Dynamics of atoms interacting with off-resonant strong laser pulses

Ultra-short strong excitation of two-level systems

“…Similarly to [39,40], defining f (t) = C a (t)/C b (t) and Ω(t) = ℘E(t)/ , we have the following Riccati equation:…”

“…and then, using the same method as in [39,40,44], we can obtain an approximated analytic solution for the Riccati equation ( 2):…”

“…In order to solve these equations we extended the method developed [39,40]. By neglecting the non-linear term f 2 (t) and the term ∝ g(t) in eq.…”

“…But since in the model we present here the change rate of levels' populations within a single opti-cal cycle is not negligible, the rotating-wave approximation can't be used. In other words in the present model we can't neglect the contribution of the counter-rotating terms in the Hamiltonian [39,40]. The two levels considered in the model can be the Zeeman-sublevels and the ultra-short (few to multi-cycle) pulse would be in the radio-frequency regime which has been reported in [41][42][43].…”

“…Moreover, optimizing the pulses parameters is proven to enhance the excited state population [37] or optimizing coherence in two-level systems (TLSs) [38]. In previous works we have already presented an analytical solution for the dynamics of a TLS excited with pulses of arbitrary shape and polarization [39,40]. But since in the model we present here the change rate of levels' populations within a single opti-cal cycle is not negligible, the rotating-wave approximation can't be used.…”