more we study. The study of the interaction of a two-level system and
electromagnetic fields is no exception. The simplest situation is when a two-
level system is irradiated by a single monochromatic field. This is the topic
presented in the chapters 4 and 5 where coherent transients are reported. The
interaction of a two-level system and a single monochromatic field can be
studied by a separate probe field. In this case, the simpler situation is to
investigate this interaction by probing a separate transition from one of the
driven two levels to a third level, in which the well-known Autler-Townes
doublets profiles can be observed (Chapters 8). For such a situation it is
possible to derive an exact analytical steady state solution even at the strong
probe field limit (Chapter 8), as the pump and probe fields couple different
transitions and hence there is no beating terms. In addition the signal is
relatively large as the probed transition is not saturated by the strong pump
field. The situation, where the probe field interacts with the same two-level
system transition as the pump field, has also been studied for both weak
(Chapter 6) and strong (Chapter 7) probe field cases. In this case, the
investigations are more difficult because (i), theoretically, as the pump and
probe fields drive the same transition, there will be many beating terms and
hence there is no simple analytical solution to the problem, and (ii),
experimentally, the signal is much more weaker than the situation when a third level is involved due to saturation.
A question naturally arises of how the absorption and dispersion profiles of a two-level system are modified by the presence of two strong near resonant monochromatic fields? As in the case of single pump field, it is expected that the situation will be simpler if the probe field couples a separate transition which has a common level with the driven transition and this is the situation studied in this chapter. There have only been a few theoretical considerations [1-3] whereas the only experimental observation is claimed by a Russian group [1] where the 63Pj<=>63Dj transition (553.587 nm) of the
barium atom was strongly driven by two strong light fields and the 63P 1<=»63D2 transition (551.95 nm) was probed by a weak field. Their work indicated that the weak probe absorption profile consists of a multi-peak feature. But the spectrum was recorded using photographic plates, it was not practical to obtain the spectral profiles.
In this chapter we report the experimental results for a V-shaped three- level system as shown in Fig.9-1, where the 11 ><=>I2> transition is driven by two strong monochromatic fields and the absorption and dispersion profiles are measured with a weak field probing the adjacent 11 ><=>I3> transition. The results presented in this chapter is, I believe, the first experimental observation of this kind. The theoretical calculation using the continued fraction formalism accurate to the first order of weak probe field will be outlined. However, detailed numerical calculation will not be carried out due to the time limitation. Discussions in terms of the dressed state are also presented. It is shown that using the dressed state picture the resonance peak positions can be conveniently predicted for some special cases of the pump intensities and detunings.
I3>
A 3
— • ] - -
Figure 9-1. Three-level system interacting with two strong pump fields and a weak probe field. The ll> <=> I2> transition is driven by two strong monochromatic fields at frequencies co j and co 2 , with Rabi intensities of % j and %2 and detuning Aj and A2 , respectively. The I1><=>I3> transition is probed by a weak field at frequency CO3 .
9.2 Outline of Theory
9.2.1 Density Matrix Equations of Motion Formalism
Consider a three-level system interacting with two strong pump fields and one weak probe field as shown in Fig.9-1. The three-level system has energy levels Ej < E2 < E3 corresponding to the three states ll>, I2> , I3>. The rf field has the form
Brf (t) = Bj cos C0j t + B2 cos co2t + B3 cos ©3 t . (9.1)
The Rabi frequencies %2 an(i detunings Aj, A2 of the two pump fields are
defined by
LI
B
LIB
M 2 1 M 2 2
y = — --- , y = — 7---- and A = oo - co, , A = co - G)
M h K 2 h 1 21 1 2 21 2
(9.2)
Similarly the Rabi frequency %3 and detuning A3 of the probe field are defined by
u
B
y = —^7---- and A = co - co .
M h 3 31 3 (9.3)
The density matrix equation of motion can be written as (Chapter 8)
eq P11 " h ( V 12P21 " V21 P12 + V 13P31 " V31 P 13 ^
Pn-P.i
1 (9.4a) P22 h ^V 12P 21 " V 21 P 12 ^ " P22 " P22 (9.4b) • _ i , \j w _ \ P33 P33 P33 ~f i V 13 P31 " V31 P 13 ’ T (9.4c) P31 i(0 3 1 P31 + /i V31 ^ P33 P 11 ^ + ^21 P32 T (9.4d) P21 " 1 ^ l P21 + h V21 ^ P22 ’ P 11 ^ + h V31 P23 ’ T (9.4e) P32 ’ 1 ^32 P32 " h V31 P 12 + h V 12 P31 " T (9.4f) With the rotating-wave-approximation the interaction terms can be written ash X1 -i C0j t ti X2 - i % t