Axial Collective Mode of a Dipolar Quantum Droplet
(This article belongs to the Section Quantum Photonics and Technologies)
Abstract
1. Introduction
2. Formalism
2.1. Ground States
2.2. Excitations
2.2.1. Bogoliubov–De Gennes Theory
2.2.2. Sum Rule Approach for Lowest Compressional Mode
3. Results for Free-Space Droplets
3.1. Energetics
3.2. Excitations
3.3. Results with Varying
4. Results for Trapped Droplet
5. Conclusions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
- Griesmaier, A.; Werner, J.; Hensler, S.; Stuhler, J.; Pfau, T. Bose-Einstein Condensation of Chromium. Phys. Rev. Lett. 2005, 94, 160401. [Google Scholar] [CrossRef] [PubMed]
- Beaufils, Q.; Chicireanu, R.; Zanon, T.; Laburthe-Tolra, B.; Maréchal, E.; Vernac, L.; Keller, J.C.; Gorceix, O. All-optical production of chromium Bose-Einstein condensates. Phys. Rev. A 2008, 77, 061601. [Google Scholar] [CrossRef]
- Lu, M.; Burdick, N.Q.; Youn, S.H.; Lev, B.L. Strongly Dipolar Bose-Einstein Condensate of Dysprosium. Phys. Rev. Lett. 2011, 107, 190401. [Google Scholar] [CrossRef]
- Aikawa, K.; Frisch, A.; Mark, M.; Baier, S.; Rietzler, A.; Grimm, R.; Ferlaino, F. Bose-Einstein Condensation of Erbium. Phys. Rev. Lett. 2012, 108, 210401. [Google Scholar] [CrossRef] [PubMed]
- Lahaye, T.; Menotti, C.; Santos, L.; Lewenstein, M.; Pfau, T. The physics of dipolar bosonic quantum gases. Rep. Prog. Phys. 2009, 72, 126401. [Google Scholar] [CrossRef]
- Chomaz, L.; Ferrier-Barbut, I.; Ferlaino, F.; Laburthe-Tolra, B.; Lev, B.L.; Pfau, T. Dipolar physics: A review of experiments with magnetic quantum gases. Rep. Prog. Phys. 2022, 86, 026401. [Google Scholar] [CrossRef]
- Lee, T.D.; Huang, K.; Yang, C.N. Eigenvalues and Eigenfunctions of a Bose System of Hard Spheres and Its Low-Temperature Properties. Phys. Rev. 1957, 106, 1135–1145. [Google Scholar] [CrossRef]
- Lima, A.R.P.; Pelster, A. Quantum fluctuations in dipolar Bose gases. Phys. Rev. A 2011, 84, 041604. [Google Scholar] [CrossRef]
- Lima, A.R.P.; Pelster, A. Beyond mean-field low-lying excitations of dipolar Bose gases. Phys. Rev. A 2012, 86, 063609. [Google Scholar] [CrossRef]
- Petrov, D.S. Quantum Mechanical Stabilization of a Collapsing Bose-Bose Mixture. Phys. Rev. Lett. 2015, 115, 155302. [Google Scholar] [CrossRef]
- Ferrier-Barbut, I.; Kadau, H.; Schmitt, M.; Wenzel, M.; Pfau, T. Observation of Quantum Droplets in a Strongly Dipolar Bose Gas. Phys. Rev. Lett. 2016, 116, 215301. [Google Scholar] [CrossRef]
- Wächtler, F.; Santos, L. Quantum filaments in dipolar Bose-Einstein condensates. Phys. Rev. A 2016, 93, 061603(R). [Google Scholar] [CrossRef]
- Bisset, R.N.; Wilson, R.M.; Baillie, D.; Blakie, P.B. Ground-state phase diagram of a dipolar condensate with quantum fluctuations. Phys. Rev. A 2016, 94, 033619. [Google Scholar] [CrossRef]
- Kadau, H.; Schmitt, M.; Wenzel, M.; Wink, C.; Maier, T.; Ferrier-Barbut, I.; Pfau, T. Observing the Rosensweig instability of a quantum ferrofluid. Nature 2016, 530, 194–197. [Google Scholar] [CrossRef]
