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

Abstract

We analyze sound waves (phonons, Bogoliubov excitations) propagating on continuous wave (cw) solutions of repulsive $F=1$ spinor Bose-Einstein condensates (BECs), such as ${}^{23}$Na (which is antiferromagnetic or polar) and ${}^{87}$Rb (which is ferromagnetic). Zeeman splitting by a uniform magnetic field is included. All cw solutions to ferromagnetic BECs with vanishing $M_F=0$ particle density and non-zero components in both $M_F=\pm 1$ fields are subject to modulational instability (MI). MI increases with increasing particle density. MI also increases with differences in the components' wavenumbers; this effect is larger at lower densities but becomes insignificant at higher particle densities. CW solutions to antiferromagnetic (polar) BECS with vanishing $M_F=0$ particle density and non-zero components in both $M_F=\pm 1$ fields do not suffer MI if the wavenumbers of the components are the same. If there is a wavenumber difference, MI initially increases with increasing particle density, then peaks before dropping to zero beyond a given particle density. The cw solutions with particles in both $M_F=\pm 1$ components and nonvanishing $M_F=0$ components do not have MI if the wavenumbers of the components are the same, but do exhibit MI when the wavenumbers are different. Direct numerical simulations of a cw with weak white noise confirm that weak noise grows fastest at wavenumbers with the largest MI, and shows 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.

22 pages, 20 figures

References in corpus (40)

• Atomic Scattering in Presence of an External Confinement and a Gas of Impenetrable Bosons
• Spinor Bose Condensates in Optical Traps
• Dark Solitons in Bose-Einstein Condensates
• Bose-Einstein condensation of chromium
• Bose-Einstein condensation with internal degrees of freedom in alkali atom gases
• Spinor Bose-Einstein condensates
• Spontaneous symmetry breaking in a quenched ferromagnetic spinor Bose condensate
• Stable 85Rb Bose-Einstein Condensates with Widely Tunable Interactions
• A Strongly Dipolar Bose-Einstein Condensate of Dysprosium
• Bose-Einstein Condensation of Atomic Hydrogen
• All Optical Formation of an Atomic Bose-Einstein Condensate
• Observation of persistent flow of a Bose-Einstein condensate in a toroidal trap
• Experimental demonstration of painting arbitrary and dynamic potentials for Bose-Einstein condensates
• Inter-isotope determination of ultracold rubidium interactions from three high-precision experiments
• Observation of spinor dynamics in optically trapped 87Rb Bose-Einstein Condensates
• Coherent spinor dynamics in a spin-1 Bose condensate
• Atom-Atom Scattering Under Cylindrical Harmonic Confinement: Numerical and Analytical Studies of the Confinement Induced Resonance
• Modulational instability in cigar shaped Bose-Einstein condensates in optical lattices
• The Excitation Spectrum of a Bose-Einstein Condensate
• Realization of a sonic black hole analogue in a Bose-Einstein condensate
• Bose-Einstein condensation in a circular waveguide
• Exact Analysis of Soliton Dynamics in Spinor Bose-Einstein Condensates
• Bose-Einstein Condensation of Strontium
• All-Optical Production of Chromium Bose-Einstein Condensates
• Coherent spin mixing dynamics in a spin-1 atomic condensate
• On the nature of spinor Bose-Einstein condensates in rubidium
• Quantum quenches in a spinor condensate
• Time-Averaged Adiabatic Potentials: Versatile traps and waveguides for ultracold quantum gases
• Bose-Einstein Condensation of an Ytterbium Isotope
• Amplification of Fluctuations in a Spinor Bose Einstein Condensate
• Dynamical instability and domain formation in a spin-1 Bose condensate
• Vortex quantum creation and winding number scaling in a quenched spinor Bose gas
• Cold atom confinement in an all-optical dark ring trap
• Topological defect formation in quenched ferromagnetic Bose-Einstein condensates
• Modulational instability of spinor condensates
• Magnetic Properties of a Bose-Einstein Condensate
• Spin dynamics and structure formation in a spin-1 condensate in a magnetic field
• Matter-wave solitons in the counterflow of two immiscible superfluids
• Continuous wave solutions in spinor Bose-Einstein condensates
• Metastable spin textures and Nambu-Goldstone modes of a ferromagnetic spin-1 Bose-Einstein condensate confined in a ring trap

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