Skip to main content
SpringerLink
Log in

Novel soliton in dipolar BEC caused by the quantum fluctuations

  • Regular Article - Cold Matter and Quantum Gases
  • Published:
The European Physical Journal D Aims and scope Submit manuscript

Abstract

Solitons in the extended hydrodynamic model of the dipolar Bose–Einstein condensates with the quantum fluctuations are considered. This model includes the continuity equation for the scalar field of concentration, the Euler equation for the vector field of velocity, the pressure evolution equation for the second rank tensor of pressure, and the evolution equation for the third rank tensor. Large amplitude soliton solution caused by the dipolar part of the quantum fluctuations is found. It appears as the bright soliton. Hence, it is the area of compression of the number of particles. Moreover, it exists for the repulsive short-range interaction.

Graphic Abstract

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

Data Availability Statement

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: Data sharing is not applicable to this article as no new data were created or analyzed in this study, which is a purely theoretical one.]

References

  1. H. Kadau, M. Schmitt, M. Wenzel, C. Wink, T. Maier, I. Ferrier-Barbut, T. Pfau, Observing the Rosensweig instability of a quantum ferrofluid. Nature 530, 194 (2016)

    Article  ADS  Google Scholar 

  2. I. Ferrier-Barbut, H. Kadau, M. Schmitt, M. Wenzel, T. Pfau, Observation of quantum droplets in a strongly dipolar Bose gas. Phys. Rev. Lett. 116, 215301 (2016)

    Article  ADS  Google Scholar 

  3. D. Baillie, R.M. Wilson, R.N. Bisset, P.B. Blakie, Self-bound dipolar droplet: a localized matter-wave in free space. Phys. Rev. A 94, 021602(R) (2016)

    Article  ADS  Google Scholar 

  4. R.N. Bisset, R.M. Wilson, D. Baillie, P.B. Blakie, Ground-state phase diagram of a dipolar condensate with quantum fluctuations. Phys. Rev. A 94, 033619 (2016)

    Article  ADS  Google Scholar 

  5. F. Wachtler, L. Santos, Quantum filaments in dipolar Bose–Einstein condensates. Phys. Rev. A 93, 061603R (2016)

    Article  ADS  Google Scholar 

  6. F. Wachtler, L. Santos, Ground-state properties and elementary excitations of quantum droplets in dipolar Bose–Einstein condensates. Phys. Rev. A 94, 043618 (2016)

    Article  ADS  Google Scholar 

  7. P.B. Blakie, Properties of a dipolar condensate with three-body interactions. Phys. Rev. A 93, 033644 (2016)

    Article  ADS  Google Scholar 

  8. A. Boudjemaa, N. Guebli, Quantum correlations in dipolar droplets: time-dependent Hartree–Fock–Bogoliubov theory. Phys. Rev. A 102, 023302 (2020)

    Article  ADS  Google Scholar 

  9. V. Heinonen, K.J. Burns, J. Dunkel, Quantum hydrodynamics for supersolid crystals and quasicrystals. Phys. Rev. A 99, 063621 (2019)

    Article  ADS  Google Scholar 

  10. B.A. Malomed, Vortex solitons: old results and new perspectives. Physica D 399, 108 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  11. E. Shamriz, Z. Chen, B.A. Malomed, Suppression of the quasi-two-dimensional quantum collapse in the attraction field by the Lee–Huang–Yang effect. Phys. Rev. A 101, 063628 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  12. Z. Li, J.-S. Pan, W. Vincent Liu, Spontaneous formation of polar superfluid droplets in a p-wave interacting Bose gas. Phys. Rev. A 100, 053620 (2019)

    Article  ADS  Google Scholar 

  13. E. Aybar, M.O. Oktel, Temperature-dependent density profiles of dipolar droplets. Phys. Rev. A 99, 013620 (2019)

    Article  ADS  Google Scholar 

  14. L. Chomaz, S. Baier, D. Petter, M.J. Mark, F. Wachtler, L. Santos, F. Ferlaino, Quantum-fluctuation-driven crossover from a Dilute Bose–Einstein condensate to a macrodroplet in a dipolar quantum fluid. Phys. Rev. X 6, 041039 (2016)

    Google Scholar 

  15. P. Examilioti, G.M. Kavoulakis, Ground state and rotational properties of two-dimensional self-bound quantum droplets. J. Phys. B: At. Mol. Opt. Phys. 53, 175301 (2020)

