Mediated interaction between polarons in a one-dimensional Bose gas

We study a weakly interacting one-dimensional Bose gas with two impurities coupled locally to the boson density. We derive analytical results for the induced interaction between the impurities at arbitrary positive coupling and separation r. At r less than or similar to xi, where xi denotes the healing length of the Bose gas, the interaction is well described by the mean-field contribution. Its form changes as the coupling is increased, approaching a linear function of r at short distances in the regime of strong coupling. The mean-field contribution decays exponentially at arbitrary coupling for r >> xi. At such long distances, however, the effect of quantum fluctuations becomes important, giving rise to a long-ranged quantum contribution to the induced interaction. At longest distances it behaves as 1/r(3), while at strong coupling we find an intermediate distance regime with a slower decay, 1/r. The quantum contribution in the crossover regime is also calculated. The induced interaction between impurities (i.e., polarons) is attractive and leads to the formation of their bound state, known as bipolaron. We discuss its binding energy.

Automated summary

We study the induced interaction between two impurities in a weakly interacting one-dimensional Bose gas. The analytical results we derive show that the form of the interaction changes as the coupling is increased, approaching a linear function of the separation at short distances in the regime of strong coupling. Quantum fluctuations play an important role at long distances, resulting in a long-ranged quantum contribution to the induced interaction.