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Universality of Li-Cs-Cs Efimov Resonances

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Abstract

This chapter investigates the universal behavior of weakly-bound LiCsCs three-body states near a scattering resonance in the s-wave regime, often called the Efimov scenario. We start with a short phenomenological introduction of Efimov physics and follow it up by a detailed mathematical description in the hyperspherical framework. The Efimov effect and its properties emerge naturally as a direct consequence of an effective \( -1/R^2 \) potential. Using an improved experimental approach for the preparation of an ultracold Cs-Li mixture, we observe a series of three consecutive Li-Cs-Cs Efimov resonances for the first time. Finally we compare these results with the universal theory and find both—universal behavior and deviations from it.

Keywords

  • Feshbach Resonance
  • Trap Depth
  • Atom Cloud
  • Magnetic Field Range
  • Reservoir Trap

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Fig. 3.1
Fig. 3.2
Fig. 3.3
Fig. 3.4
Fig. 3.5
Fig. 3.6
Fig. 3.7
Fig. 3.8
Fig. 3.9
Fig. 3.10
Fig. 3.11
Fig. 3.12
Fig. 3.13
Fig. 3.14

Notes

  1. 1.

    Most of the basic properties that are discussed in this section are independent of the exact composition of the three-body system and the nature of the scattering resonance itself, given that the Efimov effect is displayed for the considered system at all. See Sect. 3.2.2.

  2. 2.

    An exception is the \( ^4\mathrm {He}_2 \) interaction potential, which supports only a single bound state, close to the universal regime.

  3. 3.

    In realistic systems, effective scaling factor \( \lambda _n \) should be used that depends on the Efimov period n. This dependence breaks the discrete scaling symmetry, and it is typically not included in the basic description of the Efimov scenario. In the resonant limit \(( a\rightarrow \infty )\) \( \lambda =\lambda _n=\lambda _{n+1} \).

  4. 4.

    There exist several different choices for the mathematical definition of the hyperangles. Their advantages and disadvantages are discussed in great detail in [4].

  5. 5.

    Again, several different definitions for the reduced mass can be used. The combination \( \mu _3R^2 \) is invariant, so different choices of \( \mu _3 \) imply different definitions of R [1, 4].

  6. 6.

    We don’t discuss the case for a single resonant interaction, since in such systems the Efimov effect does not occur [1].

  7. 7.

    Numerical code for the calculation courtesy of D. Petrov, Université Paris-Sud.

  8. 8.

    In the author’s opinion, the most elegant way, but by far neither the easiest nor the cheapest one, of compensating the graviational sag would be to perform the mentioned ultracold mixed species experiments in gravity-free environment, to which a low Earth orbit of, say, 400 km height might be an excellent candidate.

  9. 9.

    In fact, these expressions are valid for any polarizable neutral particle in an oscillating electric field, see [95].

  10. 10.

    The maximal trap depth is limited by the saturation of the optical transition and intensity of the light.

  11. 11.

    The temperature and the trap depth of the confining potential are approximately related through the expression \( U_{dip}\approx \eta k_B T \) [105]. In our experiment we typically observe \( \eta _\mathrm {Cs}\sim 5 \) [103] and \( \eta _\mathrm {Li}\sim 10 \) [101].

  12. 12.

    Cs\( _2 \) photoassociation lines, and two-photon transitions are also found in this wavelength range. Parasitic heating effects from them were observed during this work, but are not discussed here.

  13. 13.

    Typical lifetimes of Li gas prepared in a single spin channel in our experiment is on the order of 1 min in the magnetic field range between 800 and 1000 G.

  14. 14.

    The number of Li atoms at any point during the hold time is larger than the one of Cs, hence the situation is analogous to Cs atoms being immersed in a large “reservoir” of Li atoms.

  15. 15.

    This calculation was performed by Bo Huang, University of Innsbruck, Austria [107].

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Ulmanis, J. (2017). Universality of 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_3

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