    Article  ADS  Google Scholar 

  16. T. Miyakawa, S. Nakamura, H. Yabu, Phase separation in trapped dipolar Fermi gases. Phys. Rev. A 101, 033613 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  17. F. Bottcher, Jan-Niklas Schmidt, J. Hertkorn, Kevin S. H. Ng, S. D. Graham, M. Guo, T. Langen, T. Pfau, New states of matter with fine-tuned interactions: quantum droplets and dipolar supersolids. arXiv:2007.06391

  18. R.N. Bisset, L.A. Pea Ardila, L. Santos, Quantum droplets of dipolar mixtures. arXiv:2007.00404

  19. Y. Wang, L. Guo, S. Yi, T. Shi, Theory for self-bound states of Dipolar Bose–Einstein condensates. arXiv:2002.11298

  20. M.J. Edmonds, T. Bland, N.G. Parker, Quantum droplets of quasi-one-dimensional dipolar Bose–Einstein condensates. arXiv:2002.07958

  21. D. Baillie, P.B. Blakie, Rotational tuning of the dipole–dipole interaction in a Bose gas of magnetic atoms. Phys. Rev. A 101, 043606 (2020)

    Article  ADS  Google Scholar 

  22. F. Dalfovo, S. Giorgini, L.P. Pitaevskii, S. Stringari, Theory of Bose–Einstein condensation in trapped gases. Rev. Mod. Phys. 71, 463 (1999)

    Article  ADS  Google Scholar 

  23. T.D. Lee, K. Huang, C.N. Yang, Eigenvalues and eigenfunctions of a Bose system of hard spheres and its low-temperature properties. Phys. Rev. 106, 1135 (1957)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  24. L. Pitaevskii, S. Stringari, Elementary excitations in trapped Bose–Einstein condensed gases beyond the mean-field approximation. Phys. Rev. Lett. 81, 4541 (1998)

    Article  ADS  Google Scholar 

  25. E. Braaten, J. Pearson, Semiclassical corrections to the oscillation frequencies of a trapped Bose–Einstein condensate. Phys. Rev. Lett. 82, 255 (1999)

    Article  ADS  Google Scholar 

  26. G.E. Astrakharchik, R. Combescot, X. Leyronas, S. Stringari, Equation of state and collective frequencies of a trapped fermi gas along the BEC-unitarity crossover. Phys. Rev. Lett. 95, 030404 (2005)

    Article  ADS  Google Scholar 

  27. K. Xu, Y. Liu, D.E. Miller, J.K. Chin, W. Setiawan, W. Ketterle, Observation of strong quantum depletion in a Gaseous Bose–Einstein condensate. Phys. Rev. Lett. 96, 180405 (2006)

    Article  ADS  Google Scholar 

  28. A. Altmeyer, S. Riedl, C. Kohstall, M.J. Wright, R. Geursen, M. Bartenstein, C. Chin, J. Hecker Denschlag, R. Grimm, Precision measurements of collective oscillations in the BEC-BCS crossover. Phys. Rev. Lett. 98, 040401 (2007)

    Article  ADS  Google Scholar 

  29. S.B. Papp, J.M. Pino, R.J. Wild, S. Ronen, C.E. Wieman, D.S. Jin, E.A. Cornell, Bragg spectroscopy of a strongly interacting \(^{85}\)Rb Bose–Einstein condensate. Phys. Rev. Lett. 101, 135301 (2008)

    Article  ADS  Google Scholar 

  30. K. Goral, K. Rzazewski, T. Pfau, Bose–Einstein condensation with magnetic dipole–dipole forces. Phys. Rev. A 61, 051601(R) (2000)

    Article  ADS  Google Scholar 

  31. L. Santos, G.V. Shlyapnikov, P. Zoller, M. Lewenstein, Bose–Einstein condensation in trapped dipolar gases. Phys. Rev. Lett. 85, 1791 (2000)

    Article  ADS  Google Scholar 

  32. S. Yi, L. You, Trapped atomic condensates with anisotropic interactions. Phys. Rev. A 61, 041604(R) (2000)

    Article  ADS  Google Scholar 

  33. A. Griesmaier, J. Werner, S. Hensler, J. Stuhler, T. Pfau, Bose–Einstein condensation of chromium. Phys. Rev. Lett. 94, 160401 (2005)

