1996
DOI: 10.1103/physreva.54.710
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Perturbative formulation of optimal control for two-photon transitions: Reduction to an eigenvalue problem

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Cited by 9 publications
(8 citation statements)
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“…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%
See 1 more Smart Citation
“…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
confidence: 99%
“…͑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%
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