What's the best way to measure a magnetic field? I work in a physics lab.
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             --          -----------------> metal
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             ||   atoms  ||---------------> glass 
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I have atoms (5 $\mu m^3$) levitating at the center of a metalic cubic 15 $cm^3$ box. There are glass windows on the sides of the box. The pressure inside the chamber is very low. I want to measure the magnetic field vector in the region where the atoms lie inside the chamber while minimally disturbing the atoms.
In the case where I cannot put a sensor inside the chamber, what is the best way to do so according to you ? What is the best technology available according to you ?
Same question in the case where I can put a sensor inside the chamber.
Money is not a criterion. The method should minimally disturb the magnetic field at the level of the atoms. The method should provide the direction of the magnetic field as well as its amplitude.
Typical fields to be measured are on the 1 Gauss level. But the precision of the measurement should be way way below that mGauss at least I would say.
Edit: The magnetic filed is given by a pair of coils in the Helmholtz configuration along the vertical direction mainly, however other sources (noises) can contribute to the magnetic field. One can consider the magnetic field to be fluctuating around a given value ($\simeq 1 G \pm 1 mG$) along the z direction.
 A: The following is just a crude idea, but maybe you could use the Zeeman effect: the atom spectra depend on the magnetic field, and the light intensity depends on the direction of the magnetic field and the direction at which the light is observed.
A: Isn't it the case that the external magnetic field already aligns the magnetic dipoles of the subatomic particles anyway? Do you want to measure the (partial) relaxation of the magnetic dipole moments as a function of the variance of the external field? If there is a correlation between the change in field strength of the external field, the orientation of the magnetic dipole moments and the rise or fall of the atoms in the gravitational field, you are virtually repeating the Millikan experiment.
Allow me to make a small side comment. It is worth the effort to assume the following for the evaluation of the measurement results:

*

*the magnetic dipoles of the subatomic particles are invariant constants
-the given orientation of the subatomic particles in the atomic compound is forced by the mutual influence of their dipoles

*the forced deflection of them by the external magnetic field leads to changes in the summary atomic dipole values.

