Towards a temperature-insensitive composite diamond clock

Abstract

Frequency references based on solid state spins promise simplicity, compactness, robustness, multifunctionality, ease of integration, and high densities of emitters. Nitrogen-vacancy (NV) centers in diamond are a natural candidate, but the electronic zero-field splitting exhibits a large fractional temperature dependence, which has precluded its use as a stable clock transition. Here we show that this limitation can be overcome by forming a composite frequency reference that combines measurements of the electronic splitting D with the nuclear quadrupole splitting of the $^{14}$N nuclear spin intrinsic to the NV center. We further benchmark this composite approach against alternative strategies for mitigating temperature sensitivity. By implementing a specially designed pulse sequence with an eight-phase control scheme that suppresses pulse imperfections, we interleave measurements of D and Q in a high-density NV ensemble and demonstrate a temperature-compensated composite frequency reference. The stability of this composite diamond clock is characterized over a 10-day period at room temperature through a comparison to a Rb vapor-cell clock, yielding a fractional instability below $5 \times 10^{-9}$ for an averaging time of $τ= 200$ s and below $1 \times 10^{-8}$ at $τ= 2 \times 10^5$ s, corresponding to measured improvements by a factor of 4 and 200, respectively, over a clock based purely on the single frequency D for the same periods. By characterizing the residual sensitivity to magnetic fields, optical power, and radio-frequency drive amplitudes, we find that temperature is no longer the dominant source of instability. These results establish complementary electron- and nuclear-spin transitions in diamond as a viable route to thermally robust frequency metrology, providing a pathway toward compact, multifunctional solid-state clocks and quantum sensors.

Figures (6)

• Figure 1: Composite clock operating principle.(a) The NV ground state energy level diagram at 475G. The zero-field splitting parameter $D$ is measured via the electron-spin microwave transitions $f_+$ and $f_-$. The nuclear electric quadrupole parameter $Q$ is measured via the nuclear-spin RF transitions $f_1$ and $f_2$ within the nuclear sublevels of the $m_s = 0$ state. (b) Conceptual block diagram for constructing a composite clock based on $D$ and $Q$. Drifts in the local oscillator can be tracked and corrected by monitoring $\tfrac{1}{2}(\delta f_+ + \delta f_-) \approx \delta D$ and $\tfrac{1}{2}(\delta f_1 + \delta f_2) \approx -\delta Q$, and combining them ($\delta \psi / \psi$) in such a way as to be insensitive to thermal fluctuations, while correcting for fluctuations of the local oscillator. The dimensionless quantity $\alpha$ is a constant whose value is determined by the relative fractional temperature sensitivities of $D$ and $Q$, and is defined in Eq. \ref{['eq:psi_fractional']}. The physics package is depicted in Fig. \ref{['fig:Appendix Experimental Setup']}.
• Figure 2: Diamond-based frequency reference measurement protocol.(a) The two-tone zero-field splitting-8 (TTZFS-8) pulse sequence. For both $D$ and $Q$ measurements are performed by optically polarizing the spin (into $\ket{m_s = 0}$ for $D$MAN2006, $\ket{m_I = +1}$ for $Q$JAC2009). For measuring $Q$, the polarized nuclear spin is transferred to $\ket{m_I=0}$ using an $f_1$$\pi$-pulse, with duration of $\pi/\Omega_{SQ}$, where $\Omega_{SQ}$ is the single-quantum Rabi frequency. After being prepared in $\ket{0}$ ($\ket{m_s=0,m_I=+1}$ for $D$, $\ket{m_s=0,m_I=0}$ for $Q$), the half-sum frequency splitting, $\tfrac{1}{2}(f_+ + f_-) \approx D$ or $\tfrac{1}{2}(f_1 + f_2) \approx Q$, is measured using the two-tone $\pi/2-2\pi-\pi/2$ pulse sequence (durations of $\pi/2\Omega_{DQ}$, $2\pi/\Omega_{DQ}$, $\pi/2\Omega_{DQ}$, where $\Omega_{DQ} = \sqrt{2} \Omega_{SQ}$ is the double-quantum Rabi frequency), followed by optical readout. (b) The required phases for each of the six pulses in the $\pi/2-2\pi-\pi/2$ pulse scheme to cancel out unwanted signals arising from pulse imperfections due to RF gradients. (c) Amplitude spectrum obtained by performing the pulse sequence on the nuclear spin ($Q$) and scanning $\tau$. The implementation of phase control using eight sequences (lower) suppresses several unwanted frequencies present in a single measurement (upper). The single phase plot has been scaled by a factor of eight to keep the amplitude of the desired frequency component fixed. (d) Time domain plots of TTZFS-8 measurements of $Q$, $D$ showing undersampled (aliased) oscillations decaying due to decoherence with experimental data (markers) and fits (line).
• Figure 3: Stability of single-transition and composite clocks based on $D$ and $Q$. Measurements of fluctuations in units of temperature of $D$, $Q$, and their difference over a 10-day period (top) and their corresponding Allan deviations in fractional units (bottom). The composite clock signal $\delta \psi/\psi$ based on $D$ and $Q$ exhibits better stability than either $\delta D/D$ or $\delta Q/Q$ after $200s$, achieving at least 1-2 orders of magnitude suppression of temperature fluctuations.
• Figure 4: Mitigation of temperature-induced fluctuations in $D$. Time-domain frequency shifts of $D$ measured (a) at room temperature without active temperature stabilization, showing the raw signal (black), the cryostat temperature measured at the cold finger (blue), and the temperature-compensated signal (yellow); (b) at liquid-nitrogen temperature without temperature stabilization; and (c) at room temperature with active stabilization to 300K. (d) Corresponding fractional Allan deviations for the uncompensated (black), temperature-compensated (yellow), uncompensated at liquid-nitrogen temperature (pink), and temperature-stabilized (green) measurements.
• Figure 5: Schematic of the experimental setup. A balanced photodetector measures changes in fluorescence relative to incident green light (532nm). The Halbach array produces a magnetic field of $\sim475G$ that is aligned to one of the NV orientations and perpendicular to the incident light. RF and MW signals are delivered to the ensemble of NV centers with a copper wire of diameter 160µ m placed near the optical focus.