## Abstract

We analyze sound waves (phonons, i.e. Bogoliubov excitations) propagating on continuous-wave (cw) solutions of repulsive F=1 spinor Bose-Einstein condensates (BECs) such as Na23 (which is antiferromagnetic or polar) and Rb87 (which is ferromagnetic). Zeeman splitting by a uniform magnetic field is included. All cw solutions to ferromagnetic BECs with vanishing MF=0 particle density and nonzero components in both MF=±1 fields are subject to modulational instability (MI). Modulational instability increases with increasing particle density. Modulational instability also increases with differences in the components' wave numbers; this effect is larger at lower densities but becomes insignificant at higher particle densities. Continuous-wave solutions to antiferromagnetic (polar) BECs with vanishing MF=0 particle density and nonzero components in both MF=±1 fields do not suffer MI if the wave numbers of the components are the same. If there is a wave-number difference, MI initially increases with increasing particle density and then peaks before dropping to zero beyond a given particle density. The cw solutions with particles in both MF=±1 components and nonvanishing MF=0 components do not have MI if the wave numbers of the components are the same, but do exhibit MI when the wave numbers are different. Direct numerical simulations of a continuous wave with weak white noise confirm that weak noise grows fastest at wave numbers with the largest MI and show some of the results beyond small-amplitude perturbations. Phonon dispersion curves are computed numerically; we find analytic solutions for the phonon dispersion in a variety of limiting cases.

Original language | English |
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Article number | 013615 |

Journal | Physical Review A - Atomic, Molecular, and Optical Physics |

Volume | 91 |

Issue number | 1 |

DOIs | |

State | Published - 15 Jan 2015 |