Phonon Stability of Quantum Droplets in Dipolar Bose Gases
Fan Zhang and Lan Yin*
School of Physics, Peking University, Beijing 100871, China
Abstract ：Stabilized by quantum fluctuations, dipolar Bose–Einstein condensates can form self-bound liquid-like droplets. However in the Bogoliubov theory, there are imaginary phonon energies in the long-wavelength limit, implying dynamical instability of this system. A similar instability appears in the Bogoliubov theory of a binary quantum droplet, and is removed due to higher-order quantum fluctuations as shown recently [Gu Q and Yin L 2020 Phys. Rev. B 102 220503(R)]. We study the excitation energy of a dipolar quantum droplet in the Beliaev formalism, and find that quantum fluctuations significantly enhance the phonon stability. We adopt a self-consistent approach without the problem of complex excitation energy in the Bogoliubov theory, and obtain a stable anisotropic sound velocity which is consistent with the superfluid hydrodynamic theory, but slightly different from the result of the extended Gross–Pitaevskii equation due to quantum depletion. A modified Gross–Pitaevskii equation in agreement with the Beliaev theory is proposed, which takes the effect of quantum fluctuations into account more completely.
收稿日期: 2022-04-07
Editors' Suggestion
出版日期: 2022-05-29
:
03.75.Kk
(Dynamic properties of condensates; collective and hydrodynamic excitations, superfluid flow)
03.75.Nt
(Other Bose-Einstein condensation phenomena)
67.85.De
(Dynamic properties of condensates; excitations, and superfluid flow)
03.75.Hh
(Static properties of condensates; thermodynamical, statistical, and structural properties)
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2022, Vol. 39 
