Driven dynamics and pattern formation in Bose-Einstein condensate

Abstract

Periodic modulation of interaction strength or external trap can create spontaneous for- mation of patterns in a Bose-Einstein condensate (BEC), arising from the excitation of its elementary modes. This thesis explores the dynamics of two condensate systems under periodically modulated interactions: a cylindrically confined spin-0 BEC and a homogeneous spin-1 spinor BEC. In elongated traps, periodic driving of interaction induces spontaneous longitudinal density waves. Experiments have shown that driving the system at its transverse breathing mode frequency leads to density wave formation even at very weak modulation strength, due to coupling between transverse and longitudinal motion. We generalize this phenomenon by deriving resonance conditions for the excitation of radial modes, in a cylindrically confined BEC. These resonances are the precursor for longitudinal pattern formation, which are created as the resonantly excited radial modes spontaneously decay to lower branches of excitation spectra. Resonantly excited transverse breathing mode always decays to form longitudinal density waves. The second resonantly excitable radial mode can decay to create density waves at weaker interactions and centre-of-mass oscillations (zig-zag pattern) at larger interactions. Away from radial resonances, pattern formation occurs via second-order parametric resonance, producing density waves at the quasi-one-dimensional limit of interaction, but can also excite centre-of-mass oscillations at larger interactions. Spin degrees of freedom significantly influence the dynamics of a driven spin-1 BEC. Condensate initialized in the ferromagnetic phase behaves like a spin-0 BEC and exhibits transient density patterns under periodic driving. We observe density and spin pattern formation in the condensate in polar and antiferromagnetic (AFM) phases. The pattern wavelength at a given driving frequency can be predicted from the Bogoliubov spectrum. Competition between density and spin dynamics exists, and the dominant process depends on the relative strength of spin-independent and spin-dependent interactions. In the polar phase, spin-density waves give rise to transverse spin textures featuring vortices and antivortices, and the radial spin-spin correlation follows a Bessel function. In the AFM phase, driving at a frequency less than the spin-mode gap creates domain structures, while higher driving frequencies lead to vortex–antivortex formation.