11.5 The diffraction of atoms by light 255receive a transverse kick from 2nphotons, as illustrated in Fig. 11.5, e.g.
first order arises from absorption from one of the counter-propagating
beams and stimulated emission into the other beam. This coherent
process, with no spontaneous emission, has some similarities with the
Raman transition shown in Fig. 11.6.^13
(^13) Scattering in a standing wave
changes the atomic momentum (ex-
ternal state) but not the internal
state.
11.5.1 Interferometry with Raman transitions
The description of the diffraction of two-level atoms by a standing wave,
in the previous section, as a coherent scattering process that imparts
twice the photon momentum 2h/λ, or multiples thereof, to the atom
has links with the very powerful method for manipulating the atom’s
momentum by Raman transitions shown in Fig. 11.6. Two laser beams
at frequenciesωL1andωL2drive a coherent Raman transition between
states| 1 〉and| 2 〉when
(ωL1−ωL2)=E 2 −E 1. (11.13)No population goes into the intermediate state|i〉in this coherent transi-
tion because neither of the two beams excites a single-photon transition
(see Appendix E). The Raman transition couples states| 1 〉and| 2 〉and
drives Rabi oscillations between them, e.g. when the atom starts in either
| 1 〉or| 2 〉,aπ/2-pulse creates a superposition of| 1 〉and| 2 〉with equal
amplitudes. Raman laser beams propagating in opposite directions (as
in Fig. 11.6) change the atom’s momentum during the transition.^14 The^14 Raman laser beams travelling in the
same direction have the same effect as
direct coupling between| 1 〉and| 2 〉by
microwaves.
absorption of a photon of wavevectork 1 and the stimulated emission of
one in the opposite directionk 2 −k 1 gives the atom two recoil kicks in
the same direction. This process couples the state| 1 ,p〉to| 2 ,p+2k〉.
The bra(c)ket notation denotes the|internal state,momentum〉of the
atoms. The Raman resonance condition in eqn 11.13 depends sensitively
on the atom’s velocityvfor counter-propagating beams and this provides
the basis for the Raman cooling of atoms (Section 9.8). For interferome-
try this velocity selectivity is a complicating factor and we shall assume
that the Raman pulses are sufficiently short^15 to drive transitions over^15 According to the condition in
the whole range of velocity components along the laser beam. eqn 9.58.
Figure 11.7 shows a complete Raman interferometer where the atoms
start in| 1 ,p〉and travel through three Raman interaction regions. In
Fig. 11.6A Raman transition with
two laser beams of frequenciesωL1and
ωL2that propagate in opposite direc-
tions. Equation 11.13 gives the res-
onance condition, ignoring the effects
of the atom’s motion (Doppler shift).
The Raman process couples| 1 ,p〉and
| 2 ,p+2k〉so that an atom in a Ra-
man interferometer has a wavefunction
of the formψ=A| 1 ,p〉+B| 2 ,p+2k〉
(usually with eitherB=0orA=0
initially).