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

ferred into the |F = 1,mF = 0〉 or |F = 1,mF = 1〉 state via the single-photon cooling
process. For atoms in the |F = 1,mF = 0〉 state this is a purely gravito-optical poten-
tial, while for atoms in the |F = 1,mF = 1〉 the magnetic interaction adds to the overall
potential. Both states are trappable by the optical trough. In this new state, |F = 1〉,
the atoms cannot regain the potential energy within the optical trough and are therefore
effectively cooled.
The 87 Rb ground state hyperfine splitting is 6.8 GHz, meaning that once the
atoms are transferred to the |F = 1〉 state, the demon beam is detuned by 6.8 GHz.
Scattering of the demon beam of atoms in the |F = 1〉 state is therefore negligible,
ensuring the irreversibility of the process.
By adiabatically reducing the current in the quadrupole coils, the magnetic po-
tential is collapsed. During this ramp-off time tramp (typically on the order of 1 second)
the atoms encountering the demon beam are always near their classical turning points,
ensuring the cooling process. In order for the transfer to happen near the classical turn-
ing points, 〈τ〉 ≪ tramp must be satisfied, where 〈τ〉 is the average oscillation period in
the magnetic trap. In the rubidium magnetic trap 〈τ〉 is about 20 ms.
Once the quadrupole coil current is reduced below 2.5 A (corresponding to a
magnetic field gradient of 12 G/cm) the single-photon cooling process is complete. At
this point atoms in the magnetic trap are no longer levitated against gravity and are lost
from the trap. The atoms in the optical trough are then imaged to obtain information
about the atom number, spatial distribution and temperature.
Figure 5.3 shows the incremental transfer of atoms into the optical trough as a
function of the quadrupole coil current. The current is ramped linearly in time. The
optical trough itself is a conservative trap, therefore any positive slope is indicative of
successful single-photon cooling.
In the absence of any trap losses the increase in phase space density in the optical
trough increases with a larger ramp time. However, unwanted scattering events and
collisions with background gas lead to a finite trap life time. Balancing these effects
dictates the optimum ramp time.
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