Single-Photon Atomic Cooling - Raizen Lab - The University of ...

mize their energy in high magnetic fields. The second, called low-field seeking
states, satisfy gFmF > 0 and minimize their energy in magnetic field min-
ima. Earnshaw’s theorem prohibits an electrostatic field from stably trapping
a charged particle, however it does not rule out the possibility of trapping
a dipole [38]. Clearly, for a trap to be stable atoms must accumulate at a
field extrema, but local maxima in the absence of sources are forbidden by
Maxwell’s equations [55]. Therefore atoms must be trapped at a local field
minimum, so low-field seeking atomic states must be used.
Ground state 87 Rb has three low-field seeking states. They are |2, 2〉,
|2, 1〉 and |1, −1〉, where the notation |F,mF 〉 is being used. The term “ground
state” refers to all of the states contained in the 5 2 S1/2 spectroscopic term,
not just the one with the lowest energy. The state |2, 2〉 couples most strongly
to external magnetic fields, providing the tightest confinement for a given
magnetic field. For this reason we trap 87 Rb atoms in this state.
One may worry that this state is not the lowest in energy and may decay
into the F = 1 manifold, disrupting the experiment. This concern can be put
to rest because this is not an allowed electric dipole transition as ∆L = 0
and so the lifetime of atoms in the F = 2 manifold is much longer than the
duration of the experiment.
While there are many electric current configurations which can form
suitable trapping potentials [56] we use the simplest configuration possible.
Our field is produced from a pair of circular coils with counter-propagating
currents. This geometry is known as the anti-Helmholtz configuration and it
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