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Coherent controlof ultracold molecules
Christiane P. Koch
Institut fur Theoretische Physik, Freie Universitat Berlin
Basics on Quantum Control Summer School, CargeseAugust 21, 2008
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overview
introduction 1:ultracold molecules
introduction 2:coherent control
4 examples:
making ultracoldmolecules with laser light
shaping the potentialenergy surfaces
quantum informationwith ultracold molecules
cooling molecules
summary
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introduction 1:ultracold molecules
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what means ultracold?
ultracold: T ≤ 100µK a single quantum state(or very few)
Bose-
Einstein
condensation
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why ultracold molecules
internal degrees of freedom, permant dipole moment
interesting applications:
molecular Bose-Einstein condensatequantum computer
I cold , little decoherence
precision measurements & tests offundamental symmetries
I cold , long observation times
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why ultracold molecules
internal degrees of freedom, permant dipole moment
interesting applications:
example: precisionmeasurements
I ultracold Sr2 moleculesI time dependence ofµ = me/mp
∆µ
µ=
∆ν
ν
ν transition frequencies
Zelevinsky, Kotochigova, Ye,PRL 100, 043201 (2008)
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why ultracold molecules
internal degrees of freedom, permant dipole moment
interesting applications:
molecular Bose-Einstein condensatequantum computer
I cold , little decoherence
precision measurements & test offundamental symmetries
I cold , long observation times
ultracold collisions / reactionsI cold , tunneling & resonances
coherent control
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why ultracold molecules
internal degrees of freedom, permant dipole moment
interesting applications:
molecular Bose-Einstein condensatequantum computer
I cold , little decoherence
precision measurements & test offundamental symmetries
I cold , long observation times
ultracold collisions / reactionsI cold , tunneling & resonances
coherent control
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introduction 2:coherent control
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what means coherent control?
quantum mechanics , probabilistic,deterministic theory
|ψ(t = 0)〉 Schrodinger equation |ψ(t > 0)〉
For |ψ(t = 0)〉 given,
what dynamics (, what H)
guarantees a certain |ψ(t > 0)〉?
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principle of coherent control
QM: matter ∼ waves superposition principle
Ψs =1√2φs(rA) +
1√2φs(rB)
Ψa =1√2φs(rA) − 1√
2φs(rB)
+1 = e2πi − 1 = eπi
manipulation of relative phases of different partialwavepackets control of interferences
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principle of coherent control
QM: matter ∼ waves superposition principle
Ψs =1√2φs(rA) +
1√2φs(rB)
Ψa =1√2φs(rA) − 1√
2φs(rB)
+1 = e2πi − 1 = eπi
manipulation of relative phases of different partialwavepackets control of interferences
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principle of coherent control
QM: matter ∼ waves superposition principle
Ψs =1√2φs(rA) +
1√2φs(rB)
Ψa =1√2φs(rA) − 1√
2φs(rB)
+1 = e2πi − 1 = eπi
manipulation of relative phases of different partialwavepackets control of interferences
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what is a wavepacket?
|Ψ(t)〉 =∑
i
ci e− i
~Ei t︸ ︷︷ ︸ |ϕi〉
time-dependent phases
coordinate representation:
〈R |Ψ(t)〉 = Ψ(R , t) =∑
i
cie− i
~Ei tϕi(R)
wavepacket dynamicsjava applets
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wavepacket dynamics
50 100 150 200 250
1.17
1.18
1.19
1.2x 10
4
Pot
entia
l ene
rgy
[ cm
−1 ]
Intramolecular distance [ a0 ]
t = 250.0 ps
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control in time domainTannor & Rice
spatially localizedwavepackets
manipulation of phase, variation of ∆t
Baumert, Grosser, Thalweiser, Gerber, PRL 67, 3753 (1991)
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control in time domainTannor & Rice
spatially localizedwavepackets
manipulation of phase, variation of ∆t
Baumert, Grosser, Thalweiser, Gerber, PRL 67, 3753 (1991)
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coherent control
the classic examples
Brumer & Shapiro
Ei
ω1
Ef
ω1 ω3
ω1
Shapiro & Brumer: Principles ofQuantum Control of MolecularProcesses. Wiley 2003
Tannor & Rice
Brixner & Gerber
Physikal. Blatter, April 2001
STIRAP
Bergmann, Theuer, Shore
Rev. Mod. Phys. 70, 1003 (1998)
all realized experimentally in the 1990s
but there’s more to control: optimization
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coherent control
the classic examples
Brumer & Shapiro
Ei
ω1
Ef
ω1 ω3
ω1
Shapiro & Brumer: Principles ofQuantum Control of MolecularProcesses. Wiley 2003
Tannor & Rice
Brixner & Gerber
Physikal. Blatter, April 2001
STIRAP
Bergmann, Theuer, Shore
Rev. Mod. Phys. 70, 1003 (1998)
all realized experimentally in the 1990s
but there’s more to control: optimization
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optimal control
theory: inversion problem
find the ’potential’, which
generates the desired dynamics!
