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)