Quantum Observations in Optimal Control of Quantum Dynamics Feng Shuang Herschel Rabitz Department of Chemistry, Princeton University ICGTMP 26 th, June, 2006, NY

2 Overview Introduction: Optimal Control of Quantum Dynamics Quantum Observations Optimal Observations: w/o Control Field With Control Field

3 Control: Coherence + Decoherence Coherence: Decoherence:  Laser Noise: Cooperate and Fight (1)  Dissipation: Cooperate and Fight (2)  Observations: A tool to assist control (3) 1.F.Shuang & H.Rabitz, J.Chem.Phys, 121, 9270 (2004) 2.F.Shuang & H.Rabitz, J.Chem.Phys, 124, (2006) 3.F.Shuang et al, In progress

4 Optimal Control of Quantum Dynamics  Hamiltonian:  Control Field  Objective Function  Closed-Loop Feedback Control: Herschel Rabitz Genetic Algorithm

5 Quantum Observations Instantaneous Observations: Von Neuman General Operator A: Projection Operator P Continuous Observations: Feynman & Mensky Master Equations

6 Quantum Zeno and Anti-Zeno effect Quantum Zeno Effect (QZE) –Repetitive observations prohibits evolution of quantum system Quantum Anti-Zeno Effect (QAZE) –Time-dependent observation induces state change of quantum system

7 Optimal Observations w/o Control Field Two-Level: Initial state and Final state, Projection Operators Adiabatic Limit: 100% Population Transfer (1) Number of Instantaneous Observation, N   Strength of Continuous Observations:    When N and  are finite, What’s the best? (1). A.P.Balachandran & S.M.Roy, PRL, 84, 4019(2000)

8 Optimal Instantaneous Observations N Observations. Interaction Picture After Optimization: Yield of N Observations: (QAZE)

9 Optimal Continuous Observations Weak Observation: Strong Observation: no analytical solution for general  linear form:  (t)= B opt +A opt t

10 Optimal Observations with Control Field N-Level system Control Field: Two Models: –Cooperate & Fight –Symmetry-breaking

11 Optimal Control Field with Observations Model 1 Five-level system: Population 0  4 Control field is fighting with observations of dipole, energy, population at T m =T f /2 Operator Value of observationYield with observation  % H0H % P0P % P1P % P2P % P3P % P4P %

12 Optimal Observations with Control Field : Model 1 Cooperating with the observation of dipole 

13 Optimal Observations with Control Field: Model 2 High symmetry system: Only 50% population is possible from 0 to 1

14 Optimal Control Field with Observations: Model 2 Instantaneous observation: Partial Symmetry Breaking P O [E(t),P] O [E(t),0] F % P066.90%46.04%0.76 P149.99%50.00%0.96 P266.66%46.37%0.49

15 Optimal Observations with Control Field: Model 2 Continuous observation: Symmetry Breaking, QZE Optimize: A, T 1,T 2,Gama P=P 0 P=P 2

16 Conclusions 1. Control field can fight and cooperate with observations 2. Observation can assist optimal control 3. Quantum Zeno and Anti-Zeno effects are key Question: How to implement the observations in experiments ?

17 Acknowledgements Herschel Rabitz Alex Pechen & Tak-san Ho Mianlai Zhou Other colleagues Funding: NSF, DARPA, ARO-MURI