Main

Radio-wave masers (rasers) arise from the radiofrequency Zeeman splittings of nuclear spins such as 1H, 3He, 29Al or 129Xe. Rasers using 3He and 129Xe gas as the rasing medium employ spin exchange optical pumping17 (SEOP) at T > 400 K to create sufficient population inversion6,7,8, whereas 29Al solid9 or 1H Zeeman liquid-state masers10 rely on dynamic nuclear polarization (DNP) techniques18 or photochemical excitation11 to invert populations. Solid-state maser action has been observed in pulsed mode at room temperature with pentacene12, and a continuous-mode solid-state maser based on nitrogen-vacancy centres in diamond has been proposed13.

Here we report the observation of a liquid-state para-hydrogen pumped molecular raser that operates at 300 K with protons of organic molecules in solution and thereby avoids costly high magnetic fields, high vacuum, optical pumping or DNP techniques. We continuously supply para-hydrogen (p-H2) gas into a solution containing the raser active molecules and an iridium-based SABRE catalyst14,15,16. This spin-order transfer catalyst creates population inversion, equivalent to a negative spin temperature, on target molecules without altering their molecular structure. Coupling of these hyperpolarized molecules to a high-Q resonator19 produces a sustained raser signal comprised of frequencies that originate from the scalar couplings of nuclei within the molecule.

The operating principles for the 3He Zeeman maser6,7,8 are a starting point to assess challenges associated with the design of a SABRE-pumped room-temperature proton raser working at low frequencies. Masing starts once the radiation-damping rate 1/τrd, which quantifies the coupling between the resonator and the nuclear spins, satisfies the condition

Here the apparent transverse relaxation rate 1/T2∗ = 1/T2 + 1/τp is the sum of the transverse relaxation rate 1/T2 and the pumping rate 1/τp. The radiation-damping rate 1/τrd is given by

where μ0, η, Q, γ, M0 are the vacuum permeability, the filling factor of the coil, the quality factor of the resonator, the nuclear gyromagnetic ratio and the initial magnetization, respectively. The magnetization is given by M0 = (1/2)ℏγnsP, where ℏ denotes Planck’s constant and ns, P are the spin number density and the degree of nuclear polarization, respectively. The 3He Zeeman maser operates typically at PHe ≈ −0.5, nHe ≈ 1016–1018 cm−3, Q ≈ 30 and T2He ≈ 100 s. In comparison, proton spins in liquids at 300 K have much shorter relaxation times (T2H ≈ 1 s) and we have PHT2H ≈ 10−3PHeT2He, so masing of protons is about three orders of magnitude more difficult than masing of 3He. Examination of equations (1) and (2) suggest that this hurdle may be overcome by increasing the product nsQ for protons by a factor of 1,000 compared to 3He.

We discovered that a liquid-state proton raser can be created by combining SABRE technology, producing PH ∼ 10−2 at proton densities of nH ≈ 1020–1021 cm−3, with a high-quality-factor inductive NMR detector (Q ≈ 300), such as that used in external high-quality-factor-enhanced (EHQE)-NMR19. A steady-state proton polarization is achieved by bubbling para-hydrogen gas into a liquid sample containing the SABRE catalyst and target molecules such as pyridine or acetonitrile (Fig. 1a). The strong interaction between the large proton magnetization and the input coil coupled to a high-Q external resonator leads to raser oscillations, since the radiation-damping time satisfies τrd ≈ 0.016 s ≪ T2∗ ≈ 0.7 s.Figure 1b, c depicts two examples for raser signals from pyridine and acetonitrile, respectively, oscillating at 166.66 kHz. Both signals show typical initial transients, which subsequently level into a stationary raser signal. The initial transients are well described by the nonlinear Bloch equations6,7,8 with three key parameters: 1/τrd, 1/T2∗ and the pumping rate 1/τp (Supplementary Information I).

Figure 1: The liquid-state molecular raser.
figure 1

a, Experimental schematic depicting the para-hydrogen supply (red) including generator, needle valve (NV), valve (V), pressure gauge (p) and the p-H2 injection nozzle, the high-Q resonant circuit (blue) and the applied magnetic field B0 including shim coils (green). The SABRE chemistry is shown in the insert. b,c, Proton raser signals at B0 = 3.915 mT of pyridine (b) and acetonitrile (c). Inset: Proton spectrum of the continuous raser signal, showing one peak at 166.66 kHz.

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To examine the conditions under which a molecular raser oscillates in a multi-mode regime, 15N labelled acetonitrile is considered, which shows two J-coupled lines in its corresponding 1H NMR spectrum. The stationary 1H raser signal (Fig. 2a, (i)) can be Fourier transformed, which leads to a spectrum which shows only one peak at 166.695 kHz (Fig. 2b, (i)), posing the question why the second NMR line is raser silent.

