A terahertz vibrational molecular clock with systematic uncertainty at the $10^{-14}$ level

TL;DR

This work demonstrates a pure vibrational clock based on neutral Sr2 in a magic-wavelength optical lattice, achieving a total systematic uncertainty of $4.6\times10^{-14}$ and an absolute vibrational frequency near 32 THz. The approach combines two-photon Raman spectroscopy of a tightly bound vibrational transition with careful control of lattice-induced shifts, probe-light shifts, BBR, and density-dependent effects, anchored to a GPS-disciplined timebase for absolute frequency. The result includes a record-precision dissociation energy for $^{88}$Sr2, enabling refined molecular potential information and tests of molecular quantum electrodynamics. This milestone opens pathways for THz metrology with molecules and generalizes to other neutral molecular species for fundamental-physics investigations.

Abstract

Neutral quantum absorbers in optical lattices have emerged as a leading platform for achieving clocks with exquisite spectroscopic resolution. However, the studies of these clocks and their systematic shifts have so far been limited to atoms. Here, we extend this architecture to an ensemble of diatomic molecules and experimentally realize an accurate lattice clock based on pure molecular vibration. We evaluate the leading systematics, including the characterization of nonlinear trap-induced light shifts, achieving a total systematic uncertainty of $4.6\times10^{-14}$. The absolute frequency of the vibrational splitting is measured to be 31 825 183 207 592.8(5.1) Hz, enabling the dissociation energy of our molecule to be determined with record accuracy. Our results represent an important milestone in molecular spectroscopy and THz-frequency standards, and may be generalized to other neutral molecular species with applications for fundamental physics, including tests of molecular quantum electrodynamics and the search for new interactions.

Figures (8)

• Figure 1: Vibrational molecular lattice clock. (a) Raman lasers (upleg, red arrow; downleg, orange arrow) detuned from an intermediate state in $(1)0_u^+$ probe the two-photon vibrational clock transition between $(v=62, J=0)$ and $(v=0, J=0)$ in the $X^1\Sigma_g^+$ ground potential. The optical lattice (brown arrow) off-resonantly addresses an isolated rovibronic state in $(1)1_u$ to induce magic trapping conditions. (b) Experimental setup. The upleg master laser is stabilized to a reference cavity using the Pound-Drever-Hall (PDH) technique, and its phase coherence is transferred to the downleg laser via a frequency comb. The molecules are held in the 1D optical lattice. Co-propagating clock lasers are delivered to the molecules via an optical fiber with active fiber noise cancellation (FNC). The spectroscopic signal derives from absorption imaging of $X(62,0)$ photofragments at a slight grazing angle relative to the lattice. A Rb microwave standard acts as a flywheel oscillator, linking the molecular clock to GPS time for the absolute frequency measurement. Further information is given in the main text and Appendices \ref{['sec:atomicprep']} and \ref{['sec:ramanlaser']}. (c) Two-photon Rabi oscillations between the clock states driven at the operational probe intensities (filled circles, experimental data averaged over 8 consecutive runs, error bars represent $1\sigma$ uncertainties; solid red line, analytical fit to an exponentially decaying sinusoid). We observe lines as narrow as 11(1) Hz (inset, green squares). For clock operation, we perform Rabi spectroscopy with a 30 ms $\pi$-pulse duration (indicated by the black arrow), resolving 30(2) Hz linewidths consistent with the expected Fourier limit (inset, black open circles). Each point in the inset is a single shot of the experiment, and solid lines are Lorentzian fits.
• Figure 2: (Color online) Clock shifts due to the lattice light. (a) Nonlinear shifts of the molecular clock frequency versus trap depth. For a given lattice frequency (color coded), we make interleaved measurements of clock shifts (open circles) with respect to a reference trap depth ($\sim500\,E_r$), and fit the data to parabolas (solid lines) with a global quadratic parameter, $-\beta^*$. (b) Linear light shift coefficient, $\alpha^*$, versus lattice frequency (color code matches (a)), and the linear fit (black solid line). $\alpha^*$ is predominantly due to the $E1$ differential polarizability and is nulled at $f_\mathrm{zero}$. By tuning $\alpha^*$, we can find conditions where the sensitivity of $\Delta f_\mathrm{clock}$ to fluctuations in $U_0$ is minimal at our operational trap depth of 487(4) $E_r$ (dark green points). Error bars represent 1$\sigma$ uncertainties.
• Figure 3: Clock shifts at the operational Raman detuning as a function of (a) the upleg laser intensity, and (b) the downleg laser intensity. The horizontal axes are normalized by the respective operational intensities, $I_{\uparrow,0}$ and $I_{\downarrow,0}$. Solid lines are linear fits to the data. Residuals are plotted in units of Hz. Error bars represent 1$\sigma$ uncertainties.
• Figure 4: Density shift evaluation. (a) Clock shifts due to molecular collisions extrapolated to operating conditions (1 molecule per lattice site, averaged over filled sites), plotted versus the change in molecule number per site used for the interleaved measurement. A single constant suffices to fit the data (0.20(10) Hz, $\chi^2_\mathrm{red}=1.7$). (b) In the same dataset, the shift between successive resonances taken under identical experimental settings serves as a control experiment to check for technical offsets. As expected, this averages to zero (0.03(20) Hz, $\chi^2_\mathrm{red}=2.0$). All statistical errors are scaled up by $\sqrt{\chi^2_\mathrm{red}}$. Error bars represent 1$\sigma$ uncertainties. Both insets show the histogram of normalized residuals, and the solid red lines are Gaussian fits.
• Figure 5: (a) Absolute frequency of the clock transition measured over 10 trials (filled black circles) with all known frequency offsets corrected, including that of the local Rb timebase (see main text for details). Blue error bars are 1$\sigma$ statistical uncertainties, dominated by the determination of the comb repetition rate rather than the stability of the scanned molecular clock lines. Red error bars are 1$\sigma$ systematic uncertainties due to the molecular clock only (see Table \ref{['tab:systable']}). Black error bars are 1$\sigma$ total uncertainties, where the uncertainties of the local timebase calibrations are added in quadrature with the statistical and molecular clock systematic uncertainties. The black horizontal line shows the weighted average ($\chi^2_\mathrm{red} = 0.5$), and the shaded grey area shows the associated $\pm1\sigma$ standard error of the mean. (b) Histogram of all clock frequency measurements in the 10 trials, relative to the weighted average of $f_\mathrm{clock}$. The solid red line is a Gaussian fit to the histogram.