A zero-range approach is used to model resonant two-body interactions between three identical bosons. A dimensionless phase parametrizes the three-body boundary condition while the scattering length enters the Bethe–Peierls boundary condition. The model is solved exactly at zero energy for any value of the scattering length, positive or negative. From this solution, an analytical expression for the rate of three-body recombination to the universal shallow dimer is extracted.
Les interactions résonantes à deux corps entre trois bosons identiques sont modélisées par une approche de portée nulle. Une phase, paramètre sans dimension, caractérise la condition aux limites à trois corps tandis que la longueur de diffusion entre dans la condition aux limites de Bethe–Peierls. Le modèle est résolu exactement à énergie nulle pour toute valeur de la longueur de diffusion, positive ou négative. Une expression analytique pour le taux de recombinaison à trois corps vers le dimère universel peu profond est extraite de cette solution.
Mot clés : Problème à quelques corps, Recombinaison à trois corps, Phénomène d'Efimov
Christophe Mora 1; Alexander O. Gogolin 2; Reinhold Egger 3
@article{CRPHYS_2011__12_1_27_0, author = {Christophe Mora and Alexander O. Gogolin and Reinhold Egger}, title = {Exact solution of the three-boson problem at vanishing energy}, journal = {Comptes Rendus. Physique}, pages = {27--38}, publisher = {Elsevier}, volume = {12}, number = {1}, year = {2011}, doi = {10.1016/j.crhy.2010.11.002}, language = {en}, }
TY - JOUR AU - Christophe Mora AU - Alexander O. Gogolin AU - Reinhold Egger TI - Exact solution of the three-boson problem at vanishing energy JO - Comptes Rendus. Physique PY - 2011 SP - 27 EP - 38 VL - 12 IS - 1 PB - Elsevier DO - 10.1016/j.crhy.2010.11.002 LA - en ID - CRPHYS_2011__12_1_27_0 ER -
Christophe Mora; Alexander O. Gogolin; Reinhold Egger. Exact solution of the three-boson problem at vanishing energy. Comptes Rendus. Physique, Volume 12 (2011) no. 1, pp. 27-38. doi : 10.1016/j.crhy.2010.11.002. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2010.11.002/
[1] Universality in few-body systems with large scattering length, Phys. Rep., Volume 428 (2006) no. 5–6, pp. 259-390
[2] Many-body physics with ultracold gases, Rev. Mod. Phys., Volume 80 (2008) no. 3, pp. 885-964
[3] Quantum corrections to the energy density of a homogeneous Bose gas, Eur. Phys. J. B, Volume 11 (1999) no. 1, pp. 143-159
[4] Renormalization of the three-body system with short-range interactions, Phys. Rev. Lett., Volume 82 (1999) no. 3, pp. 463-467
[5] Dilute Bose–Einstein condensate with large scattering length, Phys. Rev. Lett., Volume 88 (2002) no. 4, p. 040401
[6] Weakly bound dimers of fermionic atoms, Phys. Rev. Lett., Volume 93 (2004) no. 9, p. 090404
[7] Four-body problem and BEC-BCS crossover in a quasi-one-dimensional cold fermion gas, Phys. Rev. Lett., Volume 95 (2005) no. 8, p. 080403
[8] Low-energy recombination of identical bosons by three-body collisions, Phys. Rev. Lett., Volume 83 (1999) no. 8, pp. 1566-1569
[9] Recombination of three atoms in the ultracold limit, Phys. Rev. Lett., Volume 83 (1999) no. 9, pp. 1751-1754
[10] Three-body recombination in Bose gases with large scattering length, Phys. Rev. Lett., Volume 85 (2000) no. 5, pp. 908-911
[11] Three-boson problem near a narrow Feshbach resonance, Phys. Rev. Lett., Volume 93 (2004) no. 14, p. 143201
[12] Three fully polarized fermions close to a p-wave Feshbach resonance, Phys. Rev. A, Volume 77 (2008) no. 4, p. 043611
[13] Production of cold molecules via magnetically tunable Feshbach resonances, Rev. Mod. Phys., Volume 78 (2006) no. 4, pp. 1311-1361
