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Strong coupling of alkali-metal spins to noble-gas spins with an hour-long coherence time

Nature Physics volume 18, pages 506–510 (2022)Cite this article

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Abstract

Nuclear spins of noble gases can maintain coherence for hours at ambient conditions because they are isolated by complete electron shells1. This isolation, however, impedes the ability to manipulate and control them by optical means or by coupling to other spin gases2,3,4. Here we achieve strong coherent coupling between noble-gas spins and the optically accessible spins of an alkali-metal vapour. The coupling emerges from the coherent accumulation of stochastic spin-exchange collisions. We obtain a coupling strength ten times higher than the decay rate, observe the coherent and periodic exchange of spin excitations between the two gases and demonstrate active control over the coupling by an external magnetic field. This approach could be developed into a fast and efficient interface for noble-gas spins, enabling applications in quantum sensing and information5,6.

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Fig. 1: Experimental scheme and coherence time measurements.
Fig. 2: Exchange of collective spin excitations.
Fig. 3: Measured dynamics of the coupled alkali-metal–noble-gas spin system in three regimes.
Fig. 4: Spectral response of the alkali-metal–noble-gas spin system in the strong-coupling regime.

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Data availability

All data needed to evaluate the conclusions in the paper are present in the paper. The data that support the findings of this study and additional data are available from the corresponding author upon request.

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Acknowledgements

We thank C. Avinadav and R. Finkelstein for fruitful discussions. We acknowledge financial support by the Israel Science Foundation, the European Research Council starting investigator grant Q-PHOTONICS 678674, the Minerva Foundation with funding from the Federal German Ministry for Education and Research and the Laboratory in Memory of Leon and Blacky Broder.

Author information

Author notes

  1. O. Katz

    Present address: Department of Electrical and Computer Engineering, Duke University, Durham, NC, USA

  2. These authors contributed equally: R. Shaham, O. Katz.

Authors and Affiliations

  1. Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot, Israel

    R. Shaham, O. Katz & O. Firstenberg

  2. Rafael Ltd, Haifa, Israel

    R. Shaham & O. Katz

Authors
  1. R. Shaham
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Contributions

R.S., O.K. and O.F. all contributed to the experimental design, construction, data collection and analysis of this experiment. R.S. claims responsibility for all figures. The authors wrote the manuscript together.

Corresponding author

Correspondence to R. Shaham.

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Extended data

Extended Data Fig. 1 Spin-exchange optical pumping.

Typical measurement of the pumping process of helium-3 by optically pumped potassium vapor. Here the potassium density is na = 4.9 ⋅ 1014 cm−3, and the helium depolarization time is \({T}_{1,{{{\rm{act}}}}}^{{{{\rm{b}}}}}=3.9\) h.

Source data

Extended Data Fig. 2 Variables extracted from fitting Eq. (3) to the measured signals for each exchange time t, as exemplified in Extended Data Fig. 3.

a. The change in alkali precession frequency ωa(t, τ = 0) [see Eq. (2)] manifests the change in the slowing-down factor due to alkali depolarization. b. The degree of alkali polarization pa(t) (in semi-log scale). In a and b, dashed black line correspond to the fitted multi-exponential model, and dotted lines present its confidence bounds. These are used as uncertainty estimations when using pa(t) to scale \(\langle \hat{a}\rangle\) and \(\langle \hat{b}\rangle\). Less reliable data, extracted when the excitations reside predominantly in the noblegas spins, are marked in gray. c. The two frequency components (amplitude squared) of the normalized Faraday rotation signal \({\overline{S}}_{x}(t+\tau )\). Note the factor of (Δ/J)2 ≳ 100 between them. Each data-point is averaged over 12 to 20 repetitions of the sequence.

