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 NCTUColloquium

@Information Building CS247Sep 23, 2010

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

Quantum Control

System(Known)

External Field(to be searched for)

Result(Given)

Inverse problem

IntroductionAtoms, Molecules, and Laser

Energy and Time Scales of MoleculeEnergy

10eV

1eV

0.1eV

0.01eV

0.001eV

10-17s

10-16s

10-15s

10-14s

10-13s

10-12s0.0001eV

Time

Electronic

Vibrational

Rotational

History of Laser Intensity

History of Laser Pulse Duration

Electronic

Vibrational

Rotational

Laser Pulse

50 50

1 .0

0 .5

0 .5

1 .0

Long-Pulsed Laser

0 .0 0 .5 1 .0 1 .5 2 .0

2

4

6

8

10

12

50 50

1 .0

0 .5

0 .5

1 .0

0 .0 0 .5 1 .0 1 .5 2 .0

2

4

6

8

10

12

50 50

1 .0

0 .5

0 .5

1 .0

Short-Pulsed Laser CW Laser

0 .0 0 .5 1 .0 1 .5 2 .0

2

4

6

8

10

12

Time Domain

Frequency Domain

Broad Band

Narrow BandMonochromatic

Lasers for Control

• Coherence Interference

• High Intensity Faster Transition

• Short Pulse Broad Bandwidth

• Broad Bandwidth Various Resonance

Pulse Shaper

i j tj

j

f t c e

LCD(Transmittance & Refractive indexes are controlled.)

Fourier Expansion

Control of the Fourier coefficients

Re : Transmittance

Im : Refractive Index

j

j

c

c

How to design the pulse?

Shaped Pulsed Laser

cos F t E t t dt

Time dependent Intensity

Time dependent Frequency

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 PulseComplicated Shaping

Simple Shaped Pulse Chirping

(time dependent frequency)

FT Pulse

Time

Positive Chirp Negative Chirp

Quadratic ChirpLinear Chirp

Concave Down Concave Up

0.0

0.5

1.0

1.5

2.0

2 4 6 8 10

12・ 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)

H t T H t

di t H t t

dt

exp jt i t t

t T t

Time periodic Hamiltonian

Schrodinger Equation

Wavefunction (the Floquet theorem)

: Quasi-Energyj

t : Quasi-Statej

Quasi State (Time Independent Problems)

t T t expjj n

n

t in t

2

T

1 1

2 2

3 3

4 4

0 0

2 0

0 3

0 0 4

j j

j j

jj j

j j

H V

V H V

V H V

V H

0 00

1 1exp

2

TV H t i t dt F

T

0, cosH r t F t F t t

If

　 Energy diagram of adiabatic energy levels

0E

0E 1E

1E

0E

1E

Avoided Crossing

Frequency of laser

Intensity E

0 01

10 1

/ 2

/ 2

E FH

F E

Adiabatic ApproximationExample: Stark Effect

Electric Field

Ene

rgy

Leve

ls

( ) ( )

0, exp ,

t ja aj j

Er t i d r t

( ) ( ), , ,a aj j jH r t r t E t r t

Nonadiabatic Transition Transition due to breakdown of

the adiabatic approximation

Landau-Zener model(Frequency Sweep)

1 1

2 2

1

2

c t t V c tdi

c t V t c tdt

2

expLZ

Vp

a

4 2 2 4

4

2

2

4

adiabatic

nonadiabatic

LZp

1 LZp

1

2 2E t V

t at

Rose-Zener Type(Intensity Sweep)

1

1 exp 2RZp

exp1exp2RZ

A tH

A t

2 2E V t

expV t A t

Quadratic Crossing Model(Teranishi – Nakamura Model)

BtAt

J. Chem. Phys. 107, 1904

21 1

22 2

c t c tt Vdi

c t c tdt V t

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 　　　　　　　　　　　

dete

ctorA B

Multiple double slits

　 Bifurcation at slits

　 Interference can be controlled by A, B

A A BB

Teranishi and Nakamura, Phys. Rev. Lett. 81, 2032

Required number of transitionB

ifu

rcat

ion

pro

bab

ilit

y

The Number of transition (n)

2

1 cos /

2

n

22

2

sin / 24 1 sin

sin

nP p p

cos 1 cos 2 cosp p

0 2 12

0 2

Transition probability after n transition

Necessary bifurcation probability for complete inversion after n transitions

For p = 0.5, one period of oscillationis sufficient

One Period of Oscillation

Bifurcation Probability 0.5

Phase Difference ~ 2

p

E t

Landau-Zener model(Frequency Sweep)

1 1

2 2

c t t V c tdi

c t V t c tdt

2

expLZ

Vp

a

4 2 2 4

4

2

2

4

adiabatic

1

2 22E t V

t at

Sufficient Intensity is required to satisfy 0.5p

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)

1

1 exp 2RZp

exp

expRZ

A tH

A t

2 22E V t

expV t A t

Sufficient Intensity is required to satisfy 2E t dt 0.5 if 0 (Resonance)p

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

0.00.5

1.01.5

2.0

2 4 6 8 10 12

Collaboration with Dr. Yokoyama’s experimental group at JAEA

Basic Idea

The Ground State

The Excited State

0 /iE te

1 /iE te

0E

1E

1st pulse2nd 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 5/23/2

Interference

1st pulse 2nd pulse

760

– 78

0 nm

1/2

3/2

1/2

6S

7D

6P

+/

(a)