Figure 2: Maser oscillation and SABRE spectrum of 15N labelled acetonitrile.
figure 2

a, The 1 H raser signal (0–77 s) at 166.6 kHz is initiated by appropriate exposure to para-hydrogen (i). Then a spoiler gradient pulse is applied to destroy x, y magnetization components (ii); finally a 90° x-pulse is applied yielding the canonical 1H FID (iii). b, 1H Fourier spectrum from the time evolutions depicted in a, showing one line for the constant raser mode and a nearly antisymmetric pair of J-coupled lines. c, Vector cone representation (i) of the negative transverse MTe− and longitudinal Mze− equilibrium magnetizations. The larger positive component Mze+ (blue) points in opposite direction. After spoiler gradient we obtain state (ii) and after 90x° pulse excitation, the two vectors Mye− and Mye+ rotate around the B0-field (iii) with the two frequencies γHB0/(2π) ± J 15 NH / 2 .

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Once the transverse magnetization MTe− component of the raser (Fig. 2c (i)) is destroyed by a magnetic field gradient (Fig. 2a (ii)) the longitudinal components Mze± remain (Fig. 2c (ii)). A 90x° pulse excitation converts these into a free induction decay (FID), which starts with nearly zero amplitude and shows a pronounced beat pattern (Fig. 2a (iii)). The corresponding 1H NMR spectrum exhibits two anti-phase peaks with different amplitudes separated by 3JNH = 1.7 Hz (Fig. 2b (iii)). The anti-phase character suggests two-spin order in the initial 1H state, represented by two opposing magnetization vectors Mze+ and Mze−. Only the component Mze− was raser active since its negative sign is associated with a population inversion (Fig. 2c (i)).

In fact a multi-modal 1H raser together with its corresponding SABRE signal of 15N pyridine at 41 kHz is shown in Fig. 3. The SABRE signal after 90° pulse excitation measured right after the raser action (Fig. 3a) starts at zero amplitude. The corresponding 1H spectrum (Fig. 3c, top) is antisymmetric with respect to the centre frequency and has a complex multi-line structure. This spectrum can be simulated assuming initial 15N-1H two-spin order (Supplementary Information III) and by incorporating all homo- and heteronuclear J-coupling constants20. The 1H raser signals for three different p-H2 flow rates (Fig. 3b) exhibit specific beat patterns. The three corresponding Fourier spectra (Fig. 3c) show one, two and four lines, corresponding to different raser active modes. The four lines correspond to an ortho and a meta 1H-15N two-spin state and each line is determined by the splitting caused by the homo- and heteronuclear J-coupling constants of 15N pyridine (Fig. 3c, insets, Supplementary Information V, VI).

Figure 3: Maser oscillations of 15N labelled pyridine.
figure 3

a, Initial 1 H-SABRE signal of 15 N pyridine after 90° pulse excitation. The corresponding Fourier transformed spectrum (Fig. 3c, top) shows an antisymmetric multi-line spectrum. b, 1H raser signal measured at p-H2 flow rates of 70, 90 and 400 cm3 min−1. c, The three corresponding Fourier transformed spectra show different numbers of raser modes based on ortho and meta 1H-15N two-spin order, depending on the p-H2 flow rate. Spin states of 15N pyridine are shown for four different modes of oscillation.

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The raser presented here can operate either as an ultrahigh-precision NMR spectrometer or as a magnetic field sensor. To demonstrate both cases the 1H raser signal of 15N pyridine oscillating at two frequencies is measured over 1,200 s (Supplementary Fig. S6a). The signal is cut into 5 s time slices that are Fourier transformed and plotted versus time (Fig. 4a). The two traces running in parallel show frequency fluctuations that are typical for the magnetic field noise of an unshielded resistive electromagnet, blurring the Fourier spectrum of the entire raser signal to the point where the spectroscopic information would be lost. However, the separation between the two lines, representing two different J-coupled spin states, is independent of any magnetic field and can be extracted by data processing from the magnetic field fluctuations.

Figure 4: Spectral analysis of 15N pyridine raser signal.
figure 4

a, Evolution of two raser active frequencies (p-H2 flow = 100 cm3 min−1) extracted from Supplementary Fig. S6. The data shows magnetic field fluctuations over a time period of 800 s. b, Corresponding Fourier spectrum of Supplementary Fig. S6a after removing the magnetic field noise. Inset shows an enhanced view of the narrow line at 0.69680 Hz. c, Fourier spectrum after removing magnetic field fluctuations of the multi-mode 1H raser signal of Fig. 3b bottom. Δν1,3, Δν1,2,Δν2,3 and Δν2,4 correspond to the frequency differences between the four raser lines 1–4 from Fig. 3c.

