Thesis (pdf) - Swinburne University of Technology

magnetic field at the trap position we find
�
∂B �
�
∂r � = −
r=r0
µ0 B
2π
2 ⊥0
I
In the Gaussian cgs system this is simply
�
∂B �
� =
∂r
1 B
2
2 ⊥0
I [cgs]
� r=r0, [cgs]
Chapter 2: Theoretical Background
(2.40)
(2.41)
Of course, an infinite wire is not realisable and does not allow confinement
in the direction of the wire. Bent wires can create the offset field � B0 and
create the confining field. Here two major designs have been considered. In
the first design the wire is bent into a U-shaped form, where the connecting
parts are bent away from the ‘infinite’ part in the same direction. The overall
field of this wire alone is a quadrupole field in all three dimensions, the field
components of the side wires cancelling themselves at the trap centre. This
trap’s centre is not directly above the wire. It is shifted slightly away from the
wires in the dimension of the bent wires, see Fig. 2.4.
A more symmetric arrangement is created by bending the wire in a Z-
shape. This creates a harmonic trap, as the fields from the side wires add
constructively at the trap’s centre. The field of this trap for a current I, from
the centre of the ‘infinite’ central wire bar with length wx, perpendicular to
the chip’s plane can be calculated to:
⎛
z ·
⎜
�B(z) = I · ⎜
⎝
2wy
(w 2 x/4+z 2 ) √ w 2 x/4+z 2 +w 2 y
− 1
z · wx √
w2 x /4+z2 0
⎞
⎟
⎠ + � B0
(2.42)
In this thesis the Gaussian cgs system is used when covering magnetic fields,
as for applications in atom optics it yields convenient numbers. The field is
expressed in Cartesian coordinates, where the x-direction is chosen along the
wire and the z-axis is perpendicular to the chip’s plane. The terms wx and wy
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