(c)

(b)

Fluorescence

(86fs) (86fs)

Delay

Spin orbit splitting ΔE ＝ 21cm-1

Uncertainty limit Δt=1/ΔE ＝８００ｆｓ

2 pulse interference

Experimental Facility

RF generator

Ti:Sapphire oscillator

TeO2

AOPDF

Internal trigger

Computer

PMT-II

PMT-I

MCS

Preamplifier

Filter-I

Filter-II

Cell

2~ 0.5 GW / cm

~ 770 nm

~ 86fs

I

T

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1

7D(3/2)-400fs (exp)7D(5/2)-400fs (exp)7D(3/2)-400fs (calc)7D(5/2)-400fs (calc)

phase difference/

Delay: 　 400 ｆｓ（ Experiment and Theory ）

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

R-400fs (exp)R-400fs (calc)

phase difference/

Normalized transition probability Branching ratio

Delay 　 300fs（ Exp. & Theory ）

0

0.2

0.4

0.6

0.8

1

1.2

0 0.2 0.4 0.6 0.8 1

7D(3/2)-300fs (exp)7D(5/2)-300fs (exp)7D(3/2)-300fs (calc)7D(5/2)-300fs (calc)

phase difference/

0

0.2

0.4

0.6

0.8

1

0 0.2 0.4 0.6 0.8 1

R-300fs (exp)R-300fs (calc)

phase difference/

Normalized transition probability Branching ratio

Selection is possible even when t <Δt 　 = 　 1/ΔE 　＝８００ｆｓ　

Breakdown of the Selectivity(Theoretical simulation)

0

1 10-5

2 10-5

3 10-5

4 10-5

5 10-5

6 10-5

7 10-5

0 0.2 0.4 0.6 0.8 1

7D(3/2)-400fs-0.1G (calc)

7D(5/2)-400fs-0.1G (calc)

phase difference/

0

0.05

0.1

0.15

0.2

0.25

0 0.2 0.4 0.6 0.8 1

7D(3/2)-400fs-5G (calc)

7D(5/2)-400fs-5G (calc)

phase difference/

Peak intensity: 　 0.1GW/cm2 Peak intensity: 5.0GW/cm2

Large transition probability bad selectivity （ nonlinear effect ）

Tra

nsiti

on p

roba

bilit

y

Tra

nsiti

on p

roba

bilit

y

Basic Idea (Perturbative)

p1

p2

p2

|0>1

0

0 p2

p1

p1

1st pulse 2nd pulse

Breakdown of the selectivity

p1

1-p1-p2

p2

p2(1-p2)

|0>1

0

0 (1-p1-p2) p2

p1(1-p1)

(1-p1-p2) p1

Selection 　→　 p1, p2 <<1 　（ Linearity ）

1st pulse 2nd pulse

p2 p2

p1 p1

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

p1

1-p1

(1-p1)(1-p2)

(1-p1)p2 (1-p1)p2(1-p2)

(1-p1)(1-p2) p2

1

2

t

E0+

0

0.002

0.004

0.006

0.008

0.01

1.29 104 1.295 104 1.3 104 1.305 104 1.31 104

4P(1/2)4P(3/2)

励起

確率

B(cm-1)

Both selective

Small ProbabilityPerturbative region 　 (1 MW/cm2)

4P(1/2)4P(3/2)

B

Selective Excitaion of K atom by Quadratic chirping(Simulation ）

4P1/2

4P3/2

0

0.2

0.4

0.6

0.8

1

1.29 10 4 1.295 10 4 1.3 10 4 1.305 10 4 1.31 10 4

4P(1/2)4P(3/2)

B(cm -1)

High Intensity 　 (0.125 GW/cm2)

Complete destructionIncomplete destruction

Upper level (Red) Lower level (Black)

4P(1/2)4P(3/2)

B

4P1/2

4P3/2

Complete & selective excitation of K atom

1.22 10 4

1.24 10 4

1.26 10 4

1.28 10 4

1.3 10 4

1.32 10 4

1.34 10 4

0 100 200 300 400 500 600

0

0.2

0.4

0.6

0.8

1

1.28 10 4

1.3 10 4

1.32 10 4

1.34 10 4

1.36 10 4

1.38 10 4

0 100 200 300 400 500 600

0

0.2

0.4

0.6

0.8

1

Time (fs) Time (fs)

4S → 　 4P1/2 Excitation 4S → 　 4P3/2 Excitation

Intensity 　 0.36 GW/cm2Bandwidth 　　　　 973 　 cm-1

Intensity 　 0.125 GW/cm2Bandwidth 　　　　 803 　 cm-1

Pro

babi

lity

Fre

quen

cy (

cm-1)

4P1/2

4P1/2 4S4S 4P3/2

4P3/2

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 ChirpingNon-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)

ExternalField

Result

Field design withoutthe knowledge of system

Feedback

Feedback spectroscopy

System

ExternalFieldResult

System information is obtained from the optimal external field

A new type of inverse problem

Uniqueness?

