Lu+ Optical Frequency References Achieve Record 19th-Digit Accuracy

Experimental Sequence and State Preparation

Interrogations begin after both ions undergo Doppler cooling and preparation into the |g⟩ state with greater than 99% probability using a conditional state preparation sequence, as detailed in reference 53. According to experimental documentation, both ions experience the HA–HR sequence where parameters measure roughly $tau_{text{L}} approx 4,text{ms}$, $tau_1 = tau_2 approx 12,text{ms}$, and a total Ramsey time calculated as $T_{text{R}} = 3(T + tau_1 + tau_2)$. Frequency references are compared by measuring parity alternately for $phi = pmfrac{pi}{2}$ and steering $Pileft(frac{pi}{2}right) – Pileft(-frac{pi}{2}right)$ to zero after $N$ interrogation cycles by updating $delta f$.

For comparisons at a 0.1 mT magnetic field, microwave drive frequencies $f_1$ and $f_2$ remain identical and fixed for both ions. When evaluating the quadratic Zeeman coefficient $alpha_z$ across different magnetic fields, microwave frequencies differ to compensate for quadratic Zeeman shifts. An acousto-optic modulator designated as AOM 2a sets the frequency difference $delta f$. Interleaved auxiliary measurements include Rabi spectroscopy of the $|grangle leftrightarrow |8rangle$ optical transition to keep the 848 nm clock laser near resonance, alongside microwave spectroscopy to measure the $|^3text{D}_1, 6, pm 1rangle$ Zeeman splitting for each ion.

Magnetic Field Stability and Servo Control

Short-term magnetic field evaluation shows flicker instability of approximately 7 nT across Ramsey times spanning 1 to 50 seconds, as reported in Extended Data Fig. 2. A compensation coil steers the field to a set point of $B_0 = 0.1,text{mT}$ with a typical servo attack time $t_{text{ser}} approx 80,text{s}$ using interleaved measurements of the $|^3text{D}_1, 6, pm 1rangle$ Zeeman splitting. Out-of-loop testing verified that the true field instability is limited by projection noise and deadtime scaling as $propto (t_{text{ser}}/tau)^{1/2}$. Beyond the servo attack time, the magnetic field introduces uncertainty via the quadratic Zeeman shift, calculated as $frac{deltanu_{text{QZ}}}{nu_0} = 2alpha_z B_0 delta B(tau) approx 2 times 10^{-19} times (tau/text{s})^{-1/2}$.

Collision Detection and Background Gas Analysis

Adaptive Bayesian state detection using 646 nm fluorescence monitors background gas collisions at the end of every Ramsey cycle. If an ion is detected dark during initial detection $d_0$, three shelving attempts occur on the 848 nm clock transition. If subsequent detection intervals $d_0 dots d_3$ remain dark, researchers assume a collision occurred that reduced coupling on the 848 nm transition or lowered the 646 nm fluorescence rate. Valid interrogation cycles exclude any run where a collision is registered on either Lu-1 or Lu-2.

Estimated detectable collision rates $Gamma$ reach $1.9 times 10^{-3},text{s}^{-1}$ for Lu-1 and $5.9 times 10^{-3},text{s}^{-1}$ for Lu-2 based on measurement campaign data. Independent ground-state evaluations after a 5-second delay yielded direct collision rates of $2.9(3) times 10^{-3},text{s}^{-1}$ for Lu-1 and $6.5(6) times 10^{-3},text{s}^{-1}$ for Lu-2. Langevin collision rates $Gamma_{text{L}}$ are calculated at $1.3 times 10^{-3},text{s}^{-1}$ and $2.1 times 10^{-3},text{s}^{-1}$ respectively, pointing to molecular hydrogen background pressures of 3.5 nPa and 5.8 nPa at 300 K.

Trap Frequencies and Thermal Doppler Shifts

Modifications to helical resonators lowered the RF-drive frequency $Omega_{text{RF}}$ while increasing trap confinement without requiring higher RF power. Operating at $0.25,text{W}$ of RF power with $Omega_{text{RF}} = 2pi times 9.4,text{MHz}$ for Lu-1 and $11.2,text{MHz}$ for Lu-2 yields secular trapping frequencies of $(207, 1063, 1134),text{kHz}$ and $(138, 492, 543),text{kHz}$. Thermal motion produces a second-order Doppler shift (SODS) determined by axial and radial temperatures. Initial axial temperatures measure $190.5(5.9),mutext{K}$ for Lu-1 and $189.6(4.7),mutext{K}$ for Lu-2, with axial heating rates of $73(14),mutext{K},text{s}^{-1}$ and $119(17),mutext{K},text{s}^{-1}$ respectively.

Systematic Evaluations and Environmental Controls

Systematic frequency shifts undergo continuous evaluation to protect clock accuracy. Blackbody radiation (BBR) shifts rely on well-characterized differential dynamic polarizability for the 848 nm clock transition in $^{176}text{Lu}^+$. Temperature assessments bound operational ranges between $[299.8, 303.2],text{K}$ for Lu-1 and $[299.6, 301.9],text{K}$ for Lu-2. Excess micromotion (EMM) modulation depths measured via phase-modulated sideband spectroscopy indicate average relative shifts of $-1.6(1.3) times 10^{-20}$ for Lu-1 and $-1.4(0.4) times 10^{-20}$ for Lu-2. Autler-Townes splitting measurements on microwave transitions quantify transverse oscillating magnetic fields, establishing root-mean-square perpendicular RF magnetic field amplitudes $sqrt{langle B_perp^2 rangle}$ for Lu-1 and Lu-2.

Frequently Asked Questions

What is the primary role of Ramsey interrogation in lutetium ion clocks?

Ramsey interrogation sequences allow researchers to compare two independent frequency references by measuring atomic parity and stabilizing laser frequencies over extended dark times.

How do researchers mitigate background gas collisions?

Adaptive Bayesian state detection via 646 nm fluorescence identifies collision events by monitoring shelving failures on the 848 nm clock transition, invalidating and repeating compromised cycles.

What limits the short-term stability of the magnetic field?

Short-term stability is constrained by flicker instability around 7 nT, projection noise, and deadtime during active servo compensation.

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