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As a result, two narrow lines at zero and at Δν1,2 = 0.69680 Hz ± 10 μHz are obtained (Fig. 4b), where Δν1,2 = J24∗ − J25∗ + J26∗/2, in an experimental regime where only the two most dominant raser modes are active. The same procedure can be applied to a complex multi-mode raser signal (Fig. 3b, bottom), resulting in the corrected spectrum shown in Fig. 4c. The narrow lines are associated with the J-coupling constants {J26∗, J24∗ − J25∗ + J26∗/2} = {−0.2561,0.7357} Hz ± 100 μHz. The measured Δν1,2 of Fig. 4b differs by 39 mHz from Fig. 4c, which can be explained by differences in 15N pyridine and catalyst concentration and p-H2 flow rate (Supplementary Fig. S6c). The precision measurement of J-coupling constants of better than 100 μHz is beyond the capability of contemporary 1H NMR spectroscopy21,22,23,24. The limit of precision for measuring J-coupling constants is given by the Cramér–Rao lower bound25, which is on the order of 36 nHz for 1,000 s measurement time on the 15N pyridine raser.

In conclusion, the reported liquid-state organic raser provides opportunity for measuring molecular structures with a sub-millihertz precision. Raser operation with the sample at room temperature and for T = 155 K as the highest temperature for the production of para-hydrogen (Supplementary Information VII) is achieved, which is well above the cryogenic temperature regime (T < 123 K). More efficient para-hydrogen delivery, better SABRE catalysts and improved EHQE resonators are expected to lower the raser threshold significantly and to increase the conversion temperature. A vision of mobile NMR raser spectrometers with unprecedented resolution and sensitivity could combine small Peltier cooling devices (T > 200 K) with small well-shimmed permanent magnets26 and miniaturized EHQE circuits.

To the best of our knowledge multi-mode raser activity of molecules based on hetero-nuclear two-spin order has never been reported before. A theoretical model of SABRE-induced two-spin order leads to the conclusion that effects from distant dipolar fields (DDF) are negligible and the bound complex is raser inactive (Supplementary Information IV–VI). These advantages distinguish the two-spin ordered raser from masers based on population inversion. This allows for applications in high-precision measurements of magnetic fields, molecular coupling parameters, coherent narrow-band amplifiers, and in situ NMR monitoring of metal-organic catalytic reactions. Finally, fundamental physics25,27,28 benefits from the long-lasting raser mode free of DDF, which could be a significant improvement compared to the 3He -129Xe NMR raser8,25. All this paves the way for many applications in physics, chemistry and material sciences.

Methods

Sample preparation.

All samples were prepared using standard Schlenk techniques under argon. The solvents and substrates were dried over molecular sieves and degassed. The deuterated solvents were degassed using three pump–freeze–thaw cycles. The isotopically labelled chemicals obtained from Sigma Aldrich were used as supplied. High field spectra were measured with a Bruker 400 MHz NMR spectrometer as a reference. Samples were prepared with a parent solution of a synthesized [IrCl(cod)(IMes)] catalyst29 in d4-methanol. Specially designed low-field sample tubes were filled with 600 μl of these solutions containing typically 1.17 mg catalyst. The substrate pyridine (1 μl) which is polarized by SABRE was added. When using acetonitrile (5 μl) as a substrate 0.5 μl d5-pyridine was added to the solution stabilizing the Ir-complex. The 15N labelled samples were prepared accordingly.

Experimental setup and data processing.

Para-hydrogen gas (PH ∼ 0.92, generated at T = 36 K, Bruker) is delivered at a pressure of 5 bar in continuous flow (∼10 cm3 min−1 STP) into a liquid sample through an injection nozzle (Fig. 1a). For measuring the dependence of raser and SABRE signals versus the conversion temperature of para-hydrogen (Supplementary Fig. 5), a homemade p-H2 generator with variable temperature (300 K > T > 9 K, ARS Cryo) is used. The liquid sample is located in the centre of a cylindrical magnetic field coil, which produces a field B0 ∼ 1–16 mT and which is shimmed to ΔB/B ∼ 10−6 cm−3 by using four shimming coils. A cylindrical input coil (height H = inner diameter D = 1 cm, ≈ 100 turns copper wire) which surrounds the sample is coupled to a high-Q external ferrite resonator (Q = 300, EHQE-NMR19). The strong coupling between the EHQE resonance circuit and the SABRE polarized proton spins leads to raser oscillations. After pre-amplification the raser signal is fed into a lock-in amplifier and its output is recorded with a data acquisition system (16 kHz sampling rate, 16-bit resolution). All measured data is processed using custom software (SciPy software package).

To remove magnetic field fluctuations of the 1H multi-mode raser signals of 15N-pyridine (Fig. 3b and Supplementary Fig. 4a) one single mode is extracted as a reference from the entire recorded signal by digital bandpass filtering. This is possible as long as the chosen reference line does not overlap with any other line even after broadening. Signal multiplication of the reference signal with the complete recording leads after Fourier transformation to a broad spectrum at twice the reference frequency and to a very narrow difference spectrum around zero frequency. After low-pass filtering one obtains a spectrum which is free of magnetic field fluctuations and with the reference line at zero frequency (Fig. 4b, c). Essentially this procedure yields a spectrum shifted down to zero frequency and freed of magnetic field noise.

Data availability.

The data that support the plots within this paper and other findings of this study are available from the corresponding author upon reasonable request.

Additional Information

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