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Trap-assisted formation of atom–ion bound states

Nature Physics volume 19, pages 1573–1578 (2023)Cite this article

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Abstract

Pairs of free particles cannot form bound states in an elastic collision due to momentum and energy conservation. In many ultracold experiments, however, the particles collide in the presence of an external trapping potential that can couple their centre-of-mass and relative motions, assisting the formation of bound states. Here we report the observation of weakly bound molecular states formed between one ultracold atom and a single trapped ion in the presence of a linear Paul trap. We show that bound states can efficiently form in binary collisions, and enhance the rate of inelastic processes. By measuring the electronic spin-exchange rate, we study the dependence of these bound states on the collision energy and magnetic field, and extract the average molecular binding energy and mean lifetime of the molecule, having good agreement with molecular dynamics simulations. Our simulations predict a power-law distribution of molecular lifetimes with a mean that is dominated by extreme, long-lived events. The dependence of the molecular properties on the trapping parameters enables further studies on the characterization and control of ultracold collisions.

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Fig. 1: Bound state formation and experimental apparatus.
Fig. 2: SE as a function of collision energy.
Fig. 3: SE as a function of magnetic field and thermometry.
Fig. 4: Bound-state properties from MD simulation.

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Data availability

Source data are provided with this paper. Other data that support the findings of this study are available from the corresponding authors on a reasonable request.

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Acknowledgements

This work was supported by the Israeli Science Foundation and the Goldring Family Foundation.

Author information

Author notes

  1. Or Katz

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

Authors and Affiliations

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

    Meirav Pinkas, Or Katz, Jonathan Wengrowicz, Nitzan Akerman & Roee Ozeri

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Contributions

All authors contributed to the experimental design, construction, discussions and wrote the manuscript. M.P. collected the data and analysed the results. M.P. and O.K. wrote the numerical simulations.

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Correspondence to Meirav Pinkas or Roee Ozeri.

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Extended data

Extended Data Fig. 1 Bound state probability in a Paul trap for different axial frequencies and atom’s mass.

(a) Bound state probability as a function of radial trap frequency for axial frequency of ωax/2π = 3, 100, 480 kHz (red, blue, and green, respectively). The 3 kHz graph is the same as in Fig. 4. (b) Bound state probability as a function of the atom’s mass. All parameters, apart from the atom’s mass, are taken as in the experiment. The mass of the atom is changed without changing the polarization constant, C4. For both graphs, each point corresponds to 104 trajectories. Confidence bounds of 1σ are on the order of marker size.

Source data

Extended Data Fig. 2 Estimating the lifetime of bound state from the simple model.

Contour lines are exothermic spin-exchange amplification, \({p}_{SE}^{{{{\rm{eff}}}}}(B\to \infty )/{p}_{SE}^{{{{\rm{eff}}}}}(B=0)\), calculated by the simple bound state model, for different mean number of short-range collisions, 〈N〉, and short-range spin-exchange probability, \({p}_{{{{\rm{SE}}}}}^{0}\). Red and blue bold lines are the measured ratios and short-range spin-exchange probability, respectively, with 1σ confidence bound in shaded area. The star is indicating the mean number of short-range collisions, 〈N〉exp = 8(2).

Source data

Extended Data Fig. 3 Calibration of the number of Langevin collisions.

The probability of observing the ion in a bright state after double shelving pulses with atoms (blue) and without (red) for different optical lattice velocities. When atoms are present, this probability is proportional to the probability of at least one Langevin collision in a lattice passage. Solid line is a fit to Eq. (4), with ρKL = 0.039(3) and pbg = 0.078(8). Error bars are binomial distribution standard deviation.

Source data

Extended Data Fig. 4 Rabi carrier thermometry after post-selecting SE events.

(a-b) Exothermic transitions at 3 G (a) and 20 G (b). (c-d) endothermic transitions at 3 G (c) and 20 G (d). Temperatures and contrast of the Rabi oscillation are written in Extended Data Table 1. Error bars are 1σ binomial standard deviation.

Source data

Extended Data Fig. 5 Calibration of the EMM amplitude projection along the shelving beam axis as a function of the applied voltage on an external electrode.

Measured data (blue circles) is extracted from Eq. (12) and dashed line are a fit to Eq. (13), where γproj = 3.97(6) nm/V, V0 = − 74.68(2) V, and c = 2.8(2) nm with 1σ confidence bounds.

Source data

Extended Data Fig. 6 Amplification of the short-range spin exchange, based on the MD simulation.

The amplification, \({p}_{\mathrm{SE}}^{\mathrm{eff}}/{p}_{\mathrm{SE}}^{0}\), is calculated by Eq. (18) for different EMM energies, EEMM, and short-range spin-exchange probabilities, \({p}_{{{{\rm{SE}}}}}^{0}\), at zero magnetic field.

Source data

Extended Data Fig. 7 Double shelving (DS) efficiency after a collision in presence of EMM.

For each EMM energy, the shelving probability is calculated by averaging 104 single collision events. Exothermic reaction releasing 2.7 mK (corresponding to the energy gap at 16 G), happens after each collision.

Source data

Extended Data Fig. 8 Mean number of short-range collisions in a bound state as a function of the magnetic field as calculated by the MD simulation.

The mean number of collisions is calculated for the endothermic (blue), and exothermic (red) transitions, given short-range spin-exchange probability of \({p}_{{{{\rm{SE}}}}}^{0}=0.12\). Error bars are one standard deviation calculated by bootstrapping the data-set 10 times its size.

Source data

Extended Data Table 1 Thermometry measurements
Full size table

Supplementary information

Supplementary Information

Supplementary Notes I–III.

Source data

Source Data Fig. 2

Raw data for Fig. 2.

Source Data Fig. 3

Raw data for Fig. 3.

Source Data Fig. 4

Raw data for Fig. 4.

Source Data Extended Data Figs. 1–8

Raw data for all the extended data figures.

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Pinkas, M., Katz, O., Wengrowicz, J. et al. Trap-assisted formation of atom–ion bound states. Nat. Phys. 19, 1573–1578 (2023). https://doi.org/10.1038/s41567-023-02158-5

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