Polaron-to-molecule transition in a strongly imbalanced Fermi gas

A single down-spin fermion with an attractive zero-range interaction with a Fermi sea of up-spin fermions forms a polaronic quasiparticle. The associated quasiparticle weight vanishes beyond a critical strength of the attractive interaction, where a many-body bound state is formed. From a variational wave function in the molecular limit, we determine the critical value for the polaron-to-molecule transition. The value agrees well with the diagrammatic Monte Carlo results of Prokof’ev and Svistunov and is consistent with recent rf-spectroscopy measurements of the quasiparticle weight by Schirotzek et al. [Phys. Rev. Lett. 102, 230402 (2009)]. In addition, we calculate the contact coefficient of the strongly imbalanced gas, using the adiabatic theorem of Tan and discuss the implications of the polaron-to-molecule transition for the phase diagram of the attractive Fermi gas at finite imbalance.

Figure 1

(Color online) Quasiparticle residue $Z_{\downarrow }$ of the minority fermion as a function of ${\left(k_{F}a\right)}^{-1}$, calculated using Chevy’s variational ansatz (2.1). In the regime where the ansatz (2.1) breaks down, $Z_{\downarrow }$ is drawn as a dotted line. The red dots correspond to the experimentally measured quasiparticle residue from the MIT group [5] at a minority concentration of 5%.

Figure 2

(Color online) Ground-state energy $E-E_b$ [binding energy $E_b=-1/\left(m{a}^2\right)$ subtracted] in units of the Fermi energy ${\epsilon }_F$ as a function of ${\left(k_{F}a\right)}^{-1}$. Blue solid line: Chevy’s ansatz (2.1); red line with full squares: ansatz (3.1); black dashed line: BEC asymptotics (2.4); orange dashed-dotted line: Thouless criterion (3.10). The open black diamonds and green triangles correspond to the QMC results for the molecule and the polaron energies from Prokof’ev and Svistunov [6].

Figure 3

(Color online) Dimensionless contact coefficient $s$ as a function of ${\left(k_{F}a\right)}^{-1}$, calculated from the two variational wave functions (2.1, 3.1). Within this approach $s$ is discontinuous at the critical coupling $v_M$. The black dashed line marks the asymptotics in the molecular limit, where $s=4v/3\pi$ is fixed by the two-particle bound-state wave function in momentum space.

Figure 4

Qualitative phase diagram of the imbalanced Fermi gas as a function of the inverse coupling strength ${\left(k_{F}a\right)}^{-1}$ and the effective magnetic field $h/{\epsilon }_F$. The thick line indicates a first-order phase transition and the different phases are labeled as in [25], i.e., $N_{\text{fp}}$: fully polarized normal phase; $N_{\text{pp}}$: partially polarized normal phase; ${\text{SF}}_0$: balanced superfluid; ${\text{SF}}_{\text{p}}$: polarized superfluid. The points $M$ and $S$ are discussed in the text. The precise structure of the phase diagram in the nontrivial regime $h_c<h<h_s$ is likely to contain unconventional superfluid phases in addition to the $N_{\text{pp}}$ and ${\text{SF}}_{\text{p}}$ phases, which are not shown in our figure.