Ψ(t = t0)
Schrodinger equation
Ψ(t = t0 +T )
5 10 15 20 25 30 35internuclear distance [ a0 ]
5 6 7internuclear distance [ a0 ]
CPK, Palao, Kosloff, Masnou-Seeuws,
Phys. Rev. A 70, 013402 (2004)
experiment:feedback-loops
pulse shaper
experiment
algorithm
but: black-boxoptimization of oftencomplex systems
average over dofthermal average
ultracold atoms & molecules
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optimal control
theory: inversion problem
find the ’potential’, which
generates the desired dynamics!
Ψ(t = t0)
Schrodinger equation
Ψ(t = t0 +T )
5 10 15 20 25 30 35internuclear distance [ a0 ]
5 6 7internuclear distance [ a0 ]
CPK, Palao, Kosloff, Masnou-Seeuws,
Phys. Rev. A 70, 013402 (2004)
experiment:feedback-loops
pulse shaper
experiment
algorithm
but: black-boxoptimization of oftencomplex systems
average over dofthermal average
ultracold atoms & molecules
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optimal control
theory: inversion problem
find the ’potential’, which
generates the desired dynamics!
Ψ(t = t0)
Schrodinger equation
Ψ(t = t0 +T )
5 10 15 20 25 30 35internuclear distance [ a0 ]
5 6 7internuclear distance [ a0 ]
CPK, Palao, Kosloff, Masnou-Seeuws,
Phys. Rev. A 70, 013402 (2004)
experiment:feedback-loops
pulse shaper
experiment
algorithm
but: black-boxoptimization of oftencomplex systems
average over dofthermal average
ultracold atoms & molecules
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example 1:
making ultracold moleculeswith laser light
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formation of ultracold moleculeslaser cooling does not work for molecules (to date)!
alternative cooling methods T & 30 mK
laser & evaporative cooling of atoms, then
photoassociation
10 20 30 40Interatomic distance R (a0)
−400
−200
0
200
11000
11200
11400
11600
11800
X1Σg+
λPA
Ene
rgy
(cm
−1)
Cs(6s)+Cs(6s)
1u
a3Σu+
0u+
0g−
Cs(6s)+Cs(6p3/2)
(i)(ii)(iii)
1g
Feshbach resonances
T ∼ 10 nK . . . 100 µK
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formation of ultracold molecules
photoassociation
general (opticaltransitions)
first µK molecules
but spontaneous emission↔ coherence of BEC
Feshbach resonancesfirst molecules fromatomic BEC
first molecular BEC
but not generally availablenot generally feasible
high vibrational
excitation, J ∼> 0
5 10 15 20 25 30 35internuclear distance [ a0 ]
Na2, X 1Σ+g
v = 62
(vlast = 65)
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1 can we find an optical analogon of magneticFeshbach resonances?
2 what about coherent photoassociation?
3 how do we get ’true’ molecules?
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optical Feshbach resonances
d
2 atoms at the same site of an optical lattice
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optical Feshbach resonancesCPK, Masnou-Seeuws, Kosloff, Phys. Rev. Lett. 94, 193001 (2005)
0 200 400 600 800internuclear distance R [ Å ]
0
0.002
| ϕ (R
) |2
I = 0
first trap level (ground state potential)
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optical Feshbach resonancesCPK, Masnou-Seeuws, Kosloff, Phys. Rev. Lett. 94, 193001 (2005)
0 100 200 300 400R [ Å ]
0
0.01
| ϕ (R
) |2
I = 3 kW/cm2
I = 5 kW/cm2
I = 8 kW/cm2
∆L = 0.425 cm-1
0 200 400 600 800internuclear distance R [ Å ]
0
0.002
| ϕ (R
) |2
I = 0
0 100 200 300 400R [ Å ]
0
0.001
| ϕ (R
) |2
first trap level (ground state potential)ground state part of the
(1)
field−dressed wave functions
excited state part of the field−dressed wave function
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optical Feshbach resonancesCPK, Masnou-Seeuws, Kosloff, Phys. Rev. Lett. 94, 193001 (2005)
0 100 200 300 400R [ Å ]
0
0.01
| ϕ (R
) |2
I = 3 kW/cm2
I = 5 kW/cm2
I = 8 kW/cm2
∆L = 0.425 cm-1
0 200 400 600 800internuclear distance R [ Å ]
0
0.002
| ϕ (R
) |2
I = 0
0 100 200 300 400R [ Å ]
0
0.001
| ϕ (R
) |2
decay by spontaneous emission
first trap level (ground state potential)ground state part of the
(1)
field−dressed wave functions
excited state part of the field−dressed wave function
