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理论物理通讯：英文版

Modulational Instability of Spinor Condensates in an Optical Lattice

Zheng Gong, 简闻天, 杨玲玲

Published Jan 1, 2015• 0 citations
OpenAlex

Abstract

We obtain analytically the static states and corresponding collective-excitation spectra of a quasi-onedimensional spin-1 condensate modulated by a long-wavelength optical lattice in the weak lattice limit. It is demonstrated that both ferromagnetic and antiferromagnetic condensates may exhibit dynamical instability, which agree with the results with numerical simulation. In the homogeneous limit, our results reduce to the previous results for homogeneous spinor condensates, i.e., dynamical instability can occur only for ferromagnetic interaction and an antiferromagnetic condensate is always dynamically stable.

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We obtain analytically the static states and corresponding collective-excitation spectra of a quasi-onedimensional spin-1 condensate modulated by a long-wavelength optical lattice in the weak lattice limit. It is demonstrated that both ferromagnetic and antiferromagnetic condensates may exhibit dynamical instability, which agree with the results with numerical simulation. In the homogeneous limit, our results reduce to the previous results for homogeneous spinor condensates, i.e., dynamical instability can occur only for ferromagnetic interaction and an antiferromagnetic condensate is always dynamically stable.
Abstract We obtain analytically the static states and corresponding collective-excitation spectra of a quasi-one-dimensional spin-1 condensate modulated by a long-wavelength optical lattice in the weak lattice limit. It is demonstrated that both ferromagnetic and antiferromagnetic condensates may exhibit dynamical instability, which agree with the results with numerical simulation. In the homogeneous limit, our results reduce to the previous results for homogeneous spinor condensates, i.e., dynamical instability can occur only for ferromagnetic interaction and an antiferromagnetic condensate is always dynamically stable.
The modulational instability of coherently excited spin waves is studied in an atomic spin chain of spinor Bose-Einstein condensates (BECs) 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.
We study modulational instability of two-component Bose-Einstein condensates in an optical lattice, which is modeled as a coupled discrete nonlinear Schr\"odinger (DNLS) equation. The excitation spectrum and the modulational instability condition of the total system are presented analytically. In the long-wavelength limit, our results agree with the homogeneous two-component Bose-Einstein condensates case. The discreteness effects result in the appearance of the modulational instability for the condensates in miscible region. The numerical calculations confirm our analytical results and show that the interspecies coupling can transfer the instability from one component to another.
We first analytically examine the occurrence of modulational instability in all phases of F=2F=2F=2 spinor homogeneous condensate from the possible stationary solutions. Then we numerically show the similar results by extending our analysis to trapped condensates (inhomogeneous). From both analyses we conclude that modulation instability depends on the relative phase between the components and initial population for the polar phase. We also observe spin-mixing dynamics during evolution of the spinor condensate.
We interpret the recently observed spatial domain formation in spin-1 atomic condensates as a result of dynamical instability. Within the mean field theory, a homogeneous condensate is dynamically unstable (stable) for ferromagnetic (antiferromagnetic) atomic interactions. We find that this dynamical instability naturally leads to spontaneous domain formation as observed in several recent experiments for condensates with rather small numbers of atoms. For trapped condensates, our numerical simulations compare quantitatively to the experimental results, thus largely confirming the physical insight from our analysis of the homogeneous case.
The modulational instability (MI) of nonlinear coherent spin waves in an atomic spin chain of spinor Bose-Einstein condensates confined in an optical lattice is studied. Analytically we obtained the criteria for the MI of nonlinear coherent spin waves and its relation with the long-range nonlinear spin coupling. We analysed the MI in the case of blue-detuned and red-detuned opctical lattice respectively. It was found that the long-range nonlinear spin coupling in the optical lattice is due to light-induced and static magnetic field-induced dipole-dipole interaction.