Atomic and Molecular Processes in Laser Field

1. Atomic and MolecularProcesses in Laser Field Yoshiaki Teranishi (寺西慶哲) 國立交通大學 應用化學系 Institute of Physics NCTU Colloquium @Information Building CS247 Sep 23, 2010

2. Atomic and Molecular Processesin Laser Field(Quantum Control) • Brief review on some basics • Complete Transition • Selective excitation • Quantum Control Spectroscopy • Computation by Molecule with Shaped Laser

3. Quantum Control Result (Given) System (Known) External Field (to be searched for) Inverse problem

4. IntroductionAtoms, Molecules, and Laser

5. Energy and Time Scales of Molecule Time Energy Rotational 0.0001eV 10-12s 0.001eV 10-13s 10-14s 0.01eV Vibrational 10-15s 0.1eV 10-16s 1eV Electronic 10-17s 10eV

6. History of Laser Intensity

7. History of Laser Pulse Duration Rotational Vibrational Electronic

8. Laser Pulse Short-Pulsed Laser Long-Pulsed Laser CW Laser Time Domain Monochromatic Narrow Band Broad Band Frequency Domain

9. Lasers for Control • Coherence  Interference • High Intensity  Faster Transition • Short Pulse  Broad Bandwidth • Broad Bandwidth  Various Resonance

10. Pulse Shaper Fourier Expansion Control of the Fourier coefficients LCD (Transmittance & Refractive indexes are controlled.) How to design the pulse?

11. Shaped Pulsed Laser Time dependent Intensity Time dependent Frequency

12. Shaped Pulse Complicated Shaping Numerical optimization of the laser field for isomarization trimethylenimine M. Sugawara and Y. Fujimura J. Chem. Phys. 100 5646 (1994) Monotonically Convergent Algorithms for Solving Quantum Optimal Control Problems Phys. Rev. A75 033407

13. Simple Shaped Pulse Chirping (time dependent frequency) FT Pulse Linear Chirp Quadratic Chirp Positive Chirp Negative Chirp Concave Down Concave Up Time

14. Today’s theme ・Complete Transition ・Selective Excitation ・Spectroscopy Utilizing Quantum Control ・Computation by Molecule with Lasers

15. General Conditions for Complete Transition among Two States

16. Floquet Theory(Exact Treatment for CW Laser) Schrodinger Equation Time periodic Hamiltonian Wavefunction (the Floquet theorem)

17. Quasi State (Time Independent Problems) If

18. Energy diagram of adiabatic energy levels Avoided Crossing Frequency of laser

19. Adiabatic ApproximationExample: Stark Effect Energy Levels Nonadiabatic Transition Transition due to breakdown of the adiabatic approximation Electric Field

20. Landau-Zener model(Frequency Sweep) nonadiabatic adiabatic

21. Rose-Zener Type(Intensity Sweep)

22. Quadratic Crossing Model(Teranishi – Nakamura Model) J. Chem. Phys. 107, 1904

23. Floquet + Nonadiabatic Transition • Shaped Pulse--Time dependent frequency & intensity • Floquet State--Quasi stationary state under CW laser • Shaped Pulse --Nonadiabatic Transition How to Control ?

24. Control of nonadiabatic transition Teranishi and Nakamura, Phys. Rev. Lett. 81, 2032 Periodic sweep of adiabatic parameter Bifurcation at the crossing Phase can be controlled by DA, DB Interference effects DB DA DA DA DB DB Multiple double slits Bifurcation at slits Interference can be controlled by DA, DB detector

25. Required number of transition Necessary bifurcation probability for complete inversion after n transitions Transition probability after n transition Bifurcation probability For p = 0.5, one period of oscillation is sufficient 2 The Number of transition (n)

26. One Period of Oscillation

27. Landau-Zener model(Frequency Sweep) Frequency adiabatic

28. Example of Frequency Sweep |0>---|2> Vibrational Transition of Trimethylenimine Solid: Constant IntensityDashed: Pulsed Intensity Dotted: With Intensity Error Intensity at the transition is important