Source data

Extended Data Fig. 3 Pulse sequence and typical results of an excitation-exchange measurement.

a. First, we turn off the pumping and bring the two species to strong coupling with a small detuning Δ. We then generate a transverse excitation with a transverse magnetic field pulse. At a later time t, we halt the exchange by increasing the axial magnetic field and setting a large Δ. b. Example of a measured signal with exchange duration t = 11 ms, with Δ = − 1.15J before t, and Δ = 790 Hz ≫ J after t. We measure the alkali electron spin (red) which, once Δ is increased, can be used as a magnetometer that senses the noble-gas spin. The fast oscillations of the signal correspond to the Larmor precession of the alkali spin, and the slow modulation corresponds to the noble-gas precession. The latter is highlighted by the blue line (generated by low-pass filtering of the signal for illustrative purposes). We fit the signal to the model from Eq. (3) (dashed black line) and find the amplitudes of the alkali and noble-gas components at time t, which are used to estimate \(\langle \hat{a}(t)\rangle\) and \(\langle \hat{b}(t)\rangle\), respectively. The same fit also provides pa(t).

Source data

Supplementary information

Supplementary Information

Supplementary Sections 1 and 2, and reference.

Source data

Source Data Fig. 1

Contains the data presented in Fig. 1b (measurement of noble-gas coherence time).

Source Data Fig. 2

Contains the data presented in Fig. 2. Sheet labelled ‘exp’ contains the measured data points and error bars; coloured error bars, denoting measurements uncertainty and scattering, are presented in ‘dNa’\‘dNb’ columns, while grey error bars, denoting uncertainty in the data interpretation\scaling, are presented in ‘eNa+\-’,‘eNb+\-’ columns. Sheet labelled ‘model’ contains the data of the model presented on top of measurements (Fig. 2, solid lines).

Source Data Fig. 3

Contains the data presented in Fig. 3. Sheet ‘strong coupling’ contains the data in Fig. 3a. Sheet ‘detuned’ contains the data presented in Fig. 3b. Sheet ‘overdamped’ contains the data presented in Fig. 3c (solid and dashed lines).

Source Data Fig. 4

Contains the data presented in Fig. 4. All spectrum data (sheets ‘spectrum_exp’, ‘spectrum_model’ and ‘spectrum_imperfect_model’) appear such that the first row contains the ‘Delta/J’ values, the first column contains the ‘omega/J’ values and the rest of the table contains the normalized Fourier amplitudes presented in the figure. Sheet ‘spectrum_exp’ contains the data of Fig. 4a. Sheet ‘spectrum_model’ contains the data of Fig. 4b. Sheet ‘spectrum_imperfect_model’ contains the data of Fig. 4c. Sheet ‘eigenfrequencies’ contains the data of the dashed white lines in Fig. 4a.

Source Data Extended Data Fig. 1

Contains the data presented in Extended Data Fig. 1.

Source Data Extended Data Fig. 2

Contains the data presented in Extended Data Fig. 2. Sheet ‘alkali decoupling frequency’ contains the data in Extended Data Fig. 2a. ‘omega’ versus ‘t’ is the measured data, with ‘domega’ being the error bars (red and grey circles), and ‘omega_model’ versus ‘t_model’ is the fitted model (dashed black line) with ‘domega_model+\-’ being the upper\lower confidence bounds of the model (respectively). Sheet ‘alkali polarization’ contains the data in Extended Data Fig. 2b. Again, ‘p_a’ versus ‘t’ is the measured data, with ‘dp_a’ being the errorbars (red and grey circles), and ‘p_model’ versus ‘t_model’ is the fitted model (dashed black line) with ‘dp_model+\-’ being the upper\lower confidence bounds of the model (respectively). Sheet ‘fitting amplitudes’ contains the data in Extended Data Fig. 2c, where ‘dNa\b’ are the errorbars.

Source Data Extended Data Fig. 3

Contains the data presented in Extended Data Fig. 3b, as follows; ‘sx’ versus ‘t’ is the measured data (red line), ‘ky’ versus ‘t for ky’ is the low-pass-filtered data (blue line) and ‘model’ versus ‘t for model’ is the fitted model (dashed black line).

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Shaham, R., Katz, O. & Firstenberg, O. Strong coupling of alkali-metal spins to noble-gas spins with an hour-long coherence time. Nat. Phys. 18, 506–510 (2022). https://doi.org/10.1038/s41567-022-01535-w

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