Polaron residue and spatial structure in a Fermi gas
| Autor: | Trefzger, Christian, Castin, Yvan |
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| Rok vydání: | 2012 |
| Předmět: | |
| Zdroj: | EPL - Europhysics Letters, European Physical Society/EDP Sciences/Societ{\`a} Italiana di Fisica/IOP Publishing, 2013, 101, pp.30006 |
| Druh dokumentu: | Working Paper |
| Popis: | We study the problem of a mobile impurity of mass $M$ interacting {\sl via} a s-wave broad or narrow Feshbach resonance with a Fermi sea of particles of mass $m$. Truncating the Hilbert space to at most one pair of particle-hole excitations of the Fermi sea, we determine ground state properties of the polaronic branch other than its energy, namely the polaron quasiparticle residue $Z$, and the impurity-to-fermion pair correlation function $G(x)$. We show that $G(x)$ deviates from unity at large distances as $-(A\_4+B\_4 \cos 2 k\_F x)/(k\_F x)^4$, where $k\_F$ is the Fermi momentum; since $A\_4>0$ and $B\_4>0$, the polaron has a diverging rms radius and exhibits Friedel-like oscillations. In the weakly attractive limit, we obtain analytical results, that in particular detect the failure of the Hilbert space truncation for a diverging mass impurity, as expected from Anderson orthogonality catastrophe; at distances between $\sim 1/k\_F$ and the asymptotic distance where the $1/x^4$ law applies, they reveal that $G(x)$ exhibits an intriguing multiscale structure. Comment: With respect to published version: augmented version giving a sum rule for the pair correlation function for an infinite-mass impurity |
| Databáze: | arXiv |
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