Copyright by Kirsten Viering 2006 - Raizen Lab - The University of ...

take into account the velocity of the atoms and their accelerations due to the differential
force exerted by the potential for the initial and final state.
5.2.1 Spectral resolution limit
During the Raman process one photon is absorbed and another photon of almost the
same frequency is emitted into a co-propagating field. Thus the net momentum change
of the atom is negligible. The use of a co-propagating configuration avoids a velocity-
selection due to Doppler-Shifts which has been observed by Kasevich et al. using
a counter-propagating beam configuration [23]. Raman-induced resonance imaging
using co-propagating laser fields has been used by Thomas et al. for precision position
measurements of moving atoms [24], [25].
If the detuning of both Raman pulses from resonance is large enough to avoid
a population of an excited state, incoherent transitions between the two ground states
can be avoided. Therefore, the life-time of the ground states determines the bandwidth
of the Raman transition. Since the lifetime of the ground states is long, we are able to
neglect the bandwidth of the Raman transition.
The difference in the Raman beams can be created by passing one beam through
an acousto-optic modulator (AOM). By equalizing the optical path length it is possible
to minimize the frequency jitter in the difference frequency; in this limit the stability of
the difference frequency is then given by the AOM and is usually small and negligible.
In the limit of a very stable difference frequency the Fourier-Theorem gives the
frequency resolution of the Raman process,
∆ω ≈ 1
. (5.1)
T
For simplicity we assume the initial state |i〉 to be independant of the magnetic field.
If the frequency shift of the final state | f 〉 varies linearly with the position, the force F
exerted by the magnetic field on the final state is uniform and the frequency shifts as
∆ω = ∆E
F
F
= ∆x. The quantity is the spatial tuning rate, which determines the spatial
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