Single-Photon Atomic Cooling - Raizen Lab - The University of ...

demonstrated by Chu et al. [63].
To model the dipole force, let the applied electric field and induced
dipole moment be given as
E(r,t) = ê ˜ E(r)e −iωt + c.c. (2.42)
p(r,t) = ê ˜p(r)e −iωt + c.c. (2.43)
where these two quantities are related through the complex polarizability α
is
p = α(ω) E. (2.44)
The potential energy of the induced dipole in the driving electric field
Udip = − 1
2 〈p · E〉, (2.45)
where the angular brackets represents a time average and the 1/2 accounts for
the induced, not permanent, nature of the electric dipole. This can be written
in a more useful form by replacing the amplitude of the electric field with the
corresponding intensity through I = 2ǫ0c| ˜ E| 2 and evaluating the time average
of the two complex quantities,
Udip = − 1
Re(α)I. (2.46)
2ǫ0c
We see that the potential is proportional to the intensity of light and
the real part of the polarizability, the latter of which represents the in-phase
46