## Multisoliton complexes of Bose–Einstein condensates in nonlinear optical lattices |

JOSA B, Vol. 30, Issue 3, pp. 691-699 (2013)

http://dx.doi.org/10.1364/JOSAB.30.000691

Enhanced HTML Acrobat PDF (304 KB)

### Abstract

We theoretically study the role of the mode structure of a multicomponent Bose–Einstein condensate (BEC) in the potential created by a nonlinear optical lattice. We describe a multisoliton complex (MSC) as a superposition of different fundamental soliton modes in the matter-wave system. Using a similarity transformation, we solve the nonlinear evolution equation of the multimode coupled matter-wave field and construct a set of analytical bright soliton solutions. A perturbation method is used to examine the linear stability of the constructed solitons. Based on these particular solutions, we numerically analyze the mode structure of a MSC. The results show that the periodicity causes a Bloch modulation in the envelopes of the density distribution. When different fundamental modes collide with each other in the nonlinear lattice, the collision-induced shifts, and the space-dependent modulation of external potentials change the density profile of the multimode soliton complex. Therefore, the mode structure, which is absent in a one-mode BEC, provides the possible multiscale modeling of the matter-wave field with extra degrees of freedom.

© 2013 Optical Society of America

**OCIS Codes**

(020.1670) Atomic and molecular physics : Coherent optical effects

(020.1335) Atomic and molecular physics : Atom optics

(190.6135) Nonlinear optics : Spatial solitons

**ToC Category:**

Atomic and Molecular Physics

**History**

Original Manuscript: October 19, 2012

Revised Manuscript: December 20, 2012

Manuscript Accepted: January 29, 2013

Published: February 22, 2013

**Citation**

Jun Chen, Qiang Lin, and Yangjian Cai, "Multisoliton complexes of Bose–Einstein condensates in nonlinear optical lattices," J. Opt. Soc. Am. B **30**, 691-699 (2013)

