Stationary and moving solitons in spin–orbit-coupled spin-1 Bose–Einstein condensates

Abstract

We investigate the matter-wave solitons in a spin–orbit-coupled spin-1 Bose–Einstein condensate using a multiscale perturbation method. Beginning with the one-dimensional spin–orbit-coupled threecomponent Gross–Pitaevskii equations, we derive a single nonlinear Schrödinger equation, which allows determination of the analytical soliton solutions of the system. Stationary and moving solitons in the system are derived. In particular, a parameter space for different existing soliton types is provided. It is shown that there exist only dark or bright solitons when the spin–orbit coupling is weak, with the solitons depending on the atomic interactions. However, when the spin–orbit coupling is strong, both dark and bright solitons exist, being determined by the Raman coupling. Our analytical solutions are confirmed by direct numerical simulations.

Keywords

spin–orbit coupling / Bose–Einstein condensate / soliton / perturbation method

References

[1] M. R. Matthews, B. P. Anderson, P. C. Haljan, D. S. Hall, C. E. Wieman, and E. A. Cornell, Vortices in a Bose–Einstein condensate, Phys. Rev. Lett. 83(13), 2498 (1999)

[2] J. Billy, V. Josse, A. Bernard, B. Hambrecht, P. Lugan, D. Clement, L. Sanchez-Palencia, P. Bouyer, and A. Aspect, Direct observation of Anderson localization of matter waves in a controlled disorder, Nature 453(7197), 891 (2008)

[3] G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, and M. Inguscio, Anderson localization of a non-interacting Bose– Einstein condensate, Nature 453(7197), 895 (2008)

[4] S. Burger, K. Bongs, S. Dettmer, W. Ertmer, K. Sengstock, A. Sanpera, G. V. Shlyapnikov, and M. Lewenstein, Dark solitons in Bose–Einstein condensates, Phys. Rev. Lett. 83(25), 5198 (1999)

[5] U. Al Khawaja, H. T. C. Stoof, R. G. Hulet, K. E. Strecker, and G. B. Partridge, Bright soliton trains of trapped Bose–Einstein condensates, Phys. Rev. Lett. 89(20), 200404 (2002)

[6] G. Theocharis, D. J. Frantzeskakis, P. G. Kevrekidis, B. A. Malomed, and Y. S. Kivshar, Ring dark solitons and vortex necklaces in Bose–Einstein condensates, Phys. Rev. Lett. 90(12), 120403 (2003)

[7] B. Wu, J. Liu, and Q. Niu, Controlled generation of dark solitons with phase imprinting, Phys. Rev. Lett. 88(3), 034101 (2002)

[8] Y. Wu and L. Deng, Ultraslow optical solitons in a cold four-state medium, Phys. Rev. Lett. 93(14), 143904 (2004)

[9] J. K. Xue, Interaction of ring dark solitons with ring impurities in Bose–Einstein condensates, J. Phys. At. Mol. Opt. Phys. 38(6), 671 (2005)

[10] T. Taniuti and K. Nishihara, Nonlinear Waves, Pitman Advanced Publishing Program, 1983

[11] A. C. Newell, Solitons in Mathematics and Physics, Society for Industrial and Applied Mathematics, 1987

[12] S. Stellmer, C. Becker, P. Soltan-Panahi, E.M. Richter, S. Dörscher, M. Baumert, J. Kronjäger, K. Bongs, and K. Sengstock, Collisions of dark solitons in elongated Bose–Einstein condensates, Phys. Rev. Lett. 101(12), 120406 (2008)

[13] H. G. Luo and W. M. Liu, Matter-wave solitons in heteronuclear atomic Bose–Einstein condensates with synchronously controllable interactions and potentials, Phys. Rev. A 84(5), 053631 (2011)

[14] T. Busch and J. R. Anglin, Dark-bright solitons in inhomogeneous Bose–Einstein condensates, Phys. Rev. Lett. 87(1), 010401 (2001)

[15] C. Hamner, J. J. Chang, P. Engels, and M. A. Hoefer, Generation of dark-bright soliton trains in superfluid– superfluid counterflow, Phys. Rev. Lett. 106(6), 065302 (2011)

[16] K. Kasamatsu and M. Tsubota, Multiple domain formation induced by modulation instability in twocomponent Bose–Einstein condensates, Phys. Rev. Lett. 93(10), 100402 (2004)

[17] P. G. Kevrekidis, D. J. Frantzeskakis, B. A. Malomed, and R. Carretero-González, Families of matter-waves in two-component Bose–Einstein condensates, Eur. Phys. J. D 28(2), 181 (2004)

[18] T. W. Neely, E. C. Samson, A. S. Bradley, M. J. Davis, and B. P. Anderson, Observation of vortex dipoles in an oblate Bose–Einstein condensate, Phys. Rev. Lett. 104(16), 160401 (2010)

[19] D. V. Freilich, D. M. Bianchi, A. M. Kaufman, T. K. Langin, and D. S. Hall, Real-time dynamics of single vortex lines and vortex dipoles in a Bose–Einstein condensate, Science 329(5996), 1182 (2010)

[20] S. Middelkamp, P. J. Torres, P. G. Kevrekidis, D. J. Frantzeskakis, R. Carretero-González, P. Schmelcher, D. V. Freilich, and D. S. Hall, Guiding-center dynamics of vortex dipoles in Bose–Einstein condensates, Phys. Rev. A 84(1), 011605(R) (2011)

