The Quadrupole Field

SummaryBuilding the program of Helmholtz coils

to determine the magnetic field in x-, y-and z-directions, If it is calibrated, wewould take it for calculating the center ofQ-field.

Further, we could modulate the experi-mental set-up based upon the simulatingdata in order for obtaining the atomic cloudin the MOT.

PrincipleWe assume that we could use the Gauss-

meter to detect the magnetic field in thespace and measure the gradient of the fieldeven if the shifts of the coils were ha-ppened.

Coordination in MOT

1.4 cm

(0, 0, 0) x

z

9.96 cm

3.0 cm

3.0 cm

9.2 cm

0.2 – 0.4 cm

0.2 – 0.4 cm

(0, 0, 4.98 cm)

(x, y. z)

Upper Coils

Bottom Coils

AnalysesThe magnetic fields for x-, y- and z- com-

ponents (Bx, By, Bz) would be comparedwith them at the same position or near, asthe coils are shifted and not. These datawould present the gradient of the field andlead us to know the direction where thecenter of field moves towards, and theprocedures are as followed:

Firstly, we find the center of fieldaccording to Bz when the coils do be fixed,and z-position is 4.3 cm in the space leadsBz is zero. [fig.1] and [fig.2].

Secondly, we make sure the z-position ofthe field center in this case and do furtherfor Bx and By near the center in order forunderstanding its gradient of the field.[fig.3] and [fig.4].

fig.1: The Bz in the spacewhen z-shift is only.

fig.2: The Bz is measuredalong the central z-axis wh-en z-shift is only.

fig.3: The Bxis measured near the central z-axis when z-shift is only.

fig.4: The By is measured near the central z-axis when z-shift is only.

Thirdly, compared to the data that thecoils do be fixed w/o x-shift, we are ableto observe the variation of field at thesame positions when there are x-shift andz-shift. In addition, we could predictwhere the center of the field goes to.[fig.5], [fig.6] and [fig.7].

Name Linearly Fittingd(Bz)/dz(G/cm)

Center (Original, x = 0 & y =0) Bz = -22.56z + 96.45 22.56

Center (Later, x = 0 & y = 0) Bz = -22.61z + 96.67 22.61

Negative (Later, x=-2.4 cm & y = 0) Bz = -24.06z + 101.8 24.06

Positive (Later, x = 2.4 cm & y = 0) Bz = -23.4z + 100.9 23.40

Obviously, there would be variation offield less than 6.64 % when x-shifts are0.4 cm to the upper and bottom coilsand MAYBE, the center would move tothe certain direction???? (I roughly de-termined that the center of field mightmove ±0.04 cm.)

Again, by the same way, we wouldanalyze the data to identify whichdirection the center moves to anddetermine the shift of the center as thereference that we modulate the positionof insection of the MOT beam with thecenter of the field.

fig.5: The Bz is measured at original and near the central z-axis when z-shift amdx-shift were happened..

fig.6: The Bx is measured atd near the central x-

fig.7: The By is measured atd near the central y-

However, there is one problem

I am confused about how to define thecenter of the field when the shifts werehappened. Specifically, if meeting the situ-ation, atoms in the MOT would decidewhich direction they move to by the gra-dient of the field or the lest magnetic fieldin the space?

ConclusionsWe would scan where is near the original

center of the field in order for convergingthe optical set-up of the MOT beam if theprogram is close to the experimental para-meters and the principle is clear as well.

In addition, if we really enhace the qua-drupole field to move the center of thefield by Helmholtz coils, we could go ahead.