[14] Low-energy universality in atomic and nuclear physics, Few-Body Syst., Volume 46 (2009) no. 3, pp. 139-171
[15] Scattering length scaling laws for ultracold three-body collisions, Phys. Rev. Lett., Volume 94 (2005) no. 21, p. 213201
[16] Weakly-bound states of three resonantly-interacting particles, Sov. J. Nucl. Phys., Volume 12 (1970), p. 1080
[17] Evidence for Efimov quantum states in an ultracold gas of caesium atoms, Nature, Volume 440 (2006) no. 7082, pp. 315-318
[18] Observation of an Efimov-like trimer resonance in ultracold atom–dimer scattering, Nat. Phys., Volume 5 (2009) no. 3, pp. 227-230
[19] Observation of an Efimov spectrum in an atomic system, Nat. Phys., Volume 5 (2009) no. 8, pp. 586-591
[20] Observation of heteronuclear atomic Efimov resonances, Phys. Rev. Lett., Volume 103 (2009) no. 4, p. 043201
[21] Observation of universality in ultracold 7Li three-body recombination, Phys. Rev. Lett., Volume 103 (2009) no. 16, p. 163202
[22] Collisional stability of a three-component degenerate Fermi gas, Phys. Rev. Lett., Volume 101 (2008) no. 20, p. 203202
[23] Three-body recombination in a three-state Fermi gas with widely tunable interactions, Phys. Rev. Lett., Volume 102 (2009) no. 16, p. 165302
[24] Universality in three- and four-body bound states of ultracold atoms, Science, Volume 326 (2009) no. 5960, p. 1683
[25] Efimov physics in cold atoms, Ann. Phys. (N.Y.), Volume 322 (2007) no. 1, pp. 120-163
[26] The three-body problem with short-range interactions, Phys. Rep., Volume 347 (2001) no. 5, pp. 373-459
[27] Kontorovich–Lebedev representation for zero-range potential eigensolutions, J. Phys. A, Volume 34 (2001), pp. 8941-8954
[28] Solution for boson–diboson elastic scattering at zero energy in the shape-independent model, Phys. Rev. A, Volume 72 (2005) no. 3, p. 032709
[29] Exact solution for three particles interacting via zero-range potentials, Phys. Rev. A, Volume 73 (2006) no. 3, p. 032704
[30] The three-body problem with short-range forces. Scattering of low-energy neutrons by deuterons, Sov. Phys. JETP, Volume 31 (1956), p. 775
[31] Analytical solution of the bosonic three-body problem, Phys. Rev. Lett., Volume 100 (2008) no. 14, p. 140404
[32] Three-body problem in Fermi gases with short-range interparticle interaction, Phys. Rev. A, Volume 67 (2003) no. 1, p. 010703
[33] Atom–dimer scattering for confined ultracold fermion gases, Phys. Rev. Lett., Volume 93 (2004) no. 17, p. 170403
[34] Three-body problem for ultracold atoms in quasi-one-dimensional traps, Phys. Rev. A, Volume 71 (2005) no. 5, p. 052705
[35] On the three-body problem with short-range forces, Sov. Phys. JETP, Volume 40 (1961), p. 498
[36] The interaction between a neutron and a proton and the structure of 3H, Phys. Rev., Volume 47 (1935) no. 12, pp. 903-909
[37] Comment on the problem of three particles with point interactions, Sov. Phys. JETP, Volume 41 (1961), p. 1850
[38] On the point interaction for a three-particle system in quantum mechanics, Sov. Phys. Dokl., Volume 141 (1961), p. 1335
[39] Efimov resonances in atom–diatom scattering, Phys. Rev. A, Volume 66 (2002) no. 1, p. 012705
[40] Universal equation for Efimov states, Phys. Rev. A, Volume 67 (2003) no. 2, p. 022505
[41] Regularization of a three-body problem with zero-range potentials, J. Phys. A, Volume 34 (2001), p. 6003
[42] Three-body problem in heteronuclear mixtures with resonant interspecies interaction, Phys. Rev. A, Volume 81 (2010) no. 4, p. 042715
[43] Enhancing the observability of the Efimov effect in ultracold atomic gas mixtures, Phys. Rev. A, Volume 73 (2006) no. 3, p. 30703
[44] D.S. Petrov, unpublished results, 2005.
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