1. Atomic and Molecular Processes 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 Processes in 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 System (Known) External Field (to be searched for) Result (Given) Inverse problem

4. Introduction Atoms, Molecules, and Laser

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

6. History of Laser Intensity

7. History of Laser Pulse Duration Electronic Vibrational Rotational

8. Laser Pulse Long-Pulsed LaserShort-Pulsed LaserCW Laser Time Domain Frequency Domain Broad Band Narrow Band Monochromatic

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

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

11. Shaped Pulsed Laser Time dependent Intensity Time dependent Frequency

12. 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 Shaped Pulse Complicated Shaping

13. Simple Shaped Pulse Chirping (time dependent frequency) FT Pulse Time Positive ChirpNegative Chirp Quadratic ChirpLinear Chirp Concave DownConcave Up

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

15. General Conditions for Complete Transition among Two States

16. Floquet Theory (Exact Treatment for CW Laser) Time periodic Hamiltonian Schrodinger Equation 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 Approximation Example: Stark Effect Electric Field Energy Levels Nonadiabatic Transition Transition due to breakdown of the adiabatic approximation

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

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 Periodic sweep of adiabatic parameter Bifurcation at the crossing Phase can be controlled by  A,  B Interference effects detector AA BB Multiple double slits Bifurcation at slits Interference can be controlled by  A,  B AA AA BB BB Teranishi and Nakamura, Phys. Rev. Lett. 81, 2032

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

26. One Period of Oscillation

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

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

29. Isomarization of Trymethylenimine Numerically Obtained pulse Our control Scheme

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 The Ground State The Excited State 1st pulse 2nd pulse Young’s interference

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

35. Experimental Facility RF generator Ti:Sapphire oscillator TeO 2 AOPDF Internal trigger Computer PMT-II PMT-I MCS Preamplifier Filter-I Filter-II Cell

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

37. Delay 300fs （ 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: 0.1GW/cm 2 Peak intensity: 5.0GW/cm 2 Large transition probability bad selectivity （ nonlinear effect ） Transition probability

39. Basic Idea (Perturbative) p1p1 p2p2 p2p2   |0> 1 0 0 p2p2 p1p1 p1p1 1st pulse 2nd pulse

40. Breakdown of the selectivity p1p1 1-p 1 -p 2 p2p2 p 2 (1-p 2 )   |0> 1 0 0 (1-p 1 -p 2 ) p 2 p 1 (1-p 1 ) (1-p 1 -p 2 ) p 1 Selection → p 1, p 2 <<1 （ Linearity ） 1st pulse 2nd pulse p 2 p 1

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

42. Selective Excitation by Quadratic chirping p1p1 1-p 1 (1-p 1 )(1-p 2 ) (1- p 1 )p 2 (1-p 1 )p 2 (1-p 2 ) (1-p 1 )(1-p 2 ) p 2 11 22  t E 0 + 

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

44. High Intensity (0.125 GW/cm 2 ) Complete destructionIncomplete destruction Upper level (Red) Lower level (Black) 4P(1/2) 4P(3/2) B 4P 1/2 4P 3/2

45. Complete & selective excitation of K atom Time (fs) 4S → 4P 1/2 Excitation 4S → 4P 3/2 Excitation Intensity 0.36 GW/cm2 Bandwidth 973 cm-1 Intensity 0.125 GW/cm2 Bandwidth 803 cm-1 Probability Frequency (cm -1 ) 4P 1/2 4S 4P 3/2 Complete & Selective ⇒ Transition time ~ 1/ΔE= 570 fs

46. Selective Excitation Selection utilizing interference Two Pulse Sequence Perturbative (Small Probability) Can be faster than the uncertainty limit Quadratic Chirping Non-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 System (Known) External Field (to be searched for) Result (Given) Inverse problem

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

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

51. State Selective Spectroscopy for short lived resonance states Peaks having the natural width (dotted & broken lines) Overlapping resonance Mixture of the signals (Solid line) State selected signal -> Possible? State selective excitation

52. Excited states with decaying process decay Decay process ・ Finite Lifetime ・ Energy width (Natural width) Selective excitation to decaying state

53. Breakdown by the decay p1p1 Δτ p2p2   0 1 0 0 p2 p2 p1 p1 1st pulse 2nd pulse Incomplete interference due to the decaying process

54. How to achieve the selection Modify the intensity of the 2nd pulse Reduce the intensity （ condition for the intensity ratio ） Destructive interference （ condition for the phase ） Selection is possible even for the decaying states Intensity ratio → Lifetime （ Width ） Phase difference → Energy （ Position ）