    Article  ADS  Google Scholar 

  34. K.-K. Ni, S. Ospelkaus, D. Wang, G. Quemener, B. Neyenhuis, M.H.G. de Miranda, J.L. Bohn, J. Ye, D.S. Jin, Dipolar collisions of polar molecules in the quantum regime. Nature London 464, 1324 (2010)

    Article  ADS  Google Scholar 

  35. L.D. Carr, J. Ye, Focus on cold and ultracold molecules. New J. Phys. 11, 055009 (2009)

    Article  ADS  Google Scholar 

  36. L.D. Carr, D. DeMille, R.V. Krems, J. Ye, Cold and ultracold molecules: science, technology and applications. New J. Phys. 11, 055049 (2009)

    Article  ADS  Google Scholar 

  37. R.M. Wilson, S.T. Rittenhouse, J.L. Bohn, A dielectric superfluid of polar molecules. New J. Phys. 14, 043018 (2012)

    Article  ADS  Google Scholar 

  38. T. Lahaye, T. Koch, B. Frohlich, M. Fattori, J. Metz, A. Griesmaier, S. Giovanazzi, T. Pfau, Strong dipolar effects in a quantum ferrofluid. Nature 448, 672 (2007)

    Article  ADS  Google Scholar 

  39. T. Lahaye, C. Menotti, L. Santos, M. Lewenstein, T. Pfau, The physics of dipolar bosonic quantum gases. Rep. Prog. Phys. 72, 126401 (2009)

    Article  ADS  Google Scholar 

  40. A.R.P. Lima, A. Pelster, Collective motion of polarized dipolar Fermi gases in the hydrodynamic regime. Phys. Rev. A 81, 021606(R) (2010)

    Article  ADS  Google Scholar 

  41. A.R.P. Lima, A. Pelster, Dipolar Fermi gases in anisotropic traps. Phys. Rev. A 81, 063629 (2010)

    Article  ADS  Google Scholar 

  42. A.R.P. Lima, A. Pelster, Quantum fluctuations in dipolar Bose gases. Phys. Rev. A 84, 041604 (2011)

    Article  ADS  Google Scholar 

  43. A.R.P. Lima, A. Pelster, Beyond mean-field low-lying excitations of dipolar Bose gases. Phys. Rev. A 86, 063609 (2012)

    Article  ADS  Google Scholar 

  44. P.B. Blakie, D. Baillie, R.N. Bisset, Depletion and fluctuations of a trapped dipolar Bose–Einstein condensate in the Roton regime. Phys. Rev. A 88, 013638 (2013)

    Article  ADS  Google Scholar 

  45. A. Boudjemaa, Theory of excitations of dipolar Bose–Einstein condensate at finite temperature. J. Phys. B 48, 035302 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  46. P.A. Andreev, L.S. Kuzmenkov, Exact analytical soliton solutions in dipolar Bose–Einstein. Eur. Phys. J. D 68, 270 (2014)

    Article  ADS  Google Scholar 

  47. M.O.D. Alotaibi, L.D. Carr, Dynamics of dark-bright vector solitons in Bose–Einstein condensates. Phys. Rev. A 96, 013601 (2017)

    Article  ADS  Google Scholar 

  48. D.J. Frantzeskakis, Dark solitons in atomic Bose–Einstein condensates: from theory to experiments. J. Phys. A 43, 213001 (2010)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  49. R. Carretero-Gonzalez, D.J. Frantzeskakis, P.G. Kevrekidis, Nonlinear waves in Bose–Einstein condensates: physical relevance and mathematical techniques. Nonlinearity 21, R139 (2008)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  50. P. Naldesi, J. P. Gomez, V. Dunjko, H. Perrin, M. Olshanii, L. Amico, A. Minguzzi, Enhancing sensitivity to rotations with quantum solitonic currents. arXiv:1901.09398

  51. M. Lewenstein, B.A. Malomed, Entanglement generation by collisions of quantum solitons. New J. Phys. 11, 113014 (2009)

    Article  ADS  Google Scholar 

  52. A. Syrwid, Quantum dark solitons in ultracold one-dimensional Bose and Fermi gases. arXiv:2009.12554

  53. J. Polo, P. Naldesi, A. Minguzzi, L. Amico, The quantum solitons atomtronic interference device. arXiv:2012.06269

  54. D.V. Tsarev, S.M. Arakelian, Y.-L. Chuang, R.-K. Lee, A.P. Alodjants, Quantum metrology beyond Heisenberg limit with entangled matter wave solitons. Opt. Express 26, 19583 (2018)

