TY - JOUR

T1 - Sound waves and modulational instabilities on continuous-wave solutions in spinor Bose-Einstein condensates

AU - Tasgal, Richard S.

AU - Band, Y. B.

N1 - Publisher Copyright:
© 2015 American Physical Society.

PY - 2015/1/15

Y1 - 2015/1/15

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84921391844&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.91.013615

DO - 10.1103/PhysRevA.91.013615

M3 - Article

AN - SCOPUS:84921391844

SN - 1050-2947

VL - 91

JO - Physical Review A - Atomic, Molecular, and Optical Physics

JF - Physical Review A - Atomic, Molecular, and Optical Physics

IS - 1

M1 - 013615

ER -