Zero-energy modes of two-component Bose-Bose droplets
- URL: http://arxiv.org/abs/2011.05135v3
- Date: Tue, 23 Mar 2021 13:53:49 GMT
- Title: Zero-energy modes of two-component Bose-Bose droplets
- Authors: Pawe{\l} Zin, Maciej Pylak, and Mariusz Gajda
- Abstract summary: Quantum droplets emerge from a mixture of two interacting Bose-Einstein condensates.
During droplet formation three continuous symmetries of the system's Hamiltonian are broken.
Breaking of these symmetries must be accompanied by appearance of zero-energy excitations.
- Score: 0.0
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: 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 U1 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 Hamitonians 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 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. This gives the possibility of describing in a relatively easy way
processes of interaction of these quantum droplets, such as collisions.
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