0

0.5

1

1.5

2

9800 9900 1 104 1.01 104 1.02 104

State Selective Spectroscopyfor 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)

iE2

Selective excitation to decaying state

Breakdown by the decay

p1

Δτ

p2

01

0

0 p2

p1

1st pulse 2nd pulse

222 pee i

111 pee i

Incomplete interference due to the decaying process

How to achieve the selection• Modify the intensity of the 2nd pulse

eIIr

1

2 Reduce the intensity（ condition for the intensity ratio ）

(2 1)i n Destructive interference（ condition for the phas

e ）

Selection is possible even for the decaying states

Intensity ratio 　 →　 Lifetime 　（ Width ）Phase difference 　 →　 Energy （ Position ）

Feedback ?

System(Unknown)

ExternalField

Result

Feedback

It is impossible to know the selection ratio!

4 pulse irradiation (Suppressing both two states)

Δτ1

δ １

ｒ１

1st pulse 2nd pulse 3rd pulse 4th pulse

Δτ １

δ １

ｒ１

Δτ ２

δ ２

ｒ２

Suppressing both statesCombination 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

0

0.5

1

1.5

2

9800 9900 1 104 1.01 104 1.02 104

]cm[2710021

]cm[25100001-

2

-11

iE

iE

fs330

fs300

2

1

• Optimizing Parameters 　 →　

Feedback Scheme

2121 ,,, rr

.　　　

Intensity ratio

Phase differences

Parameters to achieve zero total excitation

Feedback Control

#　of　#　of　looploop

　　Re(Re(EE11)) Im(Im(EE11)) Re(Re(EE22)) Im(Im(EE22)) PP11//PP22 PP22//PP11

11 9999.59999.5 28.838528.8385 10018.110018.1 31.176731.1767 0.1020.102 0.0780.078

22 　　10002.710002.7

25.328525.3285 10016.710016.7 27.497727.4977 0.05650.0565 0.03250.0325

33 9999.59999.5 25.034825.0348 10019.610019.6 26.973126.9731 　　0.002380.00238

　　0.003150.00315

44 　　10000.10000.11

25.03425.03488

10020.10020.77

26.97326.97311

0.00040.00047171

0.00030.00030101

ExactExact 　　1000010000 2525 　　1002110021 2727 00 00

Spectroscopic data and the selection ratioobtained after nth optimization

Results

• State selective spectra

• Rapid convergence

• State selective pumping

• Powerful method for the study of ultrafast phenomenon

9800 9900 1 104 1.01 104 1.02 104

[cm-1]

1st loop

2nd loop

3rd loop

4th loop

Feedback spectroscopy

System

ExternalFieldResult

Pulse train of 4 pulsesZero total excitation probability

Positions and widthsSelective 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

LaserMolecule

Input

Output

Teranishi et. al. J. Chem. Phys. 124 114110 Hosaka et. al. Phys. Rev. Lett. 104 180501

Nature 465 (2010)

Quantum control and

new computer

Ultrafast Fourier Transformationwith Molecule & Pulsed Laser

J. Chem. Phys. 124 114110 Phys. Rev. Lett. 104 180501 (2010)

X state

B state

gate pulse

I ２

Quantum Fourier transformation

11

10

01

00

11

10

01

00

ii

ii

11

1111

11

1111

1000

000

0010

0001

i

Operating twice = CNOT

Unitary transformation　 (Diagonalization)

Molecular basis

Computational basis

4

3

2

4

3

2

v

v

v

v

v

v

v

v

4

3

2

4

3

2

v

v

v

v

v

v

v

v

11

10

01

00

11

10

01

00

Experimental Setup

18 19 20 21 22

Reference pulse

Gaussian pulses

Input generation

Superposition of Gaussian pulses

iii

ii EerE i

02exp

Reference pulse

Adjusting the parameters

iir ,

Desired inputs

Narrow Gaussian||

Accurate inputLong 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 TransitionsTeranishi and Nakamura, J. Chem. Phys. 107, 1904Teranishi and Nakamura, Phys. Rev. Lett. 81, 2032

• Selective ExcitationYokoyama, Teranishi, et. al. J. Chem. Phys. 120, 9446Yokoyama, Yamada, Teranishi et. al. Phys. Rev. A72 063404

• Quantum Control SpectroscopyTeranishi, Phys. Rev. Lett. 97 053001

• Computation by shaped laserTeranishi, Ohtsuki, et. al. J. Chem. Phys. 124 14110Hosaka, et. al. Phys. Rev. Lett. 104 180501

Application of Quantum Control

• Quantum Control SpectroscopyVerification Experiment By NO2 Dissociation (Collaboration with Dr. Hosaka @TIT)

• Isotope SeparationIsotope 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)

Intrinsic Excitation by Intense Laser

SpectrometerIntense Laser CH4 Photon

PhotonPhoton

Proportional to I10

(10 photon process?)

Exp

Simulation

Molecular Spectra in Quantum Solid

Line widthRovibrational Spectra (v4 mode)