  We investigate a polaronic excitation in a one-dimensional spin-1/2 Fermi gas
with contact attractive interactions, using the complex Langevin method, which
is a promising approach to evade a possible sign problem in quantum Monte Carlo
simulations. We found that the complex Langevin method works correctly in a
wide range of temperature, interaction strength, and population imbalance. The
Fermi polaron energy extracted from the two-point imaginary Green's function is
not sensitive to the temperature and the impurity concentration in the
parameter region we considered. Our results show a good agreement with the
solution of the thermodynamic Bethe ansatz at zero temperature.