55. Feedback ? System (Unknown) External Field Result Feedback It is impossible to know the selection ratio!

56. 4 pulse irradiation (Suppressing both two states) Δτ 1 δ １ ｒ １ 1st pulse2nd pulse3rd pulse4th pulse Δτ １ δ １ ｒ １ Δτ ２ δ ２ ｒ ２ Suppressing both states Combination of pulse pairs to suppress one transition Necessary & Sufficient

57. New Spectroscopy Irradiating a train of 4 pulses Searching for a condition to achieve zero total excitation probability Providing a pulse pairs for selective excitation Providing the positions and widths of both states State selective pump probe is possible

58. Model

59. Optimizing Parameters → Feedback Scheme. Intensity ratio Phase differences Parameters to achieve zero total excitation Feedback Control

60. # of loop Re(E 1 ) Re(E 1 ) Im(E 1 ) Re(E 2 ) Im(E 2 ) P1/P2P1/P2P1/P2P1/P2 P2/P1P2/P1P2/P1P2/P1 1 9999.5 9999.528.838510018.131.1767 0.102 0.102 0.078 0.078 2 10002.7 10002.725.328510016.727.4977 0.0565 0.0565 0.0325 0.0325 3 9999.5 9999.525.034810019.626.9731 0.00238 0.00238 0.00315 0.00315 4 10000.1 10000.125.034810020.726.97310.0004710.000301 Exact 10000 10000 25 25 10021 10021 27 27 0 0 Spectroscopic data and the selection ratio obtained after nth optimization

61. Results State selective spectra Rapid convergence State selective pumping Powerful method for the study of ultrafast phenomenon 1st loop 2nd loop 3rd loop 4th loop

62. Feedback spectroscopy System External Field Result Pulse train of 4 pulsesZero total excitation probability Positions and widths Selective pumping

63. Quantum Control Spectroscopy Feedback  zero total excitation Optimal pulse train  positions and widths Selective pumping pulse pair (state selective time resolved spectra) N level system  Applicable Auger and Predissociation

64. Computation by Molecule with Shaped Laser Molecule Laser Molecule Input Output

65. Teranishi et. al. J. Chem. Phys. 124 114110 Hosaka et. al. Phys. Rev. Lett. 104 180501 Nature 465 (2010) Quantum control and new computer

66. Ultrafast Fourier Transformation with Molecule & Pulsed Laser J. Chem. Phys. 124 114110 Phys. Rev. Lett. 104 180501 (2010) X state B state gate pulse I２I２

67. Quantum Fourier transformation Operating twice = CNOT Unitary transformation (Diagonalization) Molecular basis Computational basis

68. Experimental Setup

69. Reference pulse Gaussian pulses Input generation Superposition of Gaussian pulses Reference pulse Adjusting the parameters Desired inputs Narrow Gaussian || Accurate input Long duration (many cells?) ω

70. Result Fourier Transformation within 145 fs

71. Computation with Molecule and Laser Information is stored in wavefunction Input preparation, gate operation, and output readout are done by Lasers Above Lasers are designed by quantum control theory Fourier Transform was carried out by I2 molecule within 145fs

72. Reference Complete Transitions Teranishi and Nakamura, J. Chem. Phys. 107, 1904 Teranishi and Nakamura, Phys. Rev. Lett. 81, 2032 Selective Excitation Yokoyama, Teranishi, et. al. J. Chem. Phys. 120, 9446 Yokoyama, Yamada, Teranishi et. al. Phys. Rev. A72 063404 Quantum Control Spectroscopy Teranishi, Phys. Rev. Lett. 97 053001 Computation by shaped laser Teranishi, Ohtsuki, et. al. J. Chem. Phys. 124 14110 Hosaka, et. al. Phys. Rev. Lett. 104 180501

73. Application of Quantum Control Quantum Control Spectroscopy Verification Experiment By NO2 Dissociation (Collaboration with Dr. Hosaka @TIT) Isotope Separation Isotope sensitive transition of Cs2 (Collaboration with Dr. Yokoyama @JAEA) Spin Cross Polarization (Collaboration with Prof. Nishimura @IMS) Quantum Conveyance by a Moving potential (Collaboration with Prof. S. Miyashita @U. Tokyo)

74. Intrinsic Excitation by Intense Laser Spectrometer Intense Laser CH 4 Photon Proportional to I 10 (10 photon process?) Exp Simulation

75. Molecular Spectra in Quantum Solid Line widthRovibrational Spectra (v4 mode)