Sensing with discrete time crystals

Nat. Phys. 22, 367-373 (2026) · DOI: 10.1038/s41567-025-03163-6

License: CC BY 4.0.

Abstract

Prethermal discrete time crystals are non-equilibrium states of matter with long-range spatiotemporal order and a subharmonic response stabilized by many-body interactions under periodic driving. The robustness of time-crystalline order to perturbations in the drive protocol makes these systems attractive for quantum sensing. Here we exploit the sensitivity of prethermal discrete time crystal order to deviations in its order parameter to implement the frequency-selective detection of time-varying magnetic fields in a system of strongly driven, dipolar-coupled $^{13}$C nuclear spins in a diamond. Incorporating an oscillating field into the time crystal dynamics extends its lifetime exponentially, producing a sharp resonant response in the order parameter. The sensor linewidth is set by the time crystal lifetime alone, as strong interspin interactions help stabilize the time-crystalline order. The device operates in the 0.5–50-kHz range—a challenging frequency regime for sensors based on atomic vapour or electronic spins—and achieves competitive sensitivity. The sensing principle we demonstrate is robust to drive errors and sample inhomogeneities, and is applicable across a range of physical platforms including superconducting circuits, neutral atoms and trapped ions.

Figures

15 panels with data across 4 figures. Each panel page shows the plot, its columns and its files; each data.csv begins with a header naming the paper, the panel, the source, the license and the provenance route.

Fig. 1

• panel (c): Magnetization $\langle I^x \rangle$ (normalized) against time (s) for the PDTC protocol, without (blue) and with (red) the resonant a.c. field, one point per acquisition window. The dashed horizontal line marks $1/e$ and the dashed vertical lines mark where each trace first falls below it. The top axis of the print (Floquet cycles $M$) is not drawn. data.csv
• panel (c-inset-1): Inset (ii) of panel (c): tracked phase $\phi$ (rad) of the same two traces against time (s), without (blue) and with (red) the a.c. field. The dashed lines at $\phi = 0$ and $\phi = \pi$ are the $\hat{x}$ and $-\hat{x}$ rails. data.csv
• panel (c-inset-2): Inset (i) of panel (c): zoom of $\langle I^x \rangle$ (normalized) on a 20 ms window starting at 0.75 s, without (blue) and with (red) the a.c. field. Points are joined by lines. data.csv

Fig. 2

• panel (a): Lifetime extension fidelity $F$ ($\times 10^{-2}$) against the a.c. field phase $\Phi_{\mathrm{a.c.}}$ (rad), for $\gamma_y = \pi$ and $\gamma_y = 0.98\pi$; this is plot (ii) of panel (a). Points are joined by lines. The dashed horizontal lines are the bare PDTC (no a.c. field) for each kick angle; dashed vertical lines mark $0$ and $\pm\pi/2$. data.csv
• panel (b): Fidelity $F$ (left axis) and lifetime $T_2'$ (s, right axis) against the resonant a.c. field amplitude $B_{\mathrm{a.c.}}$ ($\mu$T). Points are means over repeated measurements and error bars are their standard deviation; the lines join the points. The print colours the three points marked (i), (ii), (iii) separately. data.csv
• panel (b-inset): Inset of panel (b): time-domain profiles $\langle I^x \rangle$ against time (s) at the three marked points: (i) no a.c. field, (ii) $B_{\mathrm{a.c.}} = 8.24\,\mu$T and (iii) $B_{\mathrm{a.c.}} = 82.4\,\mu$T, one point per acquisition window. data.csv

Fig. 3

• panel (a): Fidelity $F$ ($\times 10^{-2}$, left axis, blue) against the a.c. field frequency (Hz), points joined by lines, with the response of the spin-lock sensing scheme (grey points, right axis, normalized) and a dashed straight-line fit to it. The print draws no scale for the spin-lock data; the right axis here runs from 0 to 1 as in the authors\' plot. data.csv
• panel (a-inset-1): Inset (i) of panel (a): zoom of the fidelity $F$ ($\times 10^{-2}$) on the resonance, against frequency (Hz). Points are joined by lines and the dashed vertical line marks $f_{\mathrm{res}}$. The linewidth arrows and the point labels of the print are not drawn. data.csv
• panel (a-inset-2): Plot (a) of inset (ii) of panel (a): time-domain profile $\langle I^x \rangle$ against time (s) at $f = f_{\mathrm{res}} - 50$ Hz, one point per acquisition window, on the scale the print labels. The dashed line marks zero. data.csv
• panel (a-inset-3): Plot (b) of inset (ii) of panel (a): time-domain profile $\langle I^x \rangle$ against time (s) at $f = f_{\mathrm{res}}$, one point per acquisition window, on the scale the print labels. The dashed line marks zero. data.csv
• panel (a-inset-4): Plot (c) of inset (ii) of panel (a): time-domain profile $\langle I^x \rangle$ against time (s) at $f = f_{\mathrm{res}} + 0.05$ Hz, one point per acquisition window, on the scale the print labels. The dashed line marks zero. data.csv
• panel (a-inset-5): Plot (d) of inset (ii) of panel (a): time-domain profile $\langle I^x \rangle$ against time (s) at $f = f_{\mathrm{res}} + 0.2$ Hz, one point per acquisition window, on the scale the print labels. The dashed line marks zero. data.csv
• panel (b): Fidelity $F$ ($\times 10^{-2}$) against the frequency offset from resonance (Hz) for six kick angles $\gamma_y$ from $0.96\pi$ to $1.04\pi$, points joined by lines. As printed, each curve is shifted up by $2 \times 10^{-2}$ from the one below; the dashed horizontal lines are the shifted zero baselines and the dashed vertical line marks zero offset. data.csv
• panel (c): Fidelity $F$ ($\times 10^{-2}$) against the a.c. field frequency (Hz) for the two-frequency sensor: one sweep around $f^{(1)}_{\mathrm{res}}$ (pink) and one around $f^{(2)}_{\mathrm{res}}$ (purple), points joined by lines. The dashed vertical lines mark the two resonance frequencies. The linewidth arrows of the print are not drawn. data.csv

Fig. 4

• panel (b): Normalized single-axis PDTC signal $\langle I^z \rangle$ against the number of Floquet cycles $M$, without an a.c. field (black) and under a resonant a.c. field (green), in the five windows of $M$ the print shows on its broken axis. The dashed line marks zero. The lower time axis of the print is not drawn. data.csv

Cite

Leo Joon Il Moon, Paul M. Schindler, Ryan J. Smith, Emanuel Druga, Zhuo-Rui Zhang, Marin Bukov, Ashok Ajoy. Sensing with discrete time crystals. Nat. Phys. 22, 367-373 (2026). https://doi.org/10.1038/s41567-025-03163-6

When you use hosted data, cite the original paper and give the panel's URL so a reader can find the exact values you used.

All papers · About · Statistics · Submit data · API