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optical Feshbach resonancesCPK, Masnou-Seeuws, Kosloff, Phys. Rev. Lett. 94, 193001 (2005)
0 100 200 300 400R [ Å ]
0
0.01
| ϕ (R
) |2
I = 3 kW/cm2
I = 5 kW/cm2
I = 8 kW/cm2
∆L = 0.425 cm-1
0 100R [ Å ]
0
0.01
| ϕ (R
) |2
I = 0
0 200 400 600 800internuclear distance R [ Å ]
0
0.002
| ϕ (R
) |2
I = 0
0 100 200 300 400R [ Å ]
0
0.001
| ϕ (R
) |2
decay by spontaneous emission
first trap level (ground state potential)ground state part of thelast level
stable molecule
(2) (1)
field−dressed wave functions
excited state part of the field−dressed wave function
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Feshbach resonance due to intensity
when crossing theresonance, the lowest trapstate / continuum statebecomes a bound state
0 2 4 6 8 10 12Laser intensity [kW/cm2]
-3×10-4
-2×10-4
-1×10-4
0
Ene
rgy
[cm
-1]
0 1000 2000 3000 4000 5000internuclear distance R [a0]
|Ψ(R
)|2
I = 0, lowest trap stateI = 1 kW/cm2
I = 2 kW/cm2 (just above resonance)
I = 3 kW/cm2 (just below resonance)
I = 4 kW/cm2
∆L = -4.225 cm-1
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Feshbach resonance due to intensity
when crossing theresonance, the lowest trapstate / continuum statebecomes a bound state
0 2 4 6 8 10 12Laser intensity [kW/cm2]
-3×10-4
-2×10-4
-1×10-4
0
Ene
rgy
[cm
-1]
0 1000 2000 3000 4000 5000internuclear distance R [a0]
|Ψ(R
)|2
I = 0, lowest trap stateI = 1 kW/cm2
I = 2 kW/cm2 (just above resonance)
I = 3 kW/cm2 (just below resonance)
I = 4 kW/cm2
∆L = -4.225 cm-1
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Feshbach resonance due to intensity
when crossing theresonance, the lowest trapstate / continuum statebecomes a bound state
0 2 4 6 8 10 12Laser intensity [kW/cm2]
-3×10-4
-2×10-4
-1×10-4
0
Ene
rgy
[cm
-1]
0 200 400 600 800 1000internuclear distance R [a0]
|Ψ(R
)|2
I = 0, last bound level
I = 11 kW/cm2
I = 8 kW/cm2
I = 6 kW/cm2
I = 4 kW/cm2
∆L = -4.225 cm-1
0 1000 2000 3000 4000 5000internuclear distance R [a0]
|Ψ(R
)|2
I = 0, lowest trap stateI = 1 kW/cm2
I = 2 kW/cm2 (just above resonance)
I = 3 kW/cm2 (just below resonance)
I = 4 kW/cm2
∆L = -4.225 cm-1
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optical Feshbach resonances
0 100 200 300 400R [ Å ]
0
0.01
| ϕ (R
) |2
I = 3 kW/cm2
I = 5 kW/cm2
I = 8 kW/cm2
∆L = 0.425 cm-1
0 100R [ Å ]
0
0.01
| ϕ (R
) |2
I = 0
0 200 400 600 800internuclear distance R [ Å ]
0
0.002
| ϕ (R
) |2
I = 0
0 100 200 300 400R [ Å ]
0
0.001
| ϕ (R
) |2
decay by spontaneous emission
first trap level (ground state potential)ground state part of thelast level
stable molecule
(2) (1)
field−dressed wave functions
excited state part of the field−dressed wave function
can we switch on the laser adiabaticallywhile avoiding spontaneous emission?
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gain vs loss
projection :〈φbare|ϕdressed〉.= sudden switchoff of fieldgain
510
1520
2530
3540
−4.34−4.32
−4.3−4.28
−4.26−4.24
−4.22−4.2
0
0.2
0.4
0.6
Detuning [ cm−1 ]Intensity [ kW/cm2 ]
Pro
ject
ion
on la
st b
ound
sta
te
excited state partPexc = 〈e|ϕdressed〉.
= lifetime of |ϕdressed〉loss
510
1520
2530
3540
−4.34−4.32
−4.3−4.28
−4.26−4.24
−4.22−4.2
0.01
0.02
0.03
0.04
0.05
Detuning [ cm−1 ]Intensity [ kW/cm2 ]
Exc
ited
stat
e po
pula
tion
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gain vs loss
projection :〈φbare|ϕdressed〉.= sudden switchoff of fieldgain
510
1520
2530
3540
−4.34−4.32
−4.3−4.28
−4.26−4.24
−4.22−4.2
0
0.2
0.4
0.6
Detuning [ cm−1 ]Intensity [ kW/cm2 ]
Pro
ject
ion
on la
st b
ound
sta
te
excited state partPexc = 〈e|ϕdressed〉.
= lifetime of |ϕdressed〉loss
510
1520
2530
3540
−4.34−4.32
−4.3−4.28
−4.26−4.24
−4.22−4.2
0.01
0.02
0.03
0.04
0.05
Detuning [ cm−1 ]Intensity [ kW/cm2 ]
Exc
ited
stat
e po
pula
tion
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timescalesconstraint of adiabaticity
T Tad =~
E groundtrap
νtrap = 5 kHz,
E groundtrap ≈ 1.7 · 10−4 cm−1
Tad ≈ 3000 nsνtrap = 250 kHz,
E groundtrap ≈ 1.3 · 10−3 cm−1
Tad ≈ 45 ns
constraint of spont. emission
T Tspont =τatom√2Pdressed
exc
i.e. gain a factor 100 w.r.t.τatom ≈ 30 ns by choosingthe adiabatic path right!
