Investigation of one-dimensional quantum droplets in a temporally perturbed external harmonic trap

Using analytical methods we investigate the formation of quantum droplets in symmetric Bose-Bose mixture confined in temporally mutable parabolic traps. The dynamics of the droplet is observed to be heavily dependent upon dynamic nature of the trap. We demonstrate a mechanism to obtain exact droplet solution even if there are imperfections in the dynamic trap, provided the imperfections are of a certain nature. This is done through isospectral Hamiltonian technique of supersymmetric Quantum Mechanics, which also provides an intelligent way to control the dynamics of the quantum droplets through Riccati parameter. This method allows judicious tailoring of the trap frequency which in turn controls the width of the droplet, and quantum droplet can be stretched or squeezed by careful choice of this Riccati parameter. It provides a valuable tool for investigating and adapting to unforeseen variations and deviations encountered in experimental scenarios.