Laser control of population dynamics with bichromatic fields: direct search through field amplitude, frequency, and phase space

Bichromatically driven double well: Parametric perspective of the strong field control landscape reveals the influence of chaotic states

“…5 and makes it an ideal candidate to understand the origins of suboptimal structures on the control landscape from a classicalquantum correspondence perspective. Moreover, C z (λ) can be obtained with a few Floquet calculations or via the parametric equations of motion 8,41 and hence applicable to multidimensional driven systems. A further attractive feature, from the point of multidimensional systems, is that the correlator is capable of establishing the influence of the chaotic states on the control landscape without the need for visualizing/classifying the states in the underlying phase space.…”

“…Persistent theoretical and experimental efforts have led to the formulation of several ingenious control schemes 1,2,3,4 for both atomic and molecular systems. Recently researchers have been interested in determining the "control landscape" for specific systems 5,6,7,8,9,10,11,12,13 . The motivation for undertaking such extensive studies is atleast twofold.…”

“…Note that it is quite possible to have several distinct choices for the control variables which yield the same value for P if . Several such examples of control landscapes can be found in the literature 2,7,8,9,10,13 The second perspective on the control problem comes from the optimal control theory (OCT) approach 4,6 . In OCT a cost (landscape) function of the form Φ(U ) = Tr[U ρ(0)U † Θ] ≡ Θ , with ρ(0) being the initial density matrix and an arbitrary observable Θ, is extremized with respect to the field E(t).…”

Application of parametric equations of motion to study the resonance coalescence in $\text{H}_{2}^{+}$H2+

“…PEM have been applied first by Rabitz and co-authors 10 to several simple, illustrative examples. Later on, PEM were implemented by Gross and co-authors 11,12 to obtain the 3D plots of population dynamics as a function of frequency and phase or amplitude. Within PEM, time dependent Schrödinger equation was needed to be solved once to obtain the quantum dynamic behaviour in the presence of strong (nonperturbative) periodic fields having the form A cos (ωt) over a range of field amplitudes and frequencies.…”

Laser-induced multiphoton dissociation of H2+as a function of the field frequency using parametric equations of motion

“…Rabitz and co-workers [1] applied PEM to several simple, illustrative examples. Later PEM was implemented by Gross et al [5,6] to obtain the three-dimensional (3D) plots of population dynamics as a function of frequency and phase or amplitude. In their method, the time-dependent Schrödinger equation (TDSE) was needed to be solved once to obtain the quantum dynamic behavior in the presence of strong (nonperturbative) periodic fields having the form A cos(ωt) over a range of field amplitudes and frequencies.…”