Tspont ≈ 3000 ns
There is a time window allowing the adiabatic formation of
molecules via an optical Feshbach resonance while avoiding
spontaneous emission for sufficiently tight traps!
![Page 39: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/39.jpg)
timescalesconstraint of adiabaticity
T Tad =~
E groundtrap
νtrap = 5 kHz,
E groundtrap ≈ 1.7 · 10−4 cm−1
Tad ≈ 3000 nsνtrap = 250 kHz,
E groundtrap ≈ 1.3 · 10−3 cm−1
Tad ≈ 45 ns
constraint of spont. emission
T Tspont =τatom√2Pdressed
exc
i.e. gain a factor 100 w.r.t.τatom ≈ 30 ns by choosingthe adiabatic path right!
Tspont ≈ 3000 ns
There is a time window allowing the adiabatic formation of
molecules via an optical Feshbach resonance while avoiding
spontaneous emission for sufficiently tight traps!
![Page 40: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/40.jpg)
timescalesconstraint of adiabaticity
T Tad =~
E groundtrap
νtrap = 5 kHz,
E groundtrap ≈ 1.7 · 10−4 cm−1
Tad ≈ 3000 nsνtrap = 250 kHz,
E groundtrap ≈ 1.3 · 10−3 cm−1
Tad ≈ 45 ns
constraint of spont. emission
T Tspont =τatom√2Pdressed
exc
i.e. gain a factor 100 w.r.t.τatom ≈ 30 ns by choosingthe adiabatic path right!
Tspont ≈ 3000 ns
There is a time window allowing the adiabatic formation of
molecules via an optical Feshbach resonance while avoiding
spontaneous emission for sufficiently tight traps!
![Page 41: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/41.jpg)
timescalesconstraint of adiabaticity
T Tad =~
E groundtrap
νtrap = 5 kHz,
E groundtrap ≈ 1.7 · 10−4 cm−1
Tad ≈ 3000 nsνtrap = 250 kHz,
E groundtrap ≈ 1.3 · 10−3 cm−1
Tad ≈ 45 ns
constraint of spont. emission
T Tspont =τatom√2Pdressed
exc
i.e. gain a factor 100 w.r.t.τatom ≈ 30 ns by choosingthe adiabatic path right!
Tspont ≈ 3000 ns
There is a time window allowing the adiabatic formation of
molecules via an optical Feshbach resonance while avoiding
spontaneous emission for sufficiently tight traps!
![Page 42: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/42.jpg)
time-dep. simulations: ν = 250 kHzramps of field amplitude & frequency (final I = 8 kW/cm2 )
0
1
2
E(t
) [ 1
05 V/m
]
0 20 40 60 80 100 120 140 160time [ ns ]
0
0.2
0.4
0.6
0.8
1
| < Ψ
(t) |
ϕvba
re >
|2
-4.32-4.28-4.24
∆L [ cm
-1 ]
0 20 40 60 80 100 120 140 160time [ ns ]
0
0.2
0.4
0.6
0.8
1
Population
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time-dep. simulations: ν = 250 kHzramps of field amplitude & frequency (final I = 8 kW/cm2 )
0
1
2
E(t
) [ 1
05 V/m
]
0 20 40 60 80 100 120 140 160time [ ns ]
0
0.2
0.4
0.6
0.8
1
| < Ψ
(t) |
ϕvba
re >
|2
-4.32-4.28-4.24
∆L [ cm
-1 ]
0 20 40 60 80 100 120 140 160time [ ns ]
0
0.2
0.4
0.6
0.8
1
Population
total population
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time-dep. simulations: ν = 250 kHzramps of field amplitude & frequency (final I = 8 kW/cm2 )
0
1
2
E(t
) [ 1
05 V/m
]
0 20 40 60 80 100 120 140 160time [ ns ]
0
0.2
0.4
0.6
0.8
1
| < Ψ
(t) |
ϕvba
re >
|2
first trap state
-4.32-4.28-4.24
∆L [ cm
-1 ]
0 20 40 60 80 100 120 140 160time [ ns ]
0
0.2
0.4
0.6
0.8
1
Population
total population
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time-dep. simulations: ν = 250 kHz
ramps of field amplitude & frequency (final I = 8 kW/cm2 )
0
1
2
E(t
) [ 1
05 V/m
]
0 20 40 60 80 100 120 140 160time [ ns ]
0
0.2
0.4
0.6
0.8
1
| < Ψ
(t) |
ϕvba
re >
|2
first trap statesecond trap statethird trap statefourth trap state
-4.32-4.28-4.24
∆L [ cm
-1 ]
0 20 40 60 80 100 120 140 160time [ ns ]
0
0.2
0.4
0.6
0.8
1
Population
total population
