# Theory

# Impurity problems

*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. BiguĂ©, F. Chevy, X. Leyronas, Physical Review A 105 (3), 033314 (2022)

Impurity immersed in a double Fermi sea, R. Alhyder, X. Leyronas, F. Chevy Physical Review A 102 (3), 033322 (2020)

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)

Normal phase of an imbalanced fermi gas, C Mora, F Chevy, Physical review letters 104 (23), 230402 (2010)

Ground state of a tightly bound composite dimer immersed in a Fermi sea, C Mora, F Chevy Physical Review A 80 (3), 033607 (2009)

Normal state of highly polarized Fermi gases: simple many-body approaches, R Combescot, A Recati, C Lobo, F Chevy, Physical review letters 98 (18), 180402 (2007)

Universal phase diagram of a strongly interacting Fermi gas with unbalanced spin populations, F Chevy Physical Review A 74 (6), 063628 (2007)

# 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)