Quantum magnetic J-oscillators

Nat. Commun. 17, 1200 (2026) · DOI: 10.1038/s41467-026-68779-5 · arXiv: 2504.06498

License: CC BY 4.0.

Abstract

Zero-field nuclear magnetic resonance (NMR) offers magnet-free access to nuclear spin-spin (scalar J) couplings, which define an intrinsic, molecule-specific frequency scale. However, the transient nature of zero-field NMR signals constrain spectral resolution and frequency stability. Here we introduce quantum J-oscillators that exploit J-couplings in molecules to produce phase-coherent continuous oscillations. Operated in zero magnetic field and driven by a digital feedback, they generate sub-hertz to a few tens of hertz frequencies. In a proof-of-principle experiment on [15N]-acetonitrile, the oscillator achieves a 340 uHz linewidth over 3600 s, more than two orders of magnitude narrower than in conventional zero-field NMR. This methodology may facilitate precision measurements of J-coupling constants and enables discrimination of molecules whose zero-field NMR spectra are otherwise difficult to resolve. In addition, the combination of strongly coupled spin systems and programmable feedback turns J-oscillators into a compact tabletop platform for exploring nonlinear spin dynamics, including chaos and dynamical phase transitions. By uniting high-resolution spectroscopy and controllable quantum dynamics in a single, magnet-free setup, J-oscillators open new opportunities for applications where ultraprecise frequency references or molecular fingerprints are required.

Figures

33 panels with data across 5 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 (d): $J$-oscillation from 5% [$^{15}$N]-acetonitrile at $\tau = 222$ ms and $G_{\mathrm{ext}} = +30$: signal (pT) against time (s) over 600 s. The printed max and SS amplitude arrows, dashed zero line and zoom markers are not drawn. data.csv
• panel (e): First 10 s of the record in panel (d), the OPM sensor background: signal (pT) against time (s). The inset of the printed panel is the panel e-inset. data.csv
• panel (e-inset): Inset of printed panel (e): FFT (pT/Hz) of the sensor background against frequency (Hz), 0 to 100 Hz. data.csv
• panel (f): Zoom of panel (d) from 400 to 410 s, the dynamic steady state of the $J$-oscillation: signal (pT) against time (s). data.csv
• panel (g): Conventional zero-field free decay (FD) signal from the same sample as panel (d): signal (pT) against time (s). data.csv
• panel (h): FFT amplitude (nT/Hz) against frequency (Hz) of the $J$-oscillation of naturally abundant acetonitrile over 300 to 3600 s. The printed gray bands and dashed line at the $J$ lines are not drawn; the inset of the printed panel is the panel h-inset. data.csv
• panel (h-inset): Inset of printed panel (h): FFT amplitude (nT/Hz) of the $J$-oscillation line against $\Delta f$ (mHz), referenced to 3.374 Hz. The printed linewidth annotation is not drawn. data.csv
• panel (i): Zero-field NMR spectrum of the naturally abundant acetonitrile sample: FFT amplitude (pT/Hz) against frequency (Hz). The printed gray bands, dashed line and linewidth annotation are not drawn, and the large printed baseline swing below about 0.5 Hz is absent here. data.csv

Fig. 2

• panel (b): FFT spectra of the steady-state $J$-oscillations (150 to 600 s) of one sample over 11 runs, amplitude (nT/Hz) against frequency (Hz), zero-filled four-fold. Shown as a waterfall over run number instead of the printed offset stack. data.csv
• panel (c): Zero-field NMR spectra from the free decays of the same 11 runs as panel (b), amplitude (pT/Hz) against frequency (Hz), zero-filled four-fold. Shown as a waterfall over run number instead of the printed offset stack. data.csv
• panel (d): Sample 1 of three identically prepared samples: $\Delta f$ (mHz), referenced to 3.372 Hz, against run number for the $J$-oscillator and zero-field NMR frequencies. data.csv
• panel (e): Sample 2 of three identically prepared samples: $\Delta f$ (mHz), referenced to 3.372 Hz, against run number for the $J$-oscillator and zero-field NMR frequencies. data.csv
• panel (f): Sample 3 of three identically prepared samples: $\Delta f$ (mHz), referenced to 3.372 Hz, against run number for the $J$-oscillator and zero-field NMR frequencies. data.csv