    Article  ADS  Google Scholar 

  55. L. Buoninfante, G. Lambiase, A. Mazumdar, Quantum solitonic wave-packet of a meso-scopic system in singularity free gravity. Nucl. Phys. B 931, 250 (2018)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  56. P. A. Andreev, Quantum hydrodynamic theory of quantum fluctuations in dipolar Bose–Einstein condensate. Chaos. (2021). https://doi.org/10.1063/5.0036511

  57. P.A. Andreev, Hydrodynamics of the atomic Bose–Einstein condensate beyond the mean-field. arXiv:2007.15045

  58. G.C. Katsimiga, G.M. Koutentakis, S.I. Mistakidis, P.G. Kevrekidis, P. Schmelcher, Darkbright soliton dynamics beyond the mean-field approximation. New J. Phys. 19, 073004 (2017)

    Article  ADS  Google Scholar 

  59. G.C. Katsimiga, S.I. Mistakidis, G.M. Koutentakis, P.G. Kevrekidis, P. Schmelcher, Many-body quantum dynamics in the decay of bent dark solitons of Bose–Einstein condensates. New J. Phys. 19, 123012 (2017)

    Article  ADS  Google Scholar 

  60. G.C. Katsimiga, S.I. Mistakidis, G.M. Koutentakis, P.G. Kevrekidis, P. Schmelcher, Many-body dissipative flow of a confined scalar Bose–Einstein condensate driven by a Gaussian impurity. Phys. Rev. A 98, 013632 (2018)

    Article  ADS  Google Scholar 

  61. S.I. Mistakidis, G.C. Katsimiga, P.G. Kevrekidis, P. Schmelcher, Correlation effects in the quench-induced phase separation dynamics of a two species ultracold quantum gas. New J. Phys. 20, 043052 (2018)

    Article  ADS  Google Scholar 

  62. T. Koide, Spin-electromagnetic hydrodynamics and magnetization induced by spin-magnetic interaction. Phys. Rev. C 87, 034902 (2013)

    Article  ADS  Google Scholar 

  63. P.A. Andreev, L.S. Kuz’menkov, Separated spin-up and spin-down evolution of degenerated electrons in two-dimensional systems: dispersion of longitudinal collective excitations in plane and nanotube geometry. Eur. Phys. Lett. 113, 17001 (2016)

    Article  ADS  Google Scholar 

  64. P.A. Andreev, L.S. Kuz’menkov, Surface spin-electron acoustic waves in magnetically ordered metals. Appl. Phys. Lett. 108, 191605 (2016)

    Article  ADS  Google Scholar 

  65. P.A. Andreev, Extended hydrodynamics of the degenerate partially spin polarized fermions with the short-range interaction up to the third order by the interaction radius approximation. arXiv:2001.02764

  66. L.S. Kuz’menkov, S.G. Maksimov, Quantum hydrodynamics of particle systems with Coulomb interaction and quantum Bohm potential. Theor. Math. Phys. 118, 227 (1999)

    Article  MATH  Google Scholar 

  67. P.A. Andreev, L.S. Kuzmenkov, M.I. Trukhanova, Quantum hydrodynamics approach to the formation of waves in polarized two-dimensional systems of charged and neutral particles. Phys. Rev. B 84, 245401 (2011)

    Article  ADS  Google Scholar 

  68. L.S. Kuz’menkov, S.G. Maksimov, V.V. Fedoseev, Microscopic quantum hydrodynamics of systems of fermions: Part I. Theor. Math. Phys. 126, 110 (2001)

    Article  MATH  Google Scholar 

  69. K. Renziehausen, I. Barth, Many-particle quantum hydrodynamics exact equations and pressure tensors. Prog. Theor. Exp. Phys. 2018, 013A05 (2018)

    Article  Google Scholar 

  70. C. Chin, R. Grimm, P. Julienne, E. Tiesinga, Feshbach resonances in ultracold gases. Rev. Mod. Phys. 82, 1225 (2010)

    Article  ADS  Google Scholar 

  71. J. Stuhler, A. Griesmaier, J. Werner, T. Koch, M. Fattori, T. Pfau, Ultracold chromium atoms: from Feshbach resonances to a dipolar Bose–Einstein condensate. J. Mod. Opt. 54, 647 (2007)