[21] S. Wüster, T. E. Argue, and C. M. Savage, Numerical study of the stability of skyrmions in Bose–Einstein condensates, Phys. Rev. A 72(4), 043616 (2005)

[22] T. Kawakami, T. Mizushima, M. Nitta, and K. Machida, Stable skyrmions in SU(2) gauged Bose– Einstein condensates, Phys. Rev. Lett. 109(1), 015301 (2012)

[23] Y. J. Lin, K. Jimenez-Garcia, and I. B. Spielman, Spin–orbit-coupled Bose–Einstein condensates, Nature 471(7336), 83 (2011)

[24] V. Galitski and I. B. Spielman, Spin–orbit coupling in quantum gases, Nature 494(7435), 49 (2013)

[25] X. O. Xu and J. H. Han, Emergence of chiral magnetism in spinor Bose–Einstein condensates with Rashba coupling, Phys. Rev. Lett. 108(18), 185301 (2012)

[26] J. Radić, T. A. Sedrakyan, I. B. Spielman, and V. Galitski, Vortices in spin–orbit-coupled Bose–Einstein condensates, Phys. Rev. A 84(6), 063604 (2011)

[27] X. F. Zhou, J. Zhou, and C. J. Wu, Vortex structures of rotating spin–orbit-coupled Bose–Einstein condensates, Phys. Rev. A 84(6), 063624 (2011)

[28] C. Wang, C. Gao, C. M. Jian, and H. Zhai, Spin–orbit coupled spinor Bose–Einstein condensates, Phys. Rev. Lett. 105(16), 160403 (2010)

[29] T. L. Ho and S. Zhang, Bose–Einstein condensates with spin–orbit interaction, Phys. Rev. Lett. 107(15), 150403 (2011)

[30] T. Congy, A. M. Kamchatnov, and N. Pavloff, Nonlinear waves in coherently coupled Bose–Einstein condensates, Phys. Rev. A 93(4), 043613 (2016)

[31] L. Salasnich and B. A. Malomed, Localized modes in dense repulsive and attractive Bose–Einstein condensates with spin–orbit and Rabi couplings, Phys. Rev. A 87(6), 063625 (2013)

[32] V. Achilleos, D. J. Frantzeskakis, P. G. Kevrekidis, and D. E. Pelinovsky, Matter-wave bright solitons in spin– orbit coupled Bose–Einstein condensates, Phys. Rev. Lett. 110(26), 264101 (2013)

[33] V. Achilleos, D. J. Frantzeskakis, P. G. Kevrekidis, P. Schmelcher, and J. Stockhofe, Positive and negative mass solitons in spin–orbit coupled Bose–Einstein condensates, Rom. Rep. Phys. 67(1), 235 (2015)

[34] Y. V. Kartashov, V. V. Konotop, and F. Kh. Abdullaev, Gap solitons in a spin–orbit-coupled Bose–Einstein condensate, Phys. Rev. Lett. 111(6), 060402 (2013)

[35] G. X. Huang, V. A. Makarov, and M. G. Velarde, Twodimensional solitons in Bose–Einstein condensates with a disk-shaped trap, Phys. Rev. A 67(2), 023604 (2003)

[36] S. Sinha, R. Nath, and L. Santos, Trapped twodimensional condensates with synthetic spin–orbit coupling, Phys. Rev. Lett. 107(27), 270401 (2011)

[37] H. Sakaguchi, B. Li, and B. A. Malomed, Creation of two-dimensional composite solitons in spin–orbitcoupled self-attractive Bose–Einstein condensates in free space, Phys. Rev. E 89(3), 032920 (2014)

[38] V. E. Lobanov, Y. V. Kartashov, and V. V. Konotop, Fundamental, multipole, and half-vortex gap solitons in spin–orbit coupled Bose–Einstein condensates, Phys. Rev. Lett. 112(18), 180403 (2014)

[39] Y. C. Zhang, Z. W. Zhou, B. A. Malomed, and H. Pu, Stable solitons in three dimensional free space without the ground state: Self-trapped Bose–Einstein condensates with spin–orbit coupling, Phys. Rev. Lett. 115(25), 253902 (2015)

[40] D. L. Campbell, R. M. Price, A. Putra, A. Valdés-Curiel, D. Trypogeorgos, and I. B. Spielman, Magnetic phases of spin-1 spin–orbit-coupled Bose gases, Nat. Commun. 7, 10897 (2016)

[41] L. Chen, H. Pu, and Y. Zhang, Spin–orbit angular momentum coupling in a spin-1 Bose–Einstein condensate, Phys. Rev. A 93(1), 013629 (2016)

[42] S. Gautam and S. K. Adhikari, Phase separation in a spin–orbit-coupled Bose–Einstein condensate, Phys. Rev. A 90(4), 043619 (2014)

[43] G. I. Martone, F. V. Pepe, P. Facchi, S. Pascazio, and S. Stringari, Tricriticalities and quantum phases in spin–orbit-coupled spin-1 Bose gases, Phys. Rev. Lett. 117(12), 125301 (2016)

[44] Y. K. Liu and S. J. Yang, Exact solitons and manifold mixing dynamics in the spin–orbit coupled spinor condensates, Europhys. Lett. 108(3), 30004 (2014)

[45] S. Gautam and S. K. Adhikari, Mobile vector soliton in a spin–orbit coupled spin-1 condensate, Laser Phys. Lett. 12(4), 045501 (2015)

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