Abstract

In this chapter, we discuss the magnetic solitons achieved in atomic spinor Bose-Einstein condensates (BECs) confined within optical lattice. Spinor BECs at each lattice site behave like spin magnets and can interact with each other through the static magnetic dipole-dipole interaction (MDDI), due to which the magnetic soliton may exist in blue-detuned optical lattice. By imposing an external laser field into the lattice or loading atoms in a red-detuned optical lattice, the light-induced dipole-dipole interaction (LDDI) can produce new magnetic solitons. The long-range couplings induced by the MDDI and ODDI play a dominant role in the spin dynamics in an optical lattice. Compared with spin chain in solid material, the nearest-neighbor approximation, next-nearest-neighbor approximation, and long-range case are discussed, respectively.

Highlights

  • Soliton can be classified into different species, such as matter-wave soliton, magnetic soliton, optical soliton, and so on [1, 2]

  • Magnetic solitons originate from the Heisenberg-like short-range exchange interaction between electrons in solid state systems, so the theoretical models and treatment are limited to only the approximation of nearest-neighbor interaction, it is disadvantageous to the study of long-range interaction-induced dynamics

  • We have shown the existence conditions of magnetic solitons that can occur in optical lattice

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Summary

Introduction

Soliton can be classified into different species, such as matter-wave soliton, magnetic soliton, optical soliton, and so on [1, 2]. The magnetic solitons, which describe the localized magnetization, are very important excitations in the Heisenberg spin chain in solid system in condensed matter [3]. Magnetic solitons originate from the Heisenberg-like short-range exchange interaction between electrons in solid state systems, so the theoretical models and treatment are limited to only the approximation of nearest-neighbor interaction, it is disadvantageous to the study of long-range interaction-induced dynamics. Spinor BECs at each lattice site behave like spin magnets and can interact with each other through the static MDDI, which can cause the ferromagnetic phase transition and the spin wave excitation. It is atomic spin chain in optical lattice [4–7].

Atomic spin chain with magnetic dipole: dipole interaction
Atomic spin chain with light-induced dipole-dipole interaction
Magnetic soliton under the MDDI
Nearest-neighbor approximation with the MDDI
Next-nearest-neighbor approximation with the MDDI
Long-range case with the MDDI
Magnetic soliton under the LDDI
Nearest-neighbor approximation with the LDDI
Next-nearest-neighbor approximation with the LDDI
Long-range case with the LDDI
Conclusion
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