Fig. 3

• panel (a): $J$-oscillator on [$^{15}$N]-acetonitrile at $\tau = 100$ ms and $G_{\mathrm{ext}} = -20$: signal (pT) against time (s) for the total $J$-oscillation and the isolated 1$J$-oscillation obtained by Fourier filtering. data.csv
• panel (b): $J$-oscillator on [$^{15}$N]-acetonitrile at $\tau = 100$ ms and $G_{\mathrm{ext}} = -20$: signal (pT) against time (s) for the total $J$-oscillation and the isolated 2$J$-oscillation obtained by Fourier filtering. data.csv
• panel (c): Steady-state amplitude (pT) of the 1$J$ and 2$J$ oscillations against feedback delay $\tau$ (ms) at $G_{\mathrm{ext}} = -20$. Markers are measurements; solid lines are numerical simulations. data.csv
• panel (d): Steady-state amplitude (pT) of the 1$J$ and 2$J$ oscillations against feedback delay $\tau$ (ms) at $G_{\mathrm{ext}} = +20$. Markers are measurements; solid lines are numerical simulations. data.csv
• panel (e): Steady-state (SS amp) and maximal (max amp) amplitude (pT) against feedback gain $|G_{\mathrm{ext}}|$ for the 1$J$ oscillator, negative feedback at $\tau = 160$ ms. Markers are measurements; solid lines are numerical simulations. The printed below-threshold shading is drawn as a dashed line at 7.2. data.csv
• panel (f): Steady-state (SS amp) and maximal (max amp) amplitude (pT) against feedback gain $|G_{\mathrm{ext}}|$ for the 2$J$ oscillator, positive feedback at $\tau = 222$ ms. Markers are measurements; solid lines are numerical simulations. The printed below-threshold shading is drawn as a dashed line at 5.8. data.csv

Fig. 4

• panel (a): Spectra of naturally abundant acetonitrile (0.36% [$^{15}$N]-ACN), amplitude (pT) against frequency (Hz): the zero-field NMR spectrum and two $J$-oscillators, 222 ms, 150 and 160 ms, -240, labelled by feedback delay and gain. Shown as a waterfall instead of the printed offset stack; the molecular structure is not drawn. The printed axis unit Hzg is corrected to Hz. data.csv
• panel (b): Spectra of 1% [2-$^{13}$C,$^{15}$N]-ACN in [$^{14}$N]-ACN, amplitude (pT) against frequency (Hz): the zero-field NMR spectrum and three $J$-oscillators, 100 ms, -800; 114 ms, -1000 and 160 ms, -700, labelled by feedback delay and gain. Shown as a waterfall instead of the printed offset stack; the molecular structure is not drawn. data.csv
• panel (c): Spectra of 1% [1-$^{13}$C,$^{15}$N]-ACN in [$^{14}$N]-ACN, amplitude (pT) against frequency (Hz): the zero-field NMR spectrum and two $J$-oscillators, 178 ms, 1000 and 178 ms, -1000, labelled by feedback delay and gain. Shown as a waterfall instead of the printed offset stack; the molecular structure is not drawn. data.csv
• panel (d): Spectra of [$^{15}$N]-pyridine, amplitude (pT) against frequency (Hz): the zero-field NMR spectrum and two $J$-oscillators, 110 ms, 500 and 110 ms, -1000, labelled by feedback delay and gain. Shown as a waterfall instead of the printed offset stack; the molecular structure is not drawn. data.csv
• panel (e): Spectra of 4-amino[$^{15}$N]-pyridine, amplitude (pT) against frequency (Hz): the zero-field NMR spectrum and three $J$-oscillators, 120 ms, 500; 90 ms, 1000 and 150 ms, 1000, labelled by feedback delay and gain. Shown as a waterfall instead of the printed offset stack; the molecular structure is not drawn. data.csv
• panel (f): Spectra of [$^{15}$N$_3$]-metronidazole, amplitude (pT) against frequency (Hz): the zero-field NMR spectrum and two $J$-oscillators, 130 ms, 300 and 160 ms, 300, labelled by feedback delay and gain. Shown as a waterfall instead of the printed offset stack; the molecular structure is not drawn. data.csv
• panel (g): Spectra of [$^{15}$N$_2$]-imidazole, amplitude (pT) against frequency (Hz): the zero-field NMR spectrum and three $J$-oscillators, 100 ms, 500; 120 ms, 1500 and 80 ms, 1000, labelled by feedback delay and gain. Shown as a waterfall instead of the printed offset stack; the molecular structure is not drawn. data.csv
• panel (h): Spectra of [1-$^{13}$C]-pyruvate, amplitude (pT) against frequency (Hz): the zero-field NMR spectrum and one $J$-oscillator, 200 ms, -5e4, labelled by feedback delay and gain. Shown as a waterfall instead of the printed offset stack; the molecular structure is not drawn. data.csv
• panel (i): Spectra of [U-$^{13}$C,$^{15}$N]-butyronitrile, amplitude (pT) against frequency (Hz): the zero-field NMR spectrum and four $J$-oscillators, 90, 100, 120 and 160 ms, each at -3000, labelled by feedback delay and gain. Shown as a waterfall instead of the printed offset stack; the molecular structure is not drawn. data.csv

