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Finite-Range Effects in Li-Cs-Cs Efimov Resonances

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Heteronuclear Efimov Scenario in Ultracold Quantum Gases

Part of the book series: Springer Theses ((Springer Theses))

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Abstract

In this chapter we investigate departures from the universal behavior of weakly-bound LiCsCs three-body states due to finite-range effects in the heteronuclear Efimov scenario. The presented Born-Oppenheimer model illuminates the important role of finite-range physics in the heavy-heavy-light system with intuitive clarity. In the following experiments we realize the Li-Cs-Cs Efimov scenario with positive Cs-Cs scattering length for the first time, in this way pioneering the understanding of its influence on the three-body physics. Surprisingly, the resulting Efimov states are almost independent of molecular forces that govern chemical binding of atoms into molecules—the binding of the three atoms is purely quantum-mechanical and the three-body system becomes universal. Finally, we model two-body interactions between individual atoms by van der Waals tails of molecular potentials, and explain the previously observed deviations from the universal behavior.

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Notes

  1. 1.

    There exist extremely good approximations to them, which is the exact source of the universality in few-body physics [2].

  2. 2.

    This is analogous to the hyperspherical formalism, where the couplings between different scattering channels were neglected in order to obtain the single channel representation (see Sect. 3.2.1, Eqs. (3.9) and (3.10)).

  3. 3.

    Note that the length variable R used in the hyperspherical and BO approach denotes the hyperradius and the distance between the heavy particles, respectively. This implies a different definition of the reduced mass, as discussed in Sect. 3.2.1.

  4. 4.

    We do not consider the Li-Li vdW interactions, since in our experiments the fermionic Li is prepared in a single spin state, which does not undergo s-wave scattering.

  5. 5.

    In this expression the CsCs superscript is omitted for clearer presentation, i.e. \( r_\mathrm {vdW}=r_\mathrm {vdW}^\mathrm {CsCs}\).

  6. 6.

    Larger values are limited by the finite grid size of the utilized numerical method.

  7. 7.

    We thank C. Greene from Purdue University and Y. Wang from Kansas State University for performing these and all the following calculations with Lennard-Jones potentials for us.

  8. 8.

    We use the fitted absolute rates for the different data sets \(\gamma ^{(a)}_{120} =2.26\), \( \gamma ^{(b)}_{120}=1.44 \), \( \gamma _{450} =0.73\) so that the LJ and zero-range models can be directly compared. See Sect. 3.4.4.

  9. 9.

    The recording of a single three-body recombination spectrum can take a few days of continuous operation.

  10. 10.

    Even more provocative and pictorial comparison, although not strictly correct, is a continuous transition from a two-body into a three-body bound state.

  11. 11.

    We thank C. Greene for suggesting this idea to us.

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  1. Physics Institute, Heidelberg University, Heidelberg, Germany

    Juris Ulmanis

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Ulmanis, J. (2017). Finite-Range Effects in Li-Cs-Cs Efimov Resonances. In: Heteronuclear Efimov Scenario in Ultracold Quantum Gases. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-51862-6_4

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