We present a detailed theory of a technique for the adiabatic control of the population flow through a preselected decaying excited level in a three-level ladder quantum system, as was experimentally demonstrated recently by Garcia-Fernandez et al. [Phys. Rev. Lett. 95, 043001 (2005)]. Specifically, we consider a three-state excitation chain of bound states, 1-2-3, of successively increasing excitation energy, in which probability loss via fluorescence occurs from states 2 and 3. We describe a laser excitation scheme that can, by adjustment of laser parameters, alter at will the relative fraction of population that, starting from state 1, is ultimately lost through states 2 and 3. We present analytical results for the conditions under which quasiadiabatic passage can take place.
We study a method for controlling the flow of excitation through decaying levels in a three-level ladder excitation scheme in Na(2) molecules. Like the stimulated Raman adiabatic passage (STIRAP), this method is based on the control of the evolution of adiabatic states by a suitable delayed interaction of the molecules with two radiation fields. However, unlike STIRAP, which transfers a population between two stable levels g and f via a decaying intermediate level e through the interaction of partially overlapping pulses (usually in a Lambda linkage), here the final level f is not long lived. Therefore, the population reaching level f decays to other levels during the transfer process. Thus, rather than controlling the transfer into level f, we control the flow of the population through this level. In the present implementation a laser P couples a degenerate rovibrational level in the ground electronic state X 1Sigma(g)+, v" = 0, j" = 7 to the intermediate level A 1Sigma(u)+, v' = 10, J' = 8, which in turn is linked to the final level 5 1Sigma(g)+, v = 10, J = 9 by a laser S, from which decay occurs to vibrational levels in the electronic A and X states. As in STIRAP, the maximum excitation flow through level f is observed when the P laser precedes the S laser. We study the influence of the laser parameters and discuss the consequences of the detection geometry on the measured signals. In addition to verifying the control of the flow of population through level f we present a procedure for the quantitative determination of the fraction kappa(f) of molecules initially in the ground level which is driven through the final level f. This calibration method is applicable for any stepwise excitation.
A great deal of effort has been applied to understanding population dynamics within a variety of coherent excitation schemes. The goal in such studies has been to understand the conditions necessary for efficient transfer of population from one state to another. While many theoretical treatments include the effects of natural lifetimes that are present in any given system, some neglect this important aspect when considering specific cases. Adiabatic approximations are also widely made. Additionally, it is often difficult to envision how the different parameters controlling efficient population transfer are interrelated or even which parameters are the most critical, especially when the decay lifetimes are taken into account. This work describes a numerical study of coherent excitation applied to a
87Rb ladder system where spontaneous decay rates are included, and adiabaticity is not assumed. A useful method is introduced to explore the interdependence of various excitation parameters. The efficiency of population transfer as a function of several experimentally controllable parameters is explored, and other general trends are summarized.
This paper presents observations and an interpretation of laser-induced excitation and fluorescence in a ladder $g\text{\ensuremath{-}}e\text{\ensuremath{-}}f$ of three molecular levels [$X\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+}({v}^{\ensuremath{''}}=0,{J}^{\ensuremath{''}}=7)$, $A\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{u}^{+}({v}^{\ensuremath{'}}=10,{J}^{\ensuremath{'}}=8)$, and $5\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+}(v=10,J=9)$, respectively] observed in a supersonic molecular beam of
Na2. The $g\text{\ensuremath{-}}e$ coupling, by cw laser
P, is strong. A weak cw laser
S couples levels
e and
f. The basic observations are of level-
f fluorescence as a function of the detuning of the
S laser from resonance. The signal profile does not appear as the typical Autler-Townes doublet, but as a spectral structure, whose position, width, and shape depend upon several laser parameters. We interpret these results using a simple model of three nondegenerate quantum states coherently excited while undergoing population loss to states outside the three-level system. We invoke the mechanism of optical pumping and evolution along adiabatic states, together with Landau-Zener transition probabilities. We also present results from numerical studies, which include all quantum states, all radiative couplings, coherent and incoherent, as well as convolutions with the relevant distribution functions (velocities and Zeeman sublevels). Although no adjustable parameters are involved, excellent agreement with the experiment is found. Since successive avoided crossings of adiabatic eigenvalues occur, interference effects may be relevant. Such effects are not expected to be visible in the present experiment, for reasons that are discussed. However, we discuss conditions which would allow resolving the interference structure experimentally. We also suggest possible interesting applications of the interference to rapidly switch off Rydberg state population or to control its spatial distribution.
We calculate the propagator and the transition probabilities for a coherently driven three-state quantum system. The energies of the three states change linearly in time, whereas the interactions between them are pulse shaped. We derive a highly accurate analytic approximation by assuming independent pairwise Landau-Zener transitions occurring instantly at the relevant avoided crossings, and adiabatic evolution elsewhere. Quantum interferences are identified, which occur due to different possible evolution paths in Hilbert space between an initial and a final state. A detailed comparison with numerical results for Gaussian-shaped pulses demonstrates a remarkable accuracy of the analytic approximation. We use the analytic results to derive estimates for the half-width of the excitation profile, and for the parameters required for creation of a maximally coherent superposition of the three states. These results are of potential interest in ladder climbing in alkali-metal atoms by chirped laser pulses, in quantum rotors, in transitions between Zeeman sublevels of a
J=1 level in a magnetic field, and in control of entanglement of a pair of spin-
1∕2 particles. The results for the three-state system can be generalized, without essential difficulties, to higher dimensions.
The effect of the collisions on the control of coherent population transfer in a closed inverse
Y-type four-level system driven by three laser fields is investigated with the stimulated Raman adiabatic passage technique. An arbitrary coherent superposition between the initial state and target state can be created either by varying the Rabi frequency of the control laser field or by tuning the one-photon detunings of the pump and Stokes laser fields. When the three laser fields with nearly equal peak Rabi frequencies are each tuned to resonance with the respective transitions, the low transfer efficiency due to the nonadiabatic coupling between two degenerate adiabatic states could be enhanced dramatically with the increase of the collision-induced coherence decay rates to the value nearly comparable to the Rabi frequency of the control field. The enhanced transfer efficiency results from the collision-controlled electromagnetically induced transparency in the $\ensuremath{\Lambda}$-type three-level subsystem and electromagnetically induced absorption in the ladder-type three-level subsystem of the four-level system.