Modulational instability of nonlinear spin waves in an atomic chain of spinor Bose-Einstein condensates

Abstract

The modulational instability of coherently excited spin waves is studied in an atomic spin chain of spinor Bose-Einstein condensates ͑BECs͒ confined in an optical lattice. We examine the dependence of the stability on the long-range nonlinear interaction of spin waves excited at different lattice sites. The long-range nonlinear spin coupling in the optical lattice is due to light-induced and static magnetic dipole-dipole interaction between atoms. We compare the spin wave dynamics in an atomic spin chain of spinor BECs formed in an optical lattice with that in a Heisenberg-like spin chain in solid-state physics. This reveals the important differences of the spin chain with long-range spin coupling from that with the short-range one. II. HAMILTONIAN OF SPINOR BOSE-EINSTEIN CONDENSATE IN THE OPTICAL LATTICEWe consider a one-dimensional optical lattice formed by two -polarized laser beams counterpropagating along the y axis. The two lattice laser beams are detuned far from atomic resonance, and the condensate confined in the lattice is approximately in its electronic ground state. We assume that PHYSICAL REVIEW B 76, 214408 ͑2007͒

Magnetic Solitons in Optical Lattice

“…From the definition of A 2 , we can rewrite the condition as 0:25 , A 2 , 1, which agrees with the instability condition of the extended nonlinear band edge spin wave modes in the linear stability analysis in Ref. [4]. It means that one soliton solution can exist in atomic spin chain after the NNN interactions between spins are considered.…”

“…The realistic interaction strengths of the MDDI and LDDI coupling coefficients have been calculated in ref. [4], in which we find the dependency of the transverse width.…”

“…Figure 2. The spin coupling coefficients J z mn ¼ J mag mn and J ij as a function of the lattice site index for different transverse widths of the condensate in the MDDI and LDDI dominating optical lattice [4].…”

“…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][5][6][7]. By tuning the system parameters, magnetic soliton can be produced; however a key difference of the atomic spin chain from solid-state one is that we are facing a completely new spin system in which the long-range nonlinear interactions play a dominant role.…”

Modulational instability of a modified Gross-Pitaevskii equation with higher-order nonlinearity

“…The slow modulation of a monochromatic plane wave in the system leads to exponential growth of the unstable modes and eventually may result in the formation of envelope soliton train. Recently, the MI in Bose-Einstein condensate (BEC) has attracted great attention both experimentally and theoretically [11][12][13][14][15][16][17][18]. Investigations show that the MI has been responsible for the dephasing and the localization of the condensate.…”