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time-dep. simulations: ν = 250 kHz
ramps of field amplitude & frequency (final I = 8 kW/cm2 )
0
1
2
E(t
) [ 1
05 V/m
]
0 20 40 60 80 100 120 140 160time [ ns ]
0
0.2
0.4
0.6
0.8
1
| < Ψ
(t) |
ϕvba
re >
|2
last bound levelfirst trap statesecond trap statethird trap statefourth trap state
-4.32-4.28-4.24
∆L [ cm
-1 ]
0 20 40 60 80 100 120 140 160time [ ns ]
0
0.2
0.4
0.6
0.8
1
Population
total population
![Page 47: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/47.jpg)
coherent photoassociation
atoms in a MOT thermal ensemble
0 50 100 150 200 250 300 350 400internuclear distance [ a
0 ]
0
5×10-13
1×10-12
ther
mal
den
sity
ρT
,box
[ a
0-3 ]
50 µK
0 4000 8000 12000 160000
5×10-13
1×10-12
PA is difficult
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cold thermal ensemblecold collisions: s-wave
0 100 200 300
0 2000 4000 6000 8000 10000internuclear distance [ Å ]
T ≈ 50 µKT ≈ 80 µK
CPK, Kosloff, Luc-Koenig, Masnou-Seeuws, Crubellier, J Phys B 39, S1017 (2006)
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’pump’-’dump’ photoassociation
making molecules with photoassociation:cw vs short pulses
10 20 30 40Interatomic distance R (a0)
−400
−200
0
200
11000
11200
11400
11600
11800
X1Σg+
λPA
Ene
rgy
(cm
−1)
Cs(6s)+Cs(6s)
1u
a3Σu+
0u+
0g−
Cs(6s)+Cs(6p3/2)
(i)(ii)(iii)
1g
Masnou-Seeuws & Pillet, Adv. At. Mol. Opt. Phys. 47, 53 (2001)
spontaneous emission
time-reversal symmetry
11700
11800
11900
Ene
rgy
[ cm
-1 ]
20 40 60 80 100 120internuclear distance [ units of Bohr radius a
0 ]
-200
-100
0
100
tP + 135 ps
tP + 40 ps
tP + 250 ps
t = 0
tP + 40 ps
CPK, Luc-Koenig, Masnou-Seeuws, PRA 73, 033408 (2006)
![Page 50: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/50.jpg)
’pump’-’dump’ photoassociation
making molecules with photoassociation:cw vs short pulses
10 20 30 40Interatomic distance R (a0)
−400
−200
0
200
11000
11200
11400
11600
11800
X1Σg+
λPA
Ene
rgy
(cm
−1)
Cs(6s)+Cs(6s)
1u
a3Σu+
0u+
0g−
Cs(6s)+Cs(6p3/2)
(i)(ii)(iii)
1g
Masnou-Seeuws & Pillet, Adv. At. Mol. Opt. Phys. 47, 53 (2001)
spontaneous emission
time-reversal symmetry
11700
11800
11900
Ene
rgy
[ cm
-1 ]
20 40 60 80 100 120internuclear distance [ units of Bohr radius a
0 ]
-200
-100
0
100
tP + 135 ps
tP + 40 ps
tP + 250 ps
t = 0
tP + 40 ps
CPK, Luc-Koenig, Masnou-Seeuws, PRA 73, 033408 (2006)
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why is making molecules possible?
0 1000 2000 3000 4000 5000 6000 7000internuclear distance [ units of Bohr radii ]
1 / R3 E
b = 6 x 10
-5 cm
-1
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why is making molecules possible?
0 50 100 150 200 250internuclear distance [ units of Bohr radii ]
1 / R3 E
b = 1 cm
-1
![Page 53: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/53.jpg)
why is making molecules possible?
0 20 40 60 80 100 120 140 160internuclear distance [ units of Bohr radii ]
1 / R3 E
b = 4 cm
-1
![Page 54: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/54.jpg)
coherent photoassociation?
what is differentfrom previouspump-probeschemes?
initial state
timescales
y bandwidths
11700
11800
11900
Ene
rgy
[ cm
-1 ]
20 40 60 80 100 120internuclear distance [ units of Bohr radius a
0 ]
-200
-100
0
100
tP + 135 ps
tP + 40 ps
tP + 250 ps
t = 0
tP + 40 ps
CPK, Luc-Koenig, Masnou-Seeuws, PRA 73, 033408 (2006)
![Page 55: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/55.jpg)
coherent photoassociation?
what is differentfrom previouspump-probeschemes?
