Bosonic impurity in a one-dimensional quantum droplet in the Bose-Bose mixture

We study an impurity immersed in the mixture of Bose ultracold gases in the regime where a quantum droplet (QD) exists. The quasi-one-dimensional geometry is considered. We find an effective attractive potential, which acts by the QD onto the impurity. The bound states of the impurity in this potential are investigated. These impurity-bound states can provide potential probes for the presence of quantum fluctuation effects on the droplet properties. In the case of strong impurity-Bose-Einstein condensate coupling we study the properties of the nonlinear local modes on the impurity induced by the quantum fluctuations.