Laser Noise, Decoherence &Observations in the Optimal Control of Quantum Dynamics 双 丰 Department of Chemistry, Princeton University Frontiers of Bond-Selective Chemistry

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5 Rabitz Group in Princeton Effect of environments on control of Quantum Dynamics: Fighting & Cooperating Exploring Photonic Reagent Quantum Control Landscape: no local sub-optimal Controlling Quantum Dynamics Regardless of the Laser Beam Profile and Molecular Orientation Revealing Mechanisms of Laser-Controlled Dynamics Experiment: SHG, C3H6,

6 Control of Quantum Dynamics  Hamiltonian:  Control Field  Objective Function  Closed Loop Feedback Control Genetic Algorithm

7 Laser Noise: Model  Noise Model:  Objective Function Deterministic part noise part

8 Cooperating with Laser Noise The control yield under various noise conditions with the low yield target of O T =2.25%. There is notable cooperation between the noise and the field especially over the amplitude noise range 0.06≤Γ A ≤0.08. d

9 Laser Noise: Foundation of Cooperation  Control Yield from perturbation theory  Averaged over the noise distribution  Minimize the objective function, symmetric noise distribution function

10 Fighting with Laser Noise Time dependent dynamics driven by the optimal control field with a large amount of phase noise. Plots (a1) and (a2) show the dynamics when the system is driven by a control field with noise while plots (b1) and (b2) show the dynamics of the system driven by the same field but without noise. The associated state populations are shown in plots (a2) and (b2). d

11 Decoherence: Model  Decoherence described by the Lindblad Equation  Objective Function:

12 Cooperating with Decoherence Power spectra of the control fields aiming at a low yield of O T =5.0%. γ indicates the strength of decoherence. The control field intensity generally decreases with the increasing decoherence strength reflecting cooperative effects.

13 Decoherence: Foundation of Cooperation When both the control field and decoherence are weak, the objective cost function can be written in terms of the contributions from each specific control field intensity A j ² Minimize objective function: Independent of A j and  j

14 Fighting with Decoherence Decoherence is deleterious for achieving a high target value, but a good yield is still possible.

15 Observation-assisted Control o Instantaneous Observations o Continuous Observations observed operator

16 Cooperating or Fighting with Instantaneous Observations During Control (a). Yield from control field with (O [E(t),u] ) or without (O[E(t)]) observation of dipole (b). Fluence of control field optimized with (F) or without (F0) observation of dipole

17 Cooperating or Fighting with Instantaneous Observations During Control Yield from a series of instantaneous observations with or without optimal control field.

18 Optimized Continuous Observations to Break Dynamical Symmetry QaQa O[E(t),Q] b T1T1 T2T2 No % \\ P0P % P1P % 4648 P2P % To control an uncontrollable system. Goal: 0  1 a : Operator observed between times T 1 and T 2 with strength  P k indicates population at level k; b : Yield in state 1 from optimizing the control field E(t), T 1, T 2 and 

19 Optimized Continuous Observations to Break Dynamical Symmetry

20 Observation assisted optimal Control The control yield of desired state (P ₃ ) and undesired state (P 1’ ) under different strength (κ) of continuous observations on level 1′

21 Conclusions In the case of low target yields, the control field can cooperate with laser noise, decoherence and observations while minimizing the control fluence. In the case of high target yields, the control field can fight with laser noise, decoherence and observations while attaining good quality results An optimized observation can be a powerful tool the in the control of quantum dynamics

22 Where is Future of Modeling? Fighting with Noise, Decoherence. 100% yield is expected Quantum Computation Simulate Controlled Real Chemical Reaction: Systems investigated are too simple.

23 Thanks 朱清时（ USTC ）严以京（ HKUST ） Herschel Rabitz （ Princeton ） Mark Dykman （ MSU ）

24 Thanks, Family