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 Building CS247 Sep 23, 2010

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

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

Introduction Atoms, Molecules, and Laser

Energy and Time Scales of Molecule Energy 10eV 1eV 0.1eV 0.01eV 0.001eV s s s s s s eV Time Electronic Vibrational Rotational

History of Laser Intensity

History of Laser Pulse Duration Electronic Vibrational Rotational

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

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

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

Shaped Pulsed Laser Time dependent Intensity Time dependent Frequency

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

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

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

General Conditions for Complete Transition among Two States

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

Quasi State (Time Independent Problems) If

Energy diagram of adiabatic energy levels Avoided Crossing Frequency of laser

Adiabatic Approximation Example: Stark Effect Electric Field Energy Levels Nonadiabatic Transition Transition due to breakdown of the adiabatic approximation

Landau-Zener model (Frequency Sweep) adiabatic nonadiabatic

Rose-Zener Type (Intensity Sweep)

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

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

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

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

One Period of Oscillation

Landau-Zener model (Frequency Sweep) adiabatic Frequency

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

Isomarization of Trymethylenimine Numerically Obtained pulse Our control Scheme

Rose-Zener Type (Intensity Sweep)

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)

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

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

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

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

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

Delay 300fs （ Exp. & Theory ） Normalized transition probability Branching ratio Selection is possible even when t <Δt = 1/ΔE ＝８００ｆｓ

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

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

Breakdown of the selectivity p1p1 1-p 1 -p 2 p2p2 p 2 (1-p 2 )   |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

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

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 + 

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

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

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 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

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!

Spectroscopy Utilizing Quantum Control Spectroscopy for short-lived resonance states

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

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

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

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

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

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

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 ）

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

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

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

Model

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

# 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/P Exact Spectroscopic data and the selection ratio obtained after nth optimization

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

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

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

Computation by Molecule with Shaped Laser Molecule Laser Molecule Input Output

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

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

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

Experimental Setup

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

Result Fourier Transformation within 145 fs

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

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. A Quantum Control Spectroscopy Teranishi, Phys. Rev. Lett Computation by shaped laser Teranishi, Ohtsuki, et. al. J. Chem. Phys Hosaka, et. al. Phys. Rev. Lett

Application of Quantum Control Quantum Control Spectroscopy Verification Experiment By NO2 Dissociation (Collaboration with Dr. Isotope Separation Isotope sensitive transition of Cs2 (Collaboration with Dr. Spin Cross Polarization (Collaboration with Prof. Quantum Conveyance by a Moving potential (Collaboration with Prof. S. Tokyo)

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

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