- Schmitt, M.; Wenzel, M.; Böttcher, F.; Ferrier-Barbut, I.; Pfau, T. Self-bound droplets of a dilute magnetic quantum liquid. Nature 2016, 539, 259–262. [Google Scholar] [CrossRef]
- Chomaz, L.; Baier, S.; Petter, D.; Mark, M.J.; Wächtler, F.; Santos, L.; Ferlaino, F. Quantum-Fluctuation-Driven Crossover from a Dilute Bose-Einstein Condensate to a Macrodroplet in a Dipolar Quantum Fluid. Phys. Rev. X 2016, 6, 041039. [Google Scholar] [CrossRef]
- Baillie, D.; Wilson, R.M.; Blakie, P.B. Collective Excitations of Self-Bound Droplets of a Dipolar Quantum Fluid. Phys. Rev. Lett. 2017, 119, 255302. [Google Scholar] [CrossRef]
- Pal, S.; Baillie, D.; Blakie, P.B. Infinite dipolar droplet: A simple theory for the macrodroplet regime. Phys. Rev. A 2022, 105, 023308. [Google Scholar] [CrossRef]
- Wächtler, F.; Santos, L. Ground-state properties and elementary excitations of quantum droplets in dipolar Bose-Einstein condensates. Phys. Rev. A 2016, 94, 043618. [Google Scholar] [CrossRef]
- Ferrier-Barbut, I.; Wenzel, M.; Böttcher, F.; Langen, T.; Isoard, M.; Stringari, S.; Pfau, T. Scissors Mode of Dipolar Quantum Droplets of Dysprosium Atoms. Phys. Rev. Lett. 2018, 120, 160402. [Google Scholar] [CrossRef] [PubMed]
- Lee, A.C.; Baillie, D.; Blakie, P.B. Numerical calculation of dipolar-quantum-droplet stationary states. Phys. Rev. Res. 2021, 3, 013283. [Google Scholar] [CrossRef]
- Pitaevskii, L.; Stringari, S. Bose-Einstein Condensation and Superfluidity; Oxford University Press: Oxford, UK, 2016; Volume 164. [Google Scholar]
- Menotti, C.; Stringari, S. Collective oscillations of a one-dimensional trapped Bose-Einstein gas. Phys. Rev. A 2002, 66, 043610. [Google Scholar] [CrossRef]
- Tanzi, L.; Roccuzzo, S.M.; Lucioni, E.; Famà, F.; Fioretti, A.; Gabbanini, C.; Modugno, G.; Recati, A.; Stringari, S. Supersolid symmetry breaking from compressional oscillations in a dipolar quantum gas. Nature 2019, 574, 382. [Google Scholar] [CrossRef] [PubMed]
- Dalfovo, F.; Giorgini, S.; Pitaevskii, L.; Stringari, S. Theory of Bose-Einstein condensation in trapped gases. Rev. Mod. Phys. 1999, 71, 463. [Google Scholar] [CrossRef]
- Triay, A. Existence of minimizers in generalized Gross-Pitaevskii theory with the Lee-Huang-Yang correction. arXiv 2019, arXiv:1904.10672. [Google Scholar]
- Lee, A.C.; Baillie, D.; Bisset, R.N.; Blakie, P.B. Excitations of a vortex line in an elongated dipolar condensate. Phys. Rev. A 2018, 98, 063620. [Google Scholar] [CrossRef]
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Blakie, P.B. Axial Collective Mode of a Dipolar Quantum Droplet. Photonics 2023, 10, 393. https://doi.org/10.3390/photonics10040393
Blakie PB. Axial Collective Mode of a Dipolar Quantum Droplet. Photonics. 2023; 10(4):393. https://doi.org/10.3390/photonics10040393
Chicago/Turabian StyleBlakie, Peter Blair. 2023. "Axial Collective Mode of a Dipolar Quantum Droplet" Photonics 10, no. 4: 393. https://doi.org/10.3390/photonics10040393
APA StyleBlakie, P. B. (2023). Axial Collective Mode of a Dipolar Quantum Droplet. Photonics, 10(4), 393. https://doi.org/10.3390/photonics10040393