Fig. 5

• panel (1): Stack 1 of 5 from the top, pyridine/4-aminopyridine mixture with 4-aminopyridine $^{15}$N-enriched, pyridine unenriched ($^{14}$N): amplitude (pT) against frequency (Hz) for $J$-oscillators at $\tau = 115$ ms and $G_{\mathrm{ext}}$ = 500 to 900, and the zero-field NMR spectrum. Shown as a waterfall instead of the printed offset stack; the printed tenfold NMR scaling and isotope bars are not used. data.csv
• panel (2): Stack 2 of 5 from the top, pyridine/4-aminopyridine mixture with 4-aminopyridine $^{15}$N-enriched, pyridine 50% enriched: amplitude (pT) against frequency (Hz) for $J$-oscillators at $\tau = 115$ ms and $G_{\mathrm{ext}}$ = 500 to 900, and the zero-field NMR spectrum. Shown as a waterfall instead of the printed offset stack; the printed tenfold NMR scaling and isotope bars are not used. data.csv
• panel (3): Stack 3 of 5 from the top, pyridine/4-aminopyridine mixture with both 4-aminopyridine and pyridine $^{15}$N-enriched: amplitude (pT) against frequency (Hz) for $J$-oscillators at $\tau = 115$ ms and $G_{\mathrm{ext}}$ = 400 to 800, and the zero-field NMR spectrum. Shown as a waterfall instead of the printed offset stack; the printed tenfold NMR scaling and isotope bars are not used. data.csv
• panel (4): Stack 4 of 5 from the top, pyridine/4-aminopyridine mixture with pyridine $^{15}$N-enriched, 4-aminopyridine 50% enriched: amplitude (pT) against frequency (Hz) for $J$-oscillators at $\tau = 115$ ms and $G_{\mathrm{ext}}$ = 400 to 800, and the zero-field NMR spectrum. Shown as a waterfall instead of the printed offset stack; the printed tenfold NMR scaling and isotope bars are not used. data.csv
• panel (5): Stack 5 of 5 from the top, pyridine/4-aminopyridine mixture with pyridine $^{15}$N-enriched, 4-aminopyridine unenriched ($^{14}$N): amplitude (pT) against frequency (Hz) for $J$-oscillators at $\tau = 115$ ms and $G_{\mathrm{ext}}$ = 250 to 450, and the zero-field NMR spectrum. Shown as a waterfall instead of the printed offset stack; the printed tenfold NMR scaling and isotope bars are not used. data.csv

Cite

Jingyan Xu, Raphael Kircher, Oleg Tretiak, Dmitry Budker, Danila A. Barskiy. Quantum magnetic J-oscillators. Nat. Commun. 17, 1200 (2026). https://doi.org/10.1038/s41467-026-68779-5

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