initial state
timescales
y bandwidths
11700
11800
11900
Ene
rgy
[ cm
-1 ]
20 40 60 80 100 120internuclear distance [ units of Bohr radius a
0 ]
-200
-100
0
100
tP + 135 ps
tP + 40 ps
tP + 250 ps
t = 0
tP + 40 ps
CPK, Luc-Koenig, Masnou-Seeuws, PRA 73, 033408 (2006)
![Page 56: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/56.jpg)
choice of pulses
role of laser detuning and spectral bandwidth
projection of Ψexc(R, tfinal) auf Vibrationsniveaus von He(R), 87Rb2
0 5 10 15 20 25binding energy [ cm-1 ]
0
5×10-6
proj
ectio
n
τP = 7 psτP = 5 ps
∆P = 5.97 cm-1
∆P = 8.57 cm-1
∆P = 22.1 cm-1
narrow band pulses
CPK, Kosloff, Masnou-Seeuws, PRA 73, 043409 (2006)
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choice of pulses
role of laser detuning and spectral bandwidth
projection of Ψexc(R, tfinal) auf Vibrationsniveaus von He(R), 87Rb2
0 5 10 15 20 25binding energy [ cm
-1 ]
0
5×10-6
proj
ectio
n
τP = 7 ps
τP = 5 ps
∆P = 5.97 cm
-1
∆P = 8.57 cm
-1
∆P = 22.1 cm
-1
narrow band pulsesCPK, Kosloff, Masnou-Seeuws, PRA 73, 043409 (2006)
![Page 58: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/58.jpg)
choice of pulses
role of laser detuning, spectral bandwidth & intensity
ground state wavefunction after the pulse
0
5×10-6
τP = 7 ps
τP = 5 ps
0
5×10-6
| Ψ (
R;t)
|2 [ a
rbitr
ary
units
]
20 40 60 80 100 120internuclear distance R [ units of Bohr radii a
0 ]
0
5×10-6
∆P = 5.97 cm
-1
∆P = 8.57 cm
-1
∆P = 22.1 cm
-1
CPK, Kosloff, Masnou-Seeuws, PRA 73, 043409 (2006)
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photoassociation dynamics
50 100 150 200 250
1.17
1.18
1.19
1.2x 10
4
Pot
entia
l ene
rgy
[ cm
−1 ]
Intramolecular distance [ a0 ]
t = 250.0 ps
0100
200300
400 010
2030
4050
0
0.5
1
1.5
2
x 10−5
Ground state levelTime [ ps ]
Ove
rlap time-dependent
Franck-Condon factorspump-dump-delay
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open questions: PA with pulses
10 20 30
internuclear distance R [ a0 ]
-1000
0
ener
gy [
cm
-1 ]
R transfer ?
bandwidth ?
first experiments
Salzmann et al., PRL 100, 233003 (2008)
et al. = . . . Fabian Weise . . .
11700
11800
11900
Ene
rgy
[ cm
-1 ]
20 40 60 80 100 120internuclear distance [ units of Bohr radius a
0 ]
-200
-100
0
100
tP + 135 ps
tP + 40 ps
t = 0
tP + 40 ps
v = 14
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open questions: PA with pulses
10 20 30
internuclear distance R [ a0 ]
-1000
0
ener
gy [
cm
-1 ]
R transfer ?
bandwidth ?
first experiments
Salzmann et al., PRL 100, 233003 (2008)
et al. = . . . Fabian Weise . . .
11700
11800
11900
Ene
rgy
[ cm
-1 ]
20 40 60 80 100 120internuclear distance [ units of Bohr radius a
0 ]
-200
-100
0
100
tP + 135 ps
tP + 40 ps
t = 0
tP + 40 ps
v = 14
![Page 62: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/62.jpg)
example 2:
laser induced resonance
or
shaping the potentialenergy surfaces
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is the pump-dump scheme general?the perfect example: Cs2 0−g (P3/2)
1. excitation (pump)
20 40 60 80 100 120internuclear distance [ a
0 ]
11700
11800
11900
Ene
rgy
[ cm
-1 ]
at long range : 1/R3
(small ∆P)
2. stabilization (dump)
20 40 60 80 100 120internuclear distance [ a
0 ]
11700
11800
11900
Ene
rgy
[ cm
-1 ]
at short range :−1/R3 (∆D < 0)
efficiency of process
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two possible dump mechanismssoftly repulsive wall
12800
12850
20 40 60 80 100internuclear distance [ a
0 ]
-200
-100
0ener
gy [
cm
-1 ]
0g
-
1g
a3Σ
u
+
resonant coupling
see also: Dion, Drag, Dulieu, Laburthe Tolra, Masnou-Seeuws, Pillet, PRL 86, 2253 (2001)
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two possible dump mechanismssoftly repulsive wall
12800
12850
20 40 60 80 100internuclear distance [ a
0 ]
-200
-100
0ener
gy [
cm
-1 ]
0g
-
1g
a3Σ
u
+
resonant coupling
5000
10000
20 40internuclear distance [ a
0 ]
-4000
-2000
0ener
gy [
cm
-1 ]
0u
+
X1Σ
g
+
see also: Dion, Drag, Dulieu, Laburthe Tolra, Masnou-Seeuws, Pillet, PRL 86, 2253 (2001)
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resonant vs non-res. SO coupling
10 20 30 40 50internuclear distance [ a
0 ]
6000
8000
10000
12000
ener
gy [
cm
-1 ]
0u
+
b3Π
u
A1Σ
u
10 20 30 40 50internuclear distance [ a
0 ]
10000
11000
12000
13000
energy [ cm-1 ]
1g
3Πg
1Πg
3Σg
potentials and dipole moments : M. Aymar & O. Dulieu (Laboratoire Aime Cotton, Orsay)
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resonant coupling
-9.0
7
-13.
