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Graham and Walls (1996a) extended the analysis above to take into account weak interactions between atoms (treatable via the Bogoliubov approximation). The scattering function is modified to S( k, fN(1! k) )" (1#1n k2)[ ( (1# k) # )# e\@ S k k ( )]#S ( k, ! k ), (121) with the background now given by S ( k, (1#1nq2)(1#1nq k2)( q# q k) > > 2 (1! q )(1! q k) q k > $\ 1# q q k > ; 2 e\@ Sq> k ( # q! q k) > q# q k > )" # ( # q# q > )#e\@ Sq>Sq> k k ( ! q ! S. F. Walls / Physics Reports 303 (1998) 1—80 where 1n k2"[exp( and now (see Appendix A) "( " k"/2m)(" k"#16 k "1# " k"!
1996) is still limited to a regime of relatively low optical thickness. S. F. 2. Scattering of short laser pulses Lewenstein and You (1993) and You et al. (1995) investigated the scattering of short but intense laser pulses from a trapped sample of cold bosonic atoms with d &10 . They found that above the critical temperature, ¹ , for BEC, coherent scattering is weak and restricted to a very narrow cone in the forward direction (due to phase matching conditions), while below ¹ the number of scattered photons increases dramatically and coherent scattering occurs into a solid angle in the forward direction determined by the size of the condensate.
In certain configurations it is also possible for a laser beam to act as a nonlinear atomic waveguide which supports atomic solitons. 5. , a trapped condensate interacting with a single quantised field mode of a microwave cavity. Marzlin and Audretsch (1997) have considered just such a situation in which the field is resonant with an internal atomic transition "g2 "e2 (they neglect spontaneous emission and mechanical effects of the interaction). With all of the atoms initially in the excited internal state "e2 and the field mode in the vacuum state, they find that the number of atoms in the excited state can exhibit periodic dips or fractional collapses and revivals as time progresses for the case that the initial external atomic state is a number state or a coherent state, respectively.