Abstract
Solitons, that is stable localized perturbations of a medium, are the topological excitations of nonlinear systems. They can be stable and live for a long time and may have promising applications for telecommunication. The basic one is the Tsuzuki dark soliton, which can be described by an analytical solution of the Gross–Pitaevskii equation (GPE). Ultracold Bose–Einstein condensed (BEC) gases are an important example for the investigation of solitons which can be created by phase and density imprinting. New possibilities arise in mixtures of different hyperspin states of ultra-cold gases, where the so-called magnetic solitons (MS), that is localized magnetized regions, can exist. We will see that these MS permit an analytical description. New peculiar phenomena can take place in the presence of a coherent Rabi coupling between the spin states, where two different type of solitons exist—so-called \(2\pi \) and \(0\pi \) solitons. \(2\pi \) solitons, unlike the usual Tsuzuki solitons, have at small velocity a positive effective mass and consequently do not undergo the snake instability. Solitary waves can oscillate in BEC gases along elongated traps. The theoretical description of this motion requires the knowledge of the effective soliton mass and the effective number of particles in the soliton. These quantities are calculated.
Similar content being viewed by others
References
Burger S, Bongs K, Dettmer S, Ertmer W, Sengstock K, Sanpera A, Shlyapnikov GV, Lewenstein M (1999) Dark solitons in Bose–Einstein condensates. Phys Rev Lett 83:5198
Busch Th, Anglin JR (2000) Motion of dark solitons in trapped Bose–Einstein condensates. Phys Rev Lett 84:2298
Calderaro L, Fetter AL, Massignan P, Wittek P (2017) Vortex dynamics in coherently coupled Bose–Einstein condensates. Phys Rev A 95:023605
Danaila I, Khamehchi MA, Gokhroo V, Engels P, Kevrekidis PG (2016) Vector dark-antidark solitary waves in multicomponent Bose–Einstein condensates. Phys Rev A 94:053617
Denschlag J, Simsarian JE, Feder DL, Clark Charles W, Collins LA, Cubizolles J, Deng L, Hagley EW, Helmerson K, Reinhardt WP, Rolston SL, Schneider BI, Phillips WD (2000) Generating solitons by phase engineering of a Bose–Einstein condensate. Science 287:97
Emori S, Bauer U, Ahn S-M, Martinez E, Beach GSD (2013) Currentdriven dynamics of chiral ferromagnetic domain walls. Nat Mater 12:611
Kamchatnov AM, Pitaevskii LP (2008) Stabilization of solitons generated by a supersonic flow of Bose–Einstein condensate past an obstacle. Phys Rev Lett 100:160402
Khaykovich L, Schreck F, Ferrari G, Bourdel T, Cubizolles J, Carr LD, Castin Y, Salomon C (2002) Formation of a matter-wave bright soliton. Science 296:1290
Kibble TWB (1976) Topology of cosmic domains and strings. J Phys A Math Gen 9:1387
Knoop S, Schuster T, Scelle R, Trautmann A, Appmeier J, Oberthaler MK, Tiesinga E, Tiemann E (2011) Feshbach spectroscopy and analysis of the interaction potentials of ultracold sodium. Phys Rev A 83:042704
Konotop VV, Pitaevskii L (2004) Landau dynamics of a grey soliton in a trapped condensate. Phys Rev Lett 93:240403
Mollenauer LF, Stolen RH, Gordon JP (1980) Experimental observation of picosecond pulse narrowing and solitons in optical fibers. Phys Rev Lett 45:1095
Pitaevskii LP (2016) Dynamics of solitary waves in ultracold gases in terms of observable quantities. Phys Uspekhi 59(10):1028
Pitaevskii LP, Stringari S (2016) Bose–Einstein condensation and superluidity. Oxford University Press, New York
Qu C, Pitaevskii LP, Stringari S (2016) Magnetic solitons in binary Bose–Einstein condensate. Phys Rev Lett 116:160402
Qu C, Tulutki M, Stringari S, Pitaevskii LP (2017) Magnetic solitons in Rabi-coupled Bose–Einstein condensates. Phys Rev A 95:033614
Ryutova M, Shine R, Title A, Sakai JI (1998) A possible mechanism for the origin of emerging flux in the sunspot moat. Astrophys J 492:402
Son DT, Stephanov MA (2002) Domain walls of relative phase in twocomponent Bose–Einstein condensates. Phys Rev A 65:063621
Su WP, Schrieffer JR, Heeger AJ (1979) Solitons in polyacetylene. Phys Rev Lett 42:1698
Tsuzuki T (1971) Nonlinear waves in the Pitaevskii–Gross equation. J Low Temp Phys 4:441
Tylutki M, Pitaevskii LP, Recati A, Stringari S (2016) Coninement and precession of vortex pairs in coherently coupled Bose–Einstein condensates. Phys Rev A 93:043623
Usui A, Takeuchi H (2015) Rabi-coupled countersuperflow in binary Bose–Einstein condensates. Phys Rev A 91:063635
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
This contribution is the written, peer-reviewed version of a paper presented at the conference “Classical and quantum plasmas: matter under extreme conditions” held at Accademia Nazionale dei Lincei in Rome on April 5–6, 2018.
Rights and permissions
About this article
Cite this article
Pitaevskii, L.P. Magnetic solitons in binary mixtures of Bose–Einstein condensates. Rend. Fis. Acc. Lincei 30, 269–276 (2019). https://doi.org/10.1007/s12210-019-00797-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12210-019-00797-6