7
-35 -30 -25 -20 -15 -10 -5 0binding energy [ cm
-1 ]
0
2×10-3
4×10-3
6×10-3
rota
tiona
l con
stan
t [ a
.u. ]
0
1×10-1
2×10-1
110 112 114 116 118 120 122ground state vibrational level v’’
0
1×10-1
2×10-1
Fran
ck-C
ondo
n fa
ctor
Ebind
exc = 9.07 cm
-1
Ebind
exc = 13.7 cm
-1
comparison theory-experiment
Pechkis, Wang, Eyler, Gould, Stwalley, CPK, PRA 76, 022504 (2007)
![Page 68: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/68.jpg)
resonant coupling
-9.0
7
-13.
7
-35 -30 -25 -20 -15 -10 -5 0binding energy [ cm
-1 ]
0
2×10-3
4×10-3
6×10-3
rota
tiona
l con
stan
t [ a
.u. ]
0
1×10-1
2×10-1
110 112 114 116 118 120 122ground state vibrational level v’’
0
1×10-1
2×10-1
Fran
ck-C
ondo
n fa
ctor
Ebind
exc = 9.07 cm
-1
Ebind
exc = 13.7 cm
-1
comparison theory-experiment
Pechkis, Wang, Eyler, Gould, Stwalley, CPK, PRA 76, 022504 (2007)
![Page 69: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/69.jpg)
stabilization to the ground state?
time-dependent FC factors
0+u
200400
600 −15−10
−5
5
10
15
x 10−6
Energy [ cm−1 ]Time [ ps ]
Proj
ectio
n
1g
100200
300400 −6
−4−2
2468
x 10−7
Energy [ cm−1 ]Time [ ps ]Pr
ojec
tion
∆P = 4.1 cm−1
CPK, Kosloff, Masnou-Seeuws, PRA 73, 043409 (2006)
![Page 70: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/70.jpg)
dynamics with resonant SO coupling
10000
15000
3Πu(5s+5p)
t = −24.0 ps
10000
15000
Pot
entia
l ene
rgy
[ cm
−1 ]
1Σu(5s+5p)
0 25 50 75 100 125 150−4000
0
4000
Intramolecular distance [ a0 ]
1Σg(5s+5s)
![Page 71: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/71.jpg)
dynamics w/o resonant SO coupling
12000
13000
14000
3Σg(5s+5p)
t = −24.0 ps
12000
13000
14000
Pot
entia
l ene
rgy
[ cm
−1 ]
1Πg(5s+5p)
12000
13000
14000
3Πg(5s+5p)
0 25 50 75 100 125 150−200
0
200
Intramolecular distance [ a0 ]
3Σu(5s+5s)
![Page 72: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/72.jpg)
stabilization to the ground statewith resonant spin-orbit coupling
0 20 40 60 80 100 120 140pulse energy [ nJ ]
0
0.2
0.4
0.6po
pula
tion
Pg
Pbound
10 20 30 40internuclear distance R [ a
0 ]
0
0.02
0.04
0.06
| Ψg (
R;t fi
nal)
|2 [ a
rb. u
. ]
-20 -15 -10 -5 0
energy [ cm-1
]
0
0.1
0.2
0.3
0.4
0.5
proj
ectio
n8.5 nJ
53 nJ8.5 nJ
![Page 73: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/73.jpg)
route to v = 0 (generic case) : OCTstrong fields and / or many Raman transitions
0
0.2
0.4
0.6
0.8
1
Popu
latio
n
0 500 1000 1500 2000time [fs]
0
0.2
0.4
0.6
0.8
1ν = 62
ν = 0
excited state
ground state
example: Na2, vinitial = 62 (vlast = 65)
potentials: Tiemann group PRA (2000), Z Phys D (1996)
required pulse energy ∼ 4mJ
Koch, Palao, Kosloff, Masnou-Seeuws, PRA 70, 013402 (2004)
see also: Pe’er, Shapiro, Stowe, Shapiro, Ye, PRL 98, 113004 (2006)
can we do better?
![Page 74: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/74.jpg)
route to v = 0 (generic case) : OCTstrong fields and / or many Raman transitions
0
0.2
0.4
0.6
0.8
1
Popu
latio
n
0 500 1000 1500 2000time [fs]
0
0.2
0.4
0.6
0.8
1ν = 62
ν = 0
excited state
ground state
example: Na2, vinitial = 62 (vlast = 65)
potentials: Tiemann group PRA (2000), Z Phys D (1996)
required pulse energy ∼ 4mJ
Koch, Palao, Kosloff, Masnou-Seeuws, PRA 70, 013402 (2004)
see also: Pe’er, Shapiro, Stowe, Shapiro, Ye, PRL 98, 113004 (2006)
can we do better?