http://www.opticsinfobase.org/josab/abstract.cfm?URI=josab-30-3-691

Sort: Year | Journal | Reset

### References

- M. H. Anderson, J. R. Ensher, M. R. Matthews, C. E. Wieman, and E. A. Cornell, “Observation of Bose–Einstein condensation in a dilute atomic vapor,” Science 269, 198–201 (1995). [CrossRef]
- K. B. Davis, M.-O. Mewes, M. R. Andrews, N. J. van Druten, D. S. Durfee, D. M. Kurn, and W. Ketterle, “Bose–Einstein condensation in a gas of sodium atoms,” Phys. Rev. Lett. 75, 3969–3973 (1995). [CrossRef]
- C. C. Bradley, C. A. Sackett, J. J. Tollett, and R. G. Hulet, “Evidence of Bose–Einstein condensation in an atomic gas with attractive interactions,” Phys. Rev. Lett. 75, 1687–1690 (1995). [CrossRef]
- H. J. Miesner, D. M. Stamper-Kurn, J. Stenger, S. Inouye, A. P. Chikkatur, and W. Ketterle, “Observation of metastable states in spinor Bose–Einstein condensates,” Phys. Rev. Lett. 82, 2228–2231 (1999). [CrossRef]
- D. S. Hall, M. R. Matthews, C. E. Wieman, and E. A. Cornell, “Measurements of relative phase in two-component Bose–Einstein condensates,” Phys. Rev. Lett. 81, 1543–1546 (1998). [CrossRef]
- X. Ma, L. Xia, Y. Fang, X. Zhou, Y. Wang, H. Guo, and X. Chen, “Population oscillation of the multicomponent spinor Bose–Einstein condensate induced by nonadiabatic transitions,” Phys. Rev. A 73, 013624 (2006). [CrossRef]
- M. Lewenstein, A. Sanpera, and V. Ahufinger, “Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond,” Adv. Phys. 56, 243–379 (2007). [CrossRef]
- M. F. Riedel, P. Böhi, Y. Li, T. W. Hänsch, A. Sinatra, and P. Treutlein, “Atom-chip-based generation of entanglement for quantum metrology,” Nature 464, 1170–1173 (2010). [CrossRef]
- T. Byrnes, K. Wen, and Y. Yamamoto, “Macroscopic quantum computation using Bose–Einstein condensates,” Phys. Rev. A 85, 040306 (2012). [CrossRef]
- P. Öhberg, and L. Santos, “Dark solitons in a two-component Bose–Einstein condensate,” Phys. Rev. Lett. 86, 2918–2921 (2001). [CrossRef]
- S. Li, L. Fu, W. Duan, and J. Liu, “Nonlinear Ramsey interferometry with Rosen–Zener pulses on a two-component Bose–Einstein condensate,” Phys. Rev. A 78, 063621 (2008). [CrossRef]
- A.-C. Ji, W. M. Liu, J. L. Song, and F. Zhou, “Dynamical creation of fractionalized vortices and vortex lattices,” Phys. Rev. Lett. 101, 010402 (2008). [CrossRef]
- E. P. Gross, “Structure of a quantized vortex in boson systems,” Nuovo Cimento Soc. Ital. Fis. B 20, 454–477 (1961). [CrossRef]
- L. P. Pitaevsk, “Vortex lines in an imperfect Bose gas,” Sov. Phys. JETP 13, 451–454 (1961).
- Z. X. Liang, Z. D. Zhang, and W. M. Liu, “Dynamics of a bright soliton in Bose–Einstein condensates with time-dependent atomic scattering length in an expulsive parabolic potential,” Phys. Rev. Lett. 94, 050402 (2005). [CrossRef]
- W. Bao, “Ground states and dynamics of multicomponent Bose–Einstein condensates,” Multiscale Model. Simul. 2, 210–236 (2004). [CrossRef]
- M. Mitchell, Z. Chen, M.-F. Shih, and M. Segev, “Self-trapping of partially spatially incoherent light,” Phys. Rev. Lett. 77, 490–493 (1996). [CrossRef]
- M. Mitchell, M. Segev, T. H. Coskun, and D. N. Christodoulides, “Theory of self-trapped spatially incoherent light beams,” Phys. Rev. Lett. 79, 4990–4993 (1997). [CrossRef]
- A. Ankiewicz, W. Królikowski, and N. N. Akhmediev, “Partially coherent solitons of variable shape in a slow Kerr-like medium: exact solution,” Phys. Rev. E 59, 6079–6087 (1999). [CrossRef]
- A. A. Sukhorukov and N. N. Akhmediev, “Coherent and incoherent contributions to multisoliton complexes,” Phys. Rev. Lett. 83, 4736–4739 (1999). [CrossRef]
- N. Akhmediev and A. Ankiewicz, “Multi-soliton complexes,” Chaos 10, 600–612 (2000). [CrossRef]
- J. Peng, L. Zhan, T. Chen, Z. Gu, K. Qian, S. Luo, and Q. Shen, “All-fiber ultrashort similariton generation, amplification, and compression at telecommunication band,” J. Opt. Soc. Am. B 29, 2270–2274 (2012). [CrossRef]
- M. Theis, G. Thalhammer, K. Winkler, M. Hellwig, G. Ruff, R. Grimm, and J. H. Denschlag, “Tuning the scattering length with an optically induced Feshbach resonance,” Phys. Rev. Lett. 93, 123001 (2004). [CrossRef]
- C. Chin, R. Grimm, P. Julienne, and E. Tiesinga, “Feshbach resonances in ultracold gases,” Rev. Mod. Phys. 82, 1225–1286 (2010). [CrossRef]
- H. Sakaguchi and B. A. Malomed, “Matter-wave solitons in nonlinear optical lattices,” Phys. Rev. E 72, 046610 (2005). [CrossRef]
- F. K. Abdullaev, A. Gammal, H. L. F. da Luz, and L. Tomio, “Dissipative dynamics of matter-wave solitons in a nonlinear optical lattice,” Phys. Rev. A 76, 043611 (2007). [CrossRef]
- H. Sakaguchi and B. A. Malomed, “Solitons in combined linear and nonlinear lattice potentials,” Phys. Rev. A 81, 013624 (2010). [CrossRef]
- Z.-W. Xie and W. M. Liu, “Superfluid-Mott-insulator transition of dipolar bosons in an optical lattice,” Phys. Rev. A 70, 045602 (2004). [CrossRef]
- D. Tilahun, R. A. Duine, and A. H. MacDonald, “Quantum theory of cold bosonic atoms in optical lattices,” Phys. Rev. A 84, 033622 (2011). [CrossRef]
- Y. V. Kartashov, B. A. Malomed, and L. Torner, “Solitons in nonlinear lattices,” Rev. Mod. Phys. 83, 247–305 (2011). [CrossRef]
- R. Grimm and M. Weidemuller, “Optical dipole traps for neutral atoms,” Adv. At. Mol. Opt. Phys. 42, 95–170 (2000). [CrossRef]
- J. Belmonte-Beitia, V. M. Pérez-García, V. Vekslerchik, and P. J. Torres, “Lie symmetries and solitons in nonlinear systems with spatially inhomogeneous nonlinearities,” Phys. Rev. Lett. 98, 064102 (2007). [CrossRef]
- J. Belmonte-Beitia, V. M. Pérez-García, V. Vekslerchik, and V. V. Konotop, “Localized nonlinear waves in systems with time- and space-modulated nonlinearities,” Phys. Rev. Lett. 100, 164102 (2008). [CrossRef]
- J. Belmonte-Beitia, V. V. Konotop, V. M. Pérez-García, and V. E. Vekslerchik, “Localized and periodic exact solutions to the nonlinear Schrödinger equation with spatially modulated parameters: linear and nonlinear lattices,” Chaos Solitons Fractals 41, 1158–1166 (2009). [CrossRef]
- J. Belmonte-Beitia, V. M. Prez-Garca, and V. Brazhnyi, “Solitary waves in coupled nonlinear Schrödinger equations with spatially inhomogeneous nonlinearities,” Commun. Nonlinear Sci. Numer. Simul. 16, 158–172 (2011). [CrossRef]
- N. G. Vakhitov and A. A. Kolokolov, “Stationary solutions of the wave equation in a medium with nonlinearity saturation,” Radiophys. Quantum Electron. 16, 783–789 (1973). [CrossRef]
- L. N. Trefethen, Spectral Methods in MATLAB (SIAM, 2000).
- D. Pelinovsky and G. Schneider, “Moving gap solitons in periodic potentials,” Math. Methods Appl. Sci. 31, 1739–1760 (2008). [CrossRef]
- C. B. Manakov, “On the theory of two-dimensional stationary self-focusing of electromagnetic waves,” Sov. Phys. JETP 38, 248–253 (1974).
- W. Królikowski, N. Akhmediev, and B. Luther-Davies, “Collision-induced shape transformations of partially coherent solitons,” Phys. Rev. E 59, 4654–4658 (1999). [CrossRef]

## Cited By |
Alert me when this paper is cited |

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.

« Previous Article | Next Article »

OSA is a member of CrossRef.