Lowest order diagrams describing the formation of a polaraon in a spin 1/2 attractive Fermi gas.
The description of an impurity immersed in an ensemble of particles is one of the simplest though non-trivial problems in quantum many-body physics. In this kind of situation, the impurity is dressed by a cloud of excitations of the many-body background leading to the This scenario was first proposed by Landau and Pekar to describe the interaction of an electron with the excitations of a crystal and has since then been generalized to a large number of physical situations, from condensed matter to nuclear physics.
Over the past 10 years, ultracold atoms have emerged as a new platform for the study of impurity problems. We have developped a variational approach allowing its properties to be captured quantitatively and that we have first applied to the so-called Fermi polaron problem describing an atom immersed in a Fermi sea of spin-polarized non-interacting fermions.
We have then extended this approach to the case where the background is an ensemble of attractive spin 1/2 fermions. Contrary to the previous example, the zero-range limit characterizing ultracold collisions is singular and we had to cure the associated divergences by a proper treatment of three-body interactions.
Mean field versus random-phase approximation calculation of the energy of an impurity immersed in a spin-1/2 superfluid, A. Bigué, F. Chevy, X. Leyronas, Physical Review A 105 (3), 033314 (2022)
Few Versus Many-Body Physics of an Impurity Immersed in a Superfluid of Spin Attractive Fermions M Pierce, X Leyronas, F Chevy Physical Review Letters 123 (8), 080403 (2019)
Feynman diagrams for many-body physics
Initially introduced by R. Feynman to describe elementary processes in quantum electrodynamics, diagrammatic techniques have been extended to the study of the many-body problem and now form a very powerful tool in quantum statistical physics.
Three-body contact for fermions I: general relations, X. Leyronas, F. Werner ArXiv:2211.09765
Second-order virial expansion for an atomic gas in a harmonic waveguide, T. Kristensen, X. Leyronas, and L. Pricoupenko Phys. Rev. A 93, 063636 (2016)
High-temperature expansion for interacting fermions, M. Sun and X. Leyronas Phys. Rev. A 92, 053611 (2015)
Virial expansion with Feynman diagrams X. Leyronas, Phys. Rev. A 84, 053633 (2011)