Abstract

By “unitary gas”, we mean a quantum N-body problem with interactions having a vanishing range and an infinite scattering length, in 3 space dimensions. This fundamental model is relevant for nuclear physics at a quanlitative level, and for ultracold atomic gases at a Feshbach resonance at a high-precision level. First, I will review Efimov’s analytical solution of the unitary three-body problem, and the resulting dramatic differences between the bosonic and fermionic cases (due to the occurence or non-occurence of the Efimov effect). Then, I will discuss recent work about the unitary Fermi gas, using a “bold diagrammatic Monte Carlo” approach [1,2,3], and about the unitary Bose gas, using Efimov’s ansatz for the 3-body problem [4,5].

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[1] K. Van Houcke, F. Werner, E. Kozik, N. Prokofev, B. Svistunov, M. J. H. Ku, A. T. Sommer, L. W. Cheuk, A. Schirotzek, M. W. Zwierlein, “Feynman diagrams versus Fermi-gas Feynman emulator”, Nature Phys. 8, 366 (2012)

[2] K. Van Houcke, F. Werner, E. Kozik, N. Prokof’ev, B. Svistunov, “Contact and Momentum Distribution of the Unitary Fermi Gas by Bold Diagrammatic Monte Carlo”, arXiv:1303.6245

[3] K. Van Houcke, F. Werner, N. Prokof’ev, B. Svistunov, “Bold diagrammatic Monte Carlo for the resonant Fermi gas”, arXiv:1305.3901

[4] B. S. Rem, A. T. Grier, I. Ferrier-Barbut, U. Eismann, T. Langen, N. Navon, L. Khaykovich, F. Werner, D. S. Petrov, F. Chevy, C. Salomon, “Lifetime of the Bose Gas with Resonant Interactions”, Phys. Rev. Lett. 110, 163202 (2013)

[5] Y. Castin, F. Werner, “Third virial coefficient of the unitary Bose gas”, Canadian Journal of Physics 91 (2013) 382