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

The fidelity of the laser culling process is analyzed by a 1-dimensional harmonic
trap of size z, truncated at the energy Et [102]. A schematic of the truncated potential
is shown in figure 6.1.
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Figure 6.1: Trapping potentials used to calculate the fidelity of laser culling in 6 Li.
(a) Truncated harmonic trap. The truncation energy is Et and the trap size is z. (b)
Truncated harmonic trap with a magnetic field gradient. The trap size z is defined as
the length of the parabolic part of the potential profile. The lines represent the ground
and first excited state energy levels. The unit of length is given by x0 = /mω, the
unit of energy is ω. Figure courtesy of Shoupu Wan.
Controlling the strength of the trapping potential is not the only option one has
to control the number of trapped atoms. In addition, a magnetic field gradient can be
applied, see figure 6.1 (b). This has two effects: all atoms that are no longer held within
the trapping potential will be moved away from the system quickly. In addition, the
magnetic field gradient allows for additional control of the overall trapping potential. In
the presence of a magnetic field gradient true bound states no longer exist. Instead a
series of quasi-bound states exists (figure 6.1 shows the ground and first excited state).
In this situation the atoms can tunnel out of the trap. However, the atoms in the first
excited state will tunnel out much faster than atoms bound more deeply. Once the
excited state atoms have left the trap, the magnetic field gradient can be removed and
the trap depth deepened to protect the remaining ground state atoms (the Fock state).
The difference in the lifetimes of the ground and first excited quasi-bound states
determines the fidelity of creating a pair of atoms in the ground state of the trap. The
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