Impurity immersed in a double Fermi sea

We present a variational calculation of the energy of an impurity immersed in a double Fermi sea of noninteracting fermions. We show that in the strong-coupling regime, the system undergoes a first-order transition between polaronic and trimer states. Our result suggests that the smooth crossover predicted in previous literature for a superfluid background is the consequence of Cooper pairing and is absent in a normal system.