1 Laser noise and decoherence are generally viewed as deleterious in quantum control. Numerical simulations show that optimal fields can cooperate with laser noise and decoherence when seeking modest control yields, and it’s possible to find optimal fields to fight with them while seeking a high control yield. The theoretical foundations for the ability of a control field to cooperate with laser noise and decoherence are established. d Abstract

2 The use of instantaneous and continuous observations(measurements) acting as controls is explored. Quantum observations can break dynamical symmetries, and a time-dependent observation can even transfer a state to another state. Suitably optimized observations could be powerful tools in the manipulation of quantum dynamics. d Abstract: Continued

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

4 Laser Noise*: Model  Noise Model:  Objective Function * J.Chem.Phys 121, 9270 (2004) Deterministic part noise part

5 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

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

7 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

8 Decoherence*: Model  Decoherence described by the Lindblad Equation  Objective Function: * Submitted to J.Chem.Phys

9 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.

10 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

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

12 Observation-assisted Control* o Instantaneous Observations o Continuous Observations *In Progress observed operator

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

14 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 

15 Time-dependent Observations The Quantum Anti-Zeno Effect A time-dependent observation can transfer a state  0 to a target state  f, and may be a useful tool in the control of quantum dynamics. d

16 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