# What's the best way to measure a magnetic field?

I work in a physics lab.

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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.

• How is the magnetic field supplied? Is it a uniform field? Nov 15, 2022 at 14:20
• @PhilipWood, I've edited the question, tou can consider the field to be uniform in the region where atoms are, even though in reality it is not. Nov 15, 2022 at 14:55
• How are you levitating the atoms? (Don't most atom traps use magnetic fields larger than a gauss?) What is the shortest magnetic field fluctuation timescale you are interested in? More information is generally helps people understand the problem, e.g. How many and what kind of atoms? What is the physics you are studying? (These could be relevant if people have suggestions that might actually use the atoms as part of the magnetic field measurement system or if the proposed measurement method turns out to interfere with what you are studying.) Nov 15, 2022 at 15:55
• I was going to suggest that, rather than measuring the field, you could calculate it from the Helmholtz coil formula, but clearly this won't do if you're interested in small perturbations in the field due to other sources. Sorry. Nov 15, 2022 at 20:39