Zero-energy modes of two-component Bose-Bose droplets

Bose-Bose droplets are self-bound objects emerging from a mixture of two interacting Bose-Einstein condensates when their interactions are appropriately tuned. During droplet formation three continuous symmetries of the system's Hamiltonian are broken: translational symmetry and two U(1) symmetries, allowing for arbitrary choice of phases of the mean-field wavefunctions describing the two components. Breaking of these symmetries must be accompanied by appearance of zero-energy excitations in the energy spectrum of the system recovering the broken symmetries. Normal modes corresponding to these excitations are the zero-energy modes. Here we find analytic expressions for these modes and introduce Hamiltonians generating their time evolution-dynamics of the droplet's centers of mass as well as dynamics of the phases of the two droplet's wavefunctions. When internal types of excitations (quasiparticles) are neglected then the very complex system of a quantum droplet is described using only a few 'global' degrees of freedom-the position of the center of mass of the droplet and two phases of two wave-functions, all these being quantum operators. We believe that our work might be useful in describing in a relatively easy way the low energy collisions of quantum droplets in situations where coherent flow of atoms between the droplets takes place.

Automated summary

Bose-Bose droplets are self-bound objects formed from a mixture of interacting Bose-Einstein condensates, breaking three continuous symmetries in the system. This study provides analytic expressions for zero-energy excitations and introduces Hamiltonians for the dynamics of droplet motion and wavefunction phase evolution. By focusing on a few key degrees of freedom, such as droplet center of mass and wavefunction phases, the complex quantum system can be described effectively, which may have applications in studying low energy collisions of quantum droplets.