Buffer gas cooling of a trapped ion to the quantum regime

Abstract

Great advances in precision measurements in the quantum regime have been achieved with trapped ions and atomic gases at the lowest possible temperatures1,2,3. These successes have inspired ideas to merge the two systems4. In this way, we can study the unique properties of ionic impurities inside a quantum fluid5,6,7,8,9,10,11,12 or explore buffer gas cooling of a trapped-ion quantum computer13. Remarkably, in spite of its importance, experiments with atom–ion mixtures have remained firmly confined to the classical collision regime14. We report a collision energy of 1.15(±0.23) times the s-wave energy (or 9.9(±2.0) μK) for a trapped ytterbium ion in an ultracold lithium gas. We observed a deviation from classical Langevin theory by studying the spin-exchange dynamics, indicating quantum effects in the atom–ion collisions. Our results open up numerous opportunities, such as the exploration of atom–ion Feshbach resonances15,16, in analogy to neutral systems17.

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Fig. 1: Set-up.
Fig. 2: Cooling dynamics of an ion in the ultracold buffer gas.
Fig. 3: Spin-exchange rate versus collision energy.

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. Source data for Figs. 2 and 3 and Extended Data Figs. 1–4 are provided with the paper.

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Acknowledgements

This work was supported by the European Union via the European Research Council (Starting Grant 337638) and the Netherlands Organization for Scientific Research (Vidi Grant 680-47-538, Start-up Grant 740.018.008 and Vrije Programma 680.92.18.05) (R.G.). D.W. and M.T. were supported by the National Science Centre Poland (Opus Grant 2016/23/B/ST4/03231) and PL-Grid Infrastructure. We thank J. Walraven and C. Coulais for comments on the manuscript.

Author information

T.F. and R.G. conceived the experiment. T.F., H.F., H.H., N.V.E. and M.M. performed the experiment. H.F. and R.G. performed molecular dynamics simulations, D.W. and M.T. performed quantum scattering simulations. All authors contributed to discussions about the experiment, the analysis of the data and the preparation of the manuscript.

Correspondence to R. Gerritsma.

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Extended data

Extended Data Fig. 1 Time-of-flight (TOF) data of the atomic cloud after release from the dipole trap.

We plot \({\sigma }_{{\rm{x}}}\) (blue) and \({\sigma }_{{\rm{y}}}\) (yellow). We average the temperature \({T}_{{\rm{x}}}\) and \({T}_{{\rm{y}}}\) to determine the atom temperature \({T}_{{\rm{a}}}\) a, TOF data for cold atoms after a buffer gas cooling time of 1 s. We determine an average atom temperature of \({T}_{{\rm{a}}}\) = 2.0(0.8) μK. The error bars are quite large for this measurement as the atomic density is at the lower limit of what we can reliably measure in our system. b, TOF data for cold atoms before the buffer gas cooling. We determine \({T}_{{\rm{a}}}\) = 2.6(0.3) μK. c, TOF data for the atomic cloud used for the spin-exchange rate measurement, we determine a temperature of \({T}_{{\rm{a}}}\) = 11.6(0.5) μK. Error bars denote standard deviations of fitted cloud sizes.

Extended Data Fig. 2 Micromotion analysis with resolved sideband spectroscopy.

In part a and b Rabi oscillations on the carrier and the micromotion sideband for optimal compensation settings are plotted. From a comparison of the Rabi frequencies \({\varOmega }_{{\rm{car}}}=2\pi \times 32.0(0.8)\)kHz and \({\varOmega }_{{\rm{MM}}}=2\pi \times 7.0(0.5)\)kHz in combination with the applied laser powers of \({P}_{411}=32\)μW and \({P}_{411}=840\)μK, respectively we obtain a residual micromotion energy of \({\overline{E}}_{{\rm{eMM}}}/{k}_{{\rm{B}}}=21.5(1.5)\)μK. Part c shows a frequency scan over the carrier transition, carried out with a laser power of \({P}_{411}=61\)μW. A clear peak is visible. For the data plotted in part d the frequency of the laser is shifted by \(-{\varOmega }_{{\rm{rf}}}=-1.85\)MHz compared to c and the power is increased to \({P}_{411}=21.7\)mW. At the expected resonance frequency for the micromotion sideband we do not see a clear peak, only the background is higher compared to c due to off-resonant carrier excitation at these high laser powers. If we shift the ion out of the optimal position for minimal micromotion we observe a clear resonance again as plotted in e. We conclude that the Rabi frequency \({\varOmega }_{{\rm{MM}}}\) on the micromotion sideband presented in e is not larger than the Rabi frequency on the carrier \({\varOmega }_{{\rm{car}}}\) presented in c. From this we obtain an upper limit of the axial micromotion at the optimal position of \({\overline{E}}_{{\rm{eMM}}}/{k}_{{\rm{B}}}=33\)μK. Error bars correspond to quantum projection noise.

Extended Data Fig. 3 Calculated energy distribution after buffer gas cooling of the ion using the parameters from the experiment.

The frequency of average secular kinetic energies is shown and fitted with a thermal distribution for a harmonic oscillator with a temperature of \({T}_{\sec }^{\perp }=38.2\) μK. No observable deviation from the thermal distribution is found. The results shown are from 300 simulation runs. In these simulations, the secular kinetic energy of the ion was obtained by filtering out energy contributions with a frequency higher than half the trap drive frequency, \({\varOmega }_{{\rm{rf}}}/2\), as explained in ref. 26.

Extended Data Fig. 4

\({\chi }^{2}\) as a function of the singlet \({a}_{{\rm{S}}}\) and triplet \({a}_{{\rm{T}}}\) scattering lengths with the number of Langevin collisions optimized for each set of scattering lengths.

Source data

Source Data Fig. 2

a, Ion temperature (microkelvin) versus sympathetic cooling time (ms) and error. Insets and b, Probability of finding ion in S state versus laser interrogation time (microseconds) and errors. c, Probability of finding ion in S state versus laser frequency (MHz) and errors.

Source Data Fig. 3

Spin flip probability versus average collision energy (microkelvin) and errors.

Source Data Extended Data Fig. 1

Radial atomic cloud sizes (micrometres) versus time-of-flight expansion (microseconds) and errors.

Source Data Extended Data Fig. 2

a,b, Probability of finding ion in S state versus laser interrogation time (microseconds) and errors. c-e, Probability of finding ion in S state versus laser frequency (MHz) and errors.

Source Data Extended Data Fig. 3

Simulation. Calculated probability of finding an ion at an average kinetic energy (microkelvin).

Source Data Extended Data Fig. 4

\({{\rm{Chi}}}^{2}\) of best fit as a function of singlet (x-axis) and triplet (y-axis) scattering length

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Feldker, T., Fürst, H., Hirzler, H. et al. Buffer gas cooling of a trapped ion to the quantum regime. Nat. Phys. (2020). https://doi.org/10.1038/s41567-019-0772-5

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