Experiments to Control Atom Number and Phase-Space Density in ...

of atoms in the two hyperfine ground states |F = 1/2,mF = 1/2〉 and |F = 1/2,mF =
−1/2〉. Each energy level will then be filled with two atoms up to the Fermi energy.
The production of a single-atom Fock state can be separated into three steps,
and the fidelity of each of these steps has to be analyzed.
Step 1 is the production of the degenerate gas itself. The limit on the fidelity is
given by the fidelity of having the ground state of the trap filled with two atoms.
Step 2 is the laser culling sequence or the controlled reduction of the trapping
potential. In this step the fidelity will be limited by the precision with which the po-
tentials can be controlled and by the probability of exciting atoms out of the ground
state of the trap. The larger the energy splitting between different energy eigenstates,
the higher the achievable fidelity. After the laser culling process the trap depth should
be increased again to preserve the Fock state. This step is able to produce even number
Fock states.
Step 3 allows to go from a two-atom Fock state to go to a one-atom Fock state.
This is achieved by splitting the trapping potentials into two separate wells.
The ground state occupation probability in a degenerate gas will depend on the
temperature of the gas. The average number of fermions with energy ǫi in state i is
given by the Fermi-Dirac distribution
ni =
1
e (ǫi−µ)/kBT +1 . (6.1)
Approximating the chemical potential with the Fermi energy, µ ≈ EF, and assuming ǫ1
to be negligible, the ground state occupation probability can be estimated by
n1 =
1
e −EF/kBT +1 . (6.2)
Temperatures of T ≈ 0.05TF have previously been achieved in degenerate Fermi gases
[104, 105]. At this temperature the ground state occupation probability is
n1 ≈ 1−2×10 −9
(6.3)
and the loss of fidelity from vacancies in the ground state occupation are therefore
negligible.
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