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Phonon Stability of Quantum Droplets in Dipolar Bose Gases |
| Fan Zhang and Lan Yin* |
| School of Physics, Peking University, Beijing 100871, China |
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| Cite this article: |
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Fan Zhang and Lan Yin 2022 Chin. Phys. Lett. 39 060301 |
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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.
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Received: 07 April 2022
Editors' Suggestion
Published: 29 May 2022
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| PACS: |
03.75.Kk
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(Dynamic properties of condensates; collective and hydrodynamic excitations, superfluid flow)
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03.75.Nt
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(Other Bose-Einstein condensation phenomena)
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67.85.De
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(Dynamic properties of condensates; excitations, and superfluid flow)
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03.75.Hh
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(Static properties of condensates; thermodynamical, statistical, and structural properties)
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