Stability of nonstationary states of spin-1 Bose-Einstein condensates

Abstract

The stability of nonstationary states of homogeneous spin-1 Bose-Einstein condensates is studied by performing Bogoliubov analysis in a frame of reference where the state is stationary. In particular, the effect of an external magnetic field is examined. It is found that a nonzero magnetic field introduces instability in a 23 Na condensate. The wavelengths of this instability can be controlled by tuning the strength of the magnetic field. In a 87 Rb condensate this instability is present already at zero magnetic field. Furthermore, an analytical bound for the size of a stable condensate is found, and a condition for the validity of the single-mode approximation is presented. Realization of the system in a toroidal trap is discussed, and the full time development is simulated.

Interferometric measurement of interhyperfine scattering lengths in Rb87

“…Although no thermal fraction is observed, we estimate that for a conservative upper bound of 10% thermal fraction, the additional contribution of the thermal cloud is a ∼1 % effect on the measured intra-and intrer-hyperfyne dynamics, which will henceforth be neglected. During the spin-dynamics phase of the experiment, the trap conditions satisfy both static [38,39] and dynamic [40,41] criteria for stability of a single spin domain, and long-time spin relaxation measurements confirm the expected single-domain behavior [28].…”

Single-domain Bose condensate magnetometer achieves energy resolution per bandwidth below ℏ

“…Two considerations are relevant here. First, we note the conditions for single-mode dynamics: and , where ξ s is the spin-healing length ( 37 ) and λ is the threshold wavelength for spin wave amplification ( 44 ) ( SMA Validity Conditions ). In Fig.…”

Excitation spectrum of a toroidal spin-1 Bose-Einstein condensate

“…In [16] it was argued that in a homogeneous system the most unstable states are almost always of this form. This state can be written as…”

“…We calculate the linear excitation spectrum in a basis where ψ is stationary [16,20] using the Bogoliubov approach, that is, we define ψ(ϕ; t) = ψ (ϕ) + δψ(ϕ; t) and expand the time evolution equations to first order in δψ. We write δψ = (δψ 1 , δψ 0 , δψ −1 )…”

“…[16,20], we calculate the excitation spectrum in a basis where ψ is stationary. This basis can be defined easily because the time evolution operator U (t) = e −itĤ / is known.…”