional nitrogen P1 centers below 1 ppm and other color centers expected to be negligible. One face carries an anti-reflective coating (R<0.25% at 737 nm) and the other a highly reflective coating (R=99±0.5% at 737 nm), both deposited by ion beam sputtering. Surface roughness rose from Rq≈0.3 nm after mechanical polishing to Rq≈1.5 nm after coating. The authors suggest a diamond with fewer defects could reduce the absorption.

The lock held for hours, with a caveat

Short demonstrations can hide slow drift, so the authors also recorded a bare cavity locked for more than one hour. The locked error and transmission signals stayed stable across that run, and the small deviation observed was attributed to a drift in laser power rather than to a loss of lock. They state the cavity can remain locked for hours without re-locking.

The mechanical picture is less settled. A Bode-analyzer sweep of the locked cavity found resonances mainly at high frequency, around 6 kHz, 18 kHz, and 30 kHz for the bare cavity and clusters near 6 kHz and 12 kHz with the diamond. A COMSOL model of the assembly, including a roughly 280 mm copper thermalization tube, predicted modes from a few kHz to tens of kHz and an example near 8 kHz, but could not reproduce the exact measured frequencies. The authors point to unknown cryogenic parameters, such as the spring constant and amount of vacuum grease, as likely causes.

What the demonstration does and does not establish

The result is a stability measurement, not a working transducer. The paper frames stable cavity-to-laser locking at millikelvin and stabilization of a bulk-diamond cavity as two advances toward practical spin-based microwave-optical transducers, and it does not report photon conversion efficiency or entanglement fidelity. The finesse figures are estimates of what the measured length noise would allow, not cavities that were built and locked at those finesse values.

Two practical boundaries sit close to the result. The diamond cavity's finesse of about 90 is limited by absorption, so the 5.3×10³ estimate describes the vibration budget rather than the current optical performance. And the cavity assembly is manually placed on a sapphire disk with a small amount of vacuum grease at the edge, which the authors note likely changes the cavity arrangement between cooldowns. That makes cooldown-to-cooldown reproducibility a separate question from the lock stability demonstrated within a run.

The priority is lock direction plus a bulk diamond

For readers weighing this against other cryogenic cavity work, the distinguishing combination is not the millikelvin temperature alone but three things together: a cryogen-free fridge with the pulse-tube running, a cavity locked to a laser rather than a laser to a cavity, and a bulk diamond crystal inside the resonator. The bare-cavity result of 27.6±3 pm shows the vibration strategy works; the diamond result of 69.3±3.6 pm shows how much margin the crystal costs.

The most decision-relevant comparison is therefore between those two numbers and their causes. The gap between them is a loss problem in the diamond, addressable in principle by a crystal with fewer defects, while the absolute level is a vibration problem addressed by common-mode mounting and passive and active damping. A reader planning a similar setup should treat the 5.3×10³ diamond finesse estimate as the vibration-limited ceiling and the measured finesse of about 90 as the current optical ceiling, and should expect the two to be closed by different fixes.

Sources used in this answer