Mobile Spin Impurity in an Optical Lattice

Abstract

We investigate the Fermi polaron problem in a spin-1/2 Fermi gas in an optical lattice for the limit of both strong repulsive contact interactions and one dimension. In this limit, a polaronic-like behaviour is not expected, and the physics is that of a magnon or impurity. While the charge degrees of freedom of the system are frozen, the resulting tight-binding Hamiltonian for the impurity's spin exhibits an intriguing structure that strongly depends on the filling factor of the lattice potential. This filling dependency also transfers to the nature of the interactions for the case of two magnons and the important spin balanced case. At low filling, and up until near unit filling, the single impurity Hamiltonian faithfully reproduces a single-band, quasi-homogeneous tight-binding problem. As the filling is increased and the second band of the single particle spectrum of the periodic potential is progressively filled, the impurity Hamiltonian, at low energies, describes a single particle trapped in a multi-well potential. Interestingly, once the first two bands are fully filled, the impurity Hamiltonian is a near-perfect realisation of the Su-Schrieffer-Heeger model. Our studies, which go well beyond the single-band approximation, that is, the Hubbard model, pave the way for the realisation of interacting one-dimensional models of condensed matter physics.

13 pages, 12 figures, accepted in New Journal of Physics

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Cited by in corpus (5)

• Few-body Bose gases in low dimensions -- a laboratory for quantum dynamics
• Doping a lattice-trapped bosonic species with impurities: From ground state properties to correlated tunneling dynamics
• One-dimensional Repulsive Fermi Gas in a Tunable Periodic Potential
• Quantum phase transitions and the degree of nonidentity in the system with two different species of vector bosons
• Several fermions strongly interacting with a heavy mobile impurity in a one-dimensional harmonic trap