“…To facilitate this problem, there has been much effort directed toward the linear versions of control theory. 25,[35][36][37][38][39] In the following we shall describe two limiting cases in the weak control response regime in which the linear versions of control theory can be generally obtained. 32 Before proceeding, let us analyze the power law of the relevant quantities c and f Ϯ in the general Hilbert-space control theory ͓Eq.…”
Section: B Linear Theory In the Weak Response Regimementioning
confidence: 99%
“…Here, B(t,tЈ) is the Hilbert-space pump-dump control response function defined by 32,33,39 B͑t,tЈ͒ϭ ͭ…”
Section: Eigenequation For the Two-photon Pump-dump Controlmentioning
We combine theories of optimal pump-dump control and the related transient probe absorption spectroscopy in order to elucidate the relation between these two optical processes and the possibility of experimental realization. In the weak response regime, we identify the globally optimal pair of pump-dump control fields, and further propose a second-order difference detection scheme to monitor the wave packets dynamics that is jointly controlled by both the pump and dump fields. The globally optimal solution serves also as the initial input for the iterative search for the optimal control fields in the strong response regime. We use a model I 2 molecule to demonstrate numerically the pump-dump control and the detection of a highly vibrationally excited wave packet focusing dynamics on the ground X surface in both the weak and strong response regimes. The I 2 B surface serves as the intermediate to assist the pump-dump control and the optical detection processes. Demonstrated in the strong response regime are the optimal pair of pump-dump molecular-pulses that invert nearly total population onto the predefined target region within a half period of vibration motion.
“…To facilitate this problem, there has been much effort directed toward the linear versions of control theory. 25,[35][36][37][38][39] In the following we shall describe two limiting cases in the weak control response regime in which the linear versions of control theory can be generally obtained. 32 Before proceeding, let us analyze the power law of the relevant quantities c and f Ϯ in the general Hilbert-space control theory ͓Eq.…”
Section: B Linear Theory In the Weak Response Regimementioning
confidence: 99%
“…Here, B(t,tЈ) is the Hilbert-space pump-dump control response function defined by 32,33,39 B͑t,tЈ͒ϭ ͭ…”
Section: Eigenequation For the Two-photon Pump-dump Controlmentioning
We combine theories of optimal pump-dump control and the related transient probe absorption spectroscopy in order to elucidate the relation between these two optical processes and the possibility of experimental realization. In the weak response regime, we identify the globally optimal pair of pump-dump control fields, and further propose a second-order difference detection scheme to monitor the wave packets dynamics that is jointly controlled by both the pump and dump fields. The globally optimal solution serves also as the initial input for the iterative search for the optimal control fields in the strong response regime. We use a model I 2 molecule to demonstrate numerically the pump-dump control and the detection of a highly vibrationally excited wave packet focusing dynamics on the ground X surface in both the weak and strong response regimes. The I 2 B surface serves as the intermediate to assist the pump-dump control and the optical detection processes. Demonstrated in the strong response regime are the optimal pair of pump-dump molecular-pulses that invert nearly total population onto the predefined target region within a half period of vibration motion.
“…͑19͔͒, followed by the explicit first order expansion of the relevant quantity to the field it depends on. The former approach 20 is similar to the one used by Dubov and Rabitz 12 where the phase-locked pump-dump control was considered. In this paper, let us consider the latter approach.…”
Section: Pump-dump Control Of Pure State Systemsmentioning
confidence: 99%
“…To facilitate this problem, there has been considerable effort on arriving a linearized version of control formalism. [7][8][9][10][11][12][13][14][15][16] The simplest linearizable system is the control of one-photon achievable target. [7][8][9][10][11] In this case, the optimal control in the weak response regime can be reduced to an eigen-problem of a second order control response function, whose eigenfunction and eigenvalue give the optimal field and yield, respectively.…”
Section: Introductionmentioning
confidence: 99%
“…[12][13][14][15][16] In their original work, 1 Tannor and Rice considered the control with a pair of phaseunlocked weak fields and derived a linear equation for the optimal dump field with respect to a given pump field in the weak response regime. Yan 13,14 has extended Tannor-Rice's original idea and arrived at a pair of coupled quasi-linear optimal pump-dump equations in the weak response regime.…”
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