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Quantum Observations in Optimal Control of Quantum Dynamics

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

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Quantum Observations in Optimal Control of Quantum Dynamics

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  1. Quantum Observations in Optimal Control of Quantum Dynamics Feng Shuang Herschel Rabitz Department of Chemistry, Princeton University ICGTMP 26th, 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) • F.Shuang & H.Rabitz,J.Chem.Phys, 121, 9270 (2004) • F.Shuang & H.Rabitz,J.Chem.Phys, 124, 204115(2006) • 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 & MenskyMaster 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 Yield of N Observations: (QAZE) After Optimization:

  9. Optimal Continuous Observations • Weak Observation: • Strong Observation: • no analytical solution for general  • linear form: (t)= Bopt+Aopt t

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

  11. Optimal Control Field with ObservationsModel 1 • Five-level system: Population 0  4 • Control field is fighting with observations of dipole, energy, population at Tm=Tf/2

  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

  15. Optimal Observations with Control Field:Model 2 • Continuous observation: Symmetry Breaking, QZE • Optimize: A, T1,T2,Gama P=P0 P=P2

  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

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