Ground state of a tightly bound composite dimer immersed in a Fermi sea

In this paper, we present a theoretical investigation for the ground state of an impurity immersed in a Fermi sea. The molecular regime is considered where a two-body bound state between the impurity and one of the fermions is formed. Both interaction and exchange of the bound fermion take place between the dimer and the Fermi sea. We develop a formalism based on a two channel model allowing us to expand systematically the ground state energy of this immersed dimer with the scattering length $a$. Working up to order $a^3$, associated to the creation of two particle-hole pairs, reveals the first signature of the composite nature of the bosonic dimer. Finally, a complementary variational study provides an accurate estimate of the dimer energy even at large scattering length.

Figure 1

Our variational scheme takes into account only a restricted number of particle-hole excitations. First row: no particle hole excitation. Second row: one particle-hole excitation of momenta $q<k_F$ and $k>k_F$. Third row: two particle-hole excitations of momenta $q$, $q^{\prime }<k_F$ and $k$, $k^{\prime }>k_F$.

Figure 2

(Color online) Perturbative expansion of the energy of a molecular impurity immersed in a Fermi sea. Square: Monte Carlo result of [15]. Black solid line: Free molecule $E=-{\hslash }^2/m{a}^2$. Red dashed line: single particle hole excitations corresponding to the expansion up to $a^2$. Dotted blue line: expansion up to $a^3$ taking into account a second particle-hole excitation.

Figure 3

Variational calculation of the energy of a molecule immersed in a Fermi sea. Solid line: Variational calculation including formation of a single particle hole pair. Points: Monte Carlo calculation of [15].