Para-hydrogen raser delivers sub-millihertz resolution in nuclear magnetic resonance

The precision of nuclear magnetic resonance spectroscopy(1) (NMR) is limited by the signal-to-noise ratio, the measurement time T-m and the linewidth Delta nu =1/(pi T-2). Overcoming the T-2 limit is possible if the nuclear spins of a molecule emit continuous radio waves. Lasers(2,3) and masers(4-13) are self-organized systems which emit coherent radiation in the optical and microwave regime. Both are based on creating a population inversion of specific energy states. Herewe showcontinuous oscillations of proton spins of organic molecules in the radiofrequency regime (raser(5)). We achieve this by coupling a population inversion created through signal amplification by reversible exchange (SABRE)(14-16) to a high-quality-factor resonator. For the case of N-15 labelled molecules, we observe multi-mode raser activity, which reports different spin quantum states. The corresponding H-1-N-15 J-coupled NMR spectra exhibit unprecedented sub-millihertz resolution and can be explained assuming two-spin ordered quantum states. Our findings demonstrate a substantial improvement in the frequency resolution of NMR.