An impurity in a Fermi sea on a narrow Feshbach resonance: A variational study of the polaronic and dimeronic branches

Abstract

We study the problem of a single impurity of mass $M$ immersed in a Fermi sea of particles of mass $m$. The impurity and the fermions interact through a s-wave narrow Feshbach resonance, so that the Feshbach length $R_{\ast }$ naturally appears in the system. We use simple variational ansatz, limited to at most one pair of particle-hole excitations of the Fermi sea and we determine for the polaronic and dimeronic branches the phase diagram between absolute ground state, local minimum, thermodynamically unstable regions (with negative effective mass), and regions of complex energies (with negative imaginary part). We also determine the closed channel population which is experimentally accessible. Finally we identify a non-trivial weakly attractive limit where analytical results can be obtained, in particular for the crossing point between the polaronic and dimeronic energy branches.

24 pages, 12 figures

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• Superconductivity induced by strong electron-exciton coupling in doped atomically thin semiconductor heterostructures
• Emergence of Crystalline Few-body Correlations in Mass-imbalanced Fermi Polarons
• A smooth polaron-molecule crossover in a Fermi system
• The self-energy of an impurity in an ideal Fermi gas to second order in the interaction strength
• Variational approach to the two-dimensional Bose polaron
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• Ultracold-atom collisions in atomic waveguides : A two-channel analysis
• Highly polarized one-dimensional Fermi gases near a narrow $p-$wave resonance
• Competing few-body correlations in ultracold Fermi polarons
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• Second-order virial expansion for an atomic gas in a harmonic waveguide
• Repulsive Fermi and Bose Polarons in Quantum Gases
• The normal state of attractive Fermi gases from coupled-cluster theory
• Impurity in a zero-temperature three-dimensional Fermi gas