Coherent two-level dynamics of a single impurity in a self-bound quantum droplet

We study the coherent dynamics of a single impurity atom embedded in a self-bound, quasi-one-dimensional quantum droplet. The droplet, described by a cubic–quartic nonlinear Schrödinger equation, provides a self-generated potential in which the impurity supports an even–odd doublet of bound states forming an effective two-level system. Using a super-Gaussian variational model, semiclassical WKB analysis, and time-dependent simulations, we derive quantitative relations linking droplet geometry to impurity level splitting and Rabi frequency. The impurity undergoes intrinsic, field-free Rabi oscillations between edge-localized modes, which map directly to Bloch-sphere rotations. These results establish a minimal, self-stabilized platform for coherent matter-wave qubits, where control arises solely from the nonlinear droplet properties.