Bose 2.2 User Manual download pdf (Page 134)

the programmed ﬁeld value and its actual value measured by Zeeman spectroscopy. We

have identiﬁed two reasons for the deviations: (i) due to the limited bandwidth of the

active current stabilization, the PI controller may introduce delays and oscillations in the

Feshbach current when its set-point is suddenly changed and (ii) eddy currents in the

metallic vacuum chamber yield an additional delay of the real magnetic ﬁeld with respect

to the programmed value. We have experimentally addressed both issues, with the results

shown in Fig. A.2.

step

time t (ms)

0.0 1.0 2.0

1.0

0.5

0.0

-0.5

current I (norm.)

s-shaped

time t (ms)

0.0 1.0 2.0

1.0

0.5

0.0

-0.5

current I (norm.)

time t (ms)

0.0 1.0 2.0

1.0

0.5

0.0

-0.5

I,B (norm.)

linear

time t (ms)

0.0 1.0 2.0

1.0

0.5

0.0

-0.5

current I (norm.)

Fig. A.2, Measured Feshbach current and magnetic ﬁeld at cloud position:

Cur-

rent running through the Feshbach coils (red dots), measured by a transducer,

and programmed value of the current (dashed blue line), both in normalized

units. (a) We observe strong oscillations in the measured current after a sudden

change in the programmed value. (b) The oscillations are reduced when using

a linear ramp and (c) are almost suppressed when using the s-shaped ramp

given by Eq.

(A.33)

. (d) The black dots show the measured ﬁeld strength

at the position of the atoms, also in normalized units. The measured ﬁeld

exhibits a delay with respect to both the programmed value and the measured

current in the coils. The data is well described by the numerical solution

(

)

of the diﬀerential equation

(A.34)

with the parameter

= 0

(black line).

Optimized magnetic ﬁeld ramps

We measure the current in the Feshbach coils by a transducer, when the programmed

ﬁeld

prog

is changed from

= 626

= 602

by (a) a jump, (b) a linear ramp or

prog

, we observe

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