THE INTERNATIONAL SERIES OF MONOGRAPHS ON PHYSICS ...

210 CONTINUOUS STRUCTURES
b (μm)
Vortex sheet
250
200
150
Ψ Bragg
b = 320 Ω –2/3 μm
1.5 Ω (rad/s) 2.5
standing waves
between sheets
Ψ bound
ν bound (vortex-soliton satellite)
0 5 10 15
Δν (kHz)
main peak
0.6
0.4
Bragg reflection
satellite 0.2
(Bragg peak)
0
NMR Absorption
Fig. 16.12. Measurement of the distance between the planes of the vortex sheet
using the Bragg reflection of the spin waves from the sheet (after Parts et
al. 1994a).
the spin waves bound to the soliton (Fig. 16.12 bottom left), they resolved a small
peak caused by the Bragg reflection of the spin waves from the equidistant sheet
planes (Fig. 16.12 bottom right). The position of the Bragg peak as a function
of Ω gives b(Ω) (Fig. 16.12 top left), which is in quantitative agreement with the
Landau–Lifshitz equation (16.14).
The areal density of circulation quanta has the solid-body value nv =2Ω/κ0,
as in the case of an array of singly quantized vortices (see eqn (14.2)): the vortex
sheet also mimics the solid-body rotation of superfluid vacuum, 〈vs〉 = Ω ×
r. This means that the length of the vortex sheet per two circulation quanta
is p = κ0/(bΩ), which is the periodicity of the order parameter structure in
Fig. 16.9 bottom (p ≈ 180 µm at Ω = 1 rad s −1 ). The NMR absorption in the
vortex-sheet satellite is proportional to the total volume of the sheet which in
turn is proportional to 1/b ∝ Ω 2/3 . This non-linear dependence of the satellite
absorption on rotation velocity is also one of the experimental signatures of the
vortex sheet.