    Article  ADS  Google Scholar 

  72. P.A. Andreev, On the interaction constant measurement of polarized fermions via sound wave spectra obtained from hydrodynamics with the pressure evolution equation. arXiv:1912.00843

  73. P.A. Andreev, L.S. Kuz’menkov, Problem with the single-particle description and the spectra of intrinsic modes of degenerate boson-fermion systems. Phys. Rev. A 78, 053624 (2008)

    Article  ADS  Google Scholar 

  74. P.A. Andreev, Hydrodynamic model of a Bose–Einstein condensate with anisotropic short-range interaction and bright solitons in a repulsive Bose–Einstein condensate. Laser Phys. 29, 035502 (2019)

    Article  ADS  Google Scholar 

  75. I. Tokatly, O. Pankratov, Hydrodynamic theory of an electron gas. Phys. Rev. B 60, 15550 (1999)

    Article  ADS  Google Scholar 

  76. I.V. Tokatly, O. Pankratov, Hydrodynamics beyond local equilibrium: application to electron gas. Phys. Rev. B 62, 2759 (2000)

    Article  ADS  Google Scholar 

  77. P.A. Andreev, K.V. Antipin, M.Iv. Trukhanova, A bosonic bright soliton in a mixture of repulsive Bose-Einstein condensate and polarized ultracold fermions under the influence of pressure evolution. Laser Phys. 31, 015501 (2021). https://doi.org/10.1088/1555-6611/abd16e

  78. B. Bertini, M. Collura, J. De Nardis, M. Fagotti, Transport in out-of-equilibrium XXZ chains: exact profiles of charges and currents. Phys. Rev. Lett. 117, 207201 (2016)

    Article  ADS  Google Scholar 

  79. P. Ruggiero, P. Calabrese, B. Doyon, J. Dubail, Quantum generalized hydrodynamics. Phys. Rev. Lett. 124, 140603 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  80. R. Z. Sagdeev, in Reviews of Plasma Physics, edited by M. A. Leontovich (Consultants Bureau, New York, 1966), Vol. 4, p. 23

  81. H. Schamel, M.Y. Yu, P.K. Shukla, Finite amplitude envelope solitons. Phys. Fluids 20, 1286 (1977)

    Article  ADS  Google Scholar 

  82. E. Witt, W. Lotko, Ion-acoustic solitary waves in a magnetized plasma with arbitrary electron equation of state. Phys. Fluids 26, 2176 (1983)

    Article  ADS  MATH  Google Scholar 

  83. A.A. Mamun, Effects of ion temperature on electrostatic solitary structures in nonthermal plasmas. Phys. Rev. E 55, 1852 (1997)

    Article  ADS  Google Scholar 

  84. H.A. Shah, M.N.S. Qureshi, N. Tsintsadze, Effect of trapping in degenerate quantum plasmas. Phys. Plasmas 17, 032312 (2010)

    Article  ADS  Google Scholar 

  85. M. Marklund, B. Eliasson, P.K. Shukla, Magnetosonic solitons in a fermionic quantum plasma. Phys. Rev. E 76, 067401 (2007)

    Article  ADS  Google Scholar 

  86. M. Akbari-Moghanjoughi, Generalized Sagdeev potential theory for shock waves modeling. Phys. Plasmas 24, 052302 (2017)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We acknowledge that the work is supported by the Russian Foundation for Basic Research (Grant No. 20-02-00476). This paper has been supported by the RUDN University Strategic Academic Leadership Program.

Author information

Authors and Affiliations

  1. Faculty of Physics, Lomonosov Moscow State University, Moscow, Russian Federation, 119991

    Pavel A. Andreev

  2. Peoples Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Street, Moscow, 117198, Russian Federation

    Pavel A. Andreev

Authors
  1. Pavel A. Andreev
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

This paper has one author, who made the preparation of the manuscript and carried on the research presented in the manuscript.

Corresponding author

Correspondence to Pavel A. Andreev.

Supplementary Information

Below is the link to the electronic supplementary material.

Supplementary material 1 (pdf 211 KB)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Andreev, P.A. Novel soliton in dipolar BEC caused by the quantum fluctuations. Eur. Phys. J. D 75, 60 (2021). https://doi.org/10.1140/epjd/s10053-021-00071-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1140/epjd/s10053-021-00071-1

Search

Navigation