We formulate the induced potential in a finite temperature cold atomic medium between two heavy impurities, or polarons, which is shown to be \textit{complex-valued} in general. The imaginary part of the complex-valued potential describes a decoherence effect, and thus, the resulting Schrödinger equation for the two polarons acquires a non-Hermitian term. We apply the developed formulation to two representative cases of polarons interacting with medium particles through the s-wave contact interaction: (i) the normal phase of single-component (i.e., spin-polarized) fermions using the fermionic field theory, and (ii) a superfluid phase using the superfluid effective field theory, which is valid either for a Bose-Einstein condensate (BEC) of a single-component Bose gas or for the BEC-BCS crossover in two-component fermions at a low-energy regime. Computing the leading-order term, the imaginary part of the potential in both cases is found to show a universal r2 behavior at long distance. We propose three experimental ways to observe the effects of the universal imaginary potential in cold atoms.

Y. Akamatsu, S. Endo, K. Fujii, M. Hongo, “Complex-valued in-medium potential between heavy impurities in ultracold atoms”, Dec. 13, 2023, arXiv:2312 . 08241 (2023).


Related to Project C02, C03