29. Isomarization of Trymethylenimine Our control Scheme Numerically Obtained pulse

30. Rose-Zener Type(Intensity Sweep)

31. General Conditions for Complete Transition • Time Dependent Frequency & Intensity--Nonadiabatic Transition among Floquet State • Control of Nonadiabatic Transition--Interference by Multiple Transition • Compete Transition--Frequency Sweep (Landau-Zener)--Intensity Sweep (Rozen-Zener) • Fast Transition Requires High Intensity because ….--sufficient nonadiabacity (LZ case)--sufficient energy gap (RZ case)

32. Selective Excitation Among Closely Lying States--Fast Selection Collaboration with Dr. Yokoyama’s experimental group at JAEA

33. Basic Idea Young’s interference The Excited State 1st pulse 2nd pulse The Ground State

34. j 5/2 3/2 Interference +/ 7D Fluorescence (a) (b) (c) 3/2 6P 1/2 760 – 780 nm 1/2 6S 1st pulse 2nd pulse Selective Excitation of Cs atom（Selection of spin orbit state） • Parameters- Time delay- phase difference • Interference • Suppression of a specific transition 2 pulse interference Spin orbit splitting ΔE＝21cm-1 Uncertainty limit Δt=1/ΔE＝８００ｆｓ (86fs) (86fs) Delay

35. Preamplifier PMT-I Filter-I AOPDF Cell TeO2 Ti:Sapphire oscillator Filter-II RF generator PMT-II Internal trigger Computer MCS Experimental Facility

36. Delay:400ｆｓ（Experiment and Theory） Normalized transition probability Branching ratio

37. Delay300fs（Exp. & Theory） Normalized transition probability Branching ratio Selection is possible even when t <Δt=1/ΔE＝８００ｆｓ　

38. Breakdown of the Selectivity(Theoretical simulation) Peak intensity: 5.0GW/cm2 Peak intensity:0.1GW/cm2 Transition probability Transition probability Large transition probability bad selectivity（nonlinear effect）

39. Basic Idea (Perturbative) p2 p2 p2 0 |2> p1 0 p1 p1 |1> 2nd pulse 1st pulse 1 |0>

40. Breakdown of the selectivity p2(1-p2) p2 (1-p1-p2) p2 0 |2> p2 p2 p1(1-p1) p1 0 (1-p1-p2) p1 |1> 2nd pulse 1st pulse p1 p1 1-p1-p2 1 |0> Selection　→　p1, p2 <<1　（Linearity）

41. Non-Perturbative Selective Excitation Separation of Potassium 4P(1/2) 4P(3/2) Quadratic Chirping Spin orbit splitting ΔE＝58cm-1 Uncertainty limit Δt=1/ΔE＝570 ｆｓ

42. Selective Excitation by Quadratic chirping E E0+hw (1-p1)(1-p2) (1-p1)(1-p2) p2 E2 (1-p1)p2 (1-p1)p2(1-p2) 1-p1 E1 p1 t

43. Selective Excitaion of K atom by Quadratic chirping (Simulation） Perturbative region(1 MW/cm2) Small Probability Both selective 4P3/2 4P1/2 B 4P(3/2) 4P(1/2)

44. High Intensity(0.125 GW/cm2) 4P1/2 B 4P(3/2) 4P3/2 4P(1/2) Upper level (Red) Lower level (Black) Incomplete destruction Complete destruction

45. Complete& selective excitation of K atom 4S →4P3/2 Excitation 4S →4P1/2 Excitation Intensity 0.36 GW/cm2 Bandwidth973cm-1 Intensity0.125 GW/cm2 Bandwidth803cm-1 4S 4P1/2 4P3/2 4S Probability 4P3/2 4P1/2 Frequency (cm-1) Time (fs) Time (fs) Complete & Selective　⇒ Transition time ~1/ΔE= 570 fs

46. Selective Excitation • Selection utilizing interference • Two Pulse SequencePerturbative (Small Probability)Can be faster than the uncertainty limit • Quadratic ChirpingNon-perturbative (Large Probability)Complete & Selective Excitation (Cannot be faster then the uncertainty limit)More than 3 state  Possible!

47. Spectroscopy Utilizing Quantum Control Spectroscopy for short-lived resonance states

48. Quantum Control Result (Given) System (Known) External Field (to be searched for) Inverse problem

49. Feedback quantum control (Experiment) System (Unknown) Result Feedback External Field Field design without the knowledge of system

50. Feedback spectroscopy System information is obtained from the optimal external field External Field Result A new type of inverse problem System Uniqueness?