![Page 75: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/75.jpg)
field-induced resonant couplingin collaboration with R. Moszynski
5000
10000
15000
20000
25000
ener
gy [
cm-1
]
5 10 15 20 25 30internuclear distance R [ Bohr radii ]
-1000
-500
0
500
50 100 150
Ca2 X1Σg
+
Ca2 B1Σu
+
![Page 76: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/76.jpg)
field-induced resonant couplingin collaboration with R. Moszynski
5000
10000
15000
20000
25000
ener
gy [
cm-1
]
5 10 15 20 25 30internuclear distance R [ Bohr radii ]
-1000
-500
0
500
50 100 150
Ca2 X1Σg
+
Ca2 (1)1Πg
Ca2 B1Σu
+
![Page 77: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/77.jpg)
field-induced resonant couplingin collaboration with R. Moszynski
5000
10000
15000
20000
25000
ener
gy [
cm-1
]
5 10 15 20 25 30internuclear distance R [ Bohr radii ]
-1000
-500
0
500
50 100 150
coupling
![Page 78: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/78.jpg)
field-induced resonant couplingin collaboration with R. Moszynski
5000
10000
15000
20000
25000
ener
gy [
cm-1
]
5 10 15 20 25 30internuclear distance R [ Bohr radii ]
-1000
-500
0
500
50 100 150
pump
coupling
![Page 79: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/79.jpg)
field-induced resonant couplingin collaboration with R. Moszynski
5000
10000
15000
20000
25000
ener
gy [
cm-1
]
5 10 15 20 25 30internuclear distance R [ Bohr radii ]
-1000
-500
0
500
50 100 150
pump
coupling
wavepacket motion
![Page 80: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/80.jpg)
field-induced resonant couplingin collaboration with R. Moszynski
5000
10000
15000
20000
25000
ener
gy [
cm-1
]
5 10 15 20 25 30internuclear distance R [ Bohr radii ]
-1000
-500
0
500
50 100 150
pump
dump
coupling
wavepacket motion
![Page 81: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/81.jpg)
field-induced resonant couplingin collaboration with R. Moszynski
5000
10000
15000
20000
25000e
ne
rgy [
cm
-1 ]
5 10 15 20 25 30
internuclear distance R [ Bohr radii ]
-1000-500
0500
50 100 150
pump
dump
coupling
wavepacket motion
![Page 82: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/82.jpg)
field-induced resonant couplingin collaboration with R. Moszynski
ener
gy
internuclear distance R
pump
dump
coupling
wavepacket motion
![Page 83: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/83.jpg)
when is the coupling resonant?
20 40 60internuclear distance [ a
0 ]
12400
12800
13200
ener
gy
[ c
m-1
]
0u
+( A
1Σu
+ )
0u
+( b
3Πu )
Ebind
= 9.07 cm-1
H =
(T + V1(R) W
W T + V2(R)
)
spin-orbit coupling:
W = VSO(R) −→ 237.6 cm−1
for Rb
field-induced coupling:
W = ~Ω =1
2µ(R) · E (t)
if µ(R) ∼ 1 at.u.then E0 ∼ 1.0× 107 V/cm
I ∼ 1.4× 1011 W/cm2
![Page 84: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/84.jpg)
when is the coupling resonant?
20 40 60internuclear distance [ a
0 ]
12400
12800
13200
ener
gy
[ c
m-1
]
0u
+( A
1Σu
+ )
0u
+( b
3Πu )
Ebind
= 9.07 cm-1
H =
(T + V1(R) W
W T + V2(R)
)
spin-orbit coupling:
W = VSO(R) −→ 237.6 cm−1
for Rb
field-induced coupling:
W = ~Ω =1
2µ(R) · E (t)
if µ(R) ∼ 1 at.u.then E0 ∼ 1.0× 107 V/cm
I ∼ 1.4× 1011 W/cm2
![Page 85: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/85.jpg)
res. coupling & photoassociation
coupling needs to be comparable to levelspacings
-5000 -4000 -3000 -2000 -1000 0
binding energy [ cm-1
]
1×10-6
1×10-4
1×10-2
1×100
1×102
leve
l sp
ac
ing
[ c
m-1
]
-30 -20 -10 0
1×10-6
1×10-4
1×10-2
1×100
Ca2 B
1Σu
+
level spacings drop to ∼ 1 cm−1 in range of PA detunings
![Page 86: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/86.jpg)
res. coupling & photoassociation
coupling needs to be comparable to levelspacings
-5000 -4000 -3000 -2000 -1000 0
binding energy [ cm-1
]
1×10-6
1×10-4
1×10-2
1×100
1×102
leve
l sp
ac
ing
[ c
m-1
]
-30 -20 -10 0
1×10-6
1×10-4
1×10-2
1×100
Ca2 B
1Σu
+
level spacings drop to ∼ 1 cm−1 in range of PA detunings
![Page 87: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/87.jpg)
minimal model for Ca2
HCa2 =
0BBBBBBBBBB@
HX1Σ+
g (1S+1S)µ12(R) · E1(t) 0 0 0
µ12(R) · E∗1 (t) HB1Σ+
u (1P+1S)µ23(R) · E2(t) 0 0
0 µ23(R) · E∗2 (t) H(1)1Πg (1D+1S)
ξ(R) 0
0 0 ξ(R) H(1)3Σ+
g (3P+1S)ζ(R)
0 0 0 ζ(R) H(1)3Πg (3P+1S)
1CCCCCCCCCCA
10 20internuclear distance [ Bohr radii ]
0
5000
10000
15000
20000
25000
ener
gy
[ c
m-1
]
1 1S+
1S
1P+
1S
1D+
1S
3P+
1S
23
4
50
1
2
3
4
dip
ole [ cm
-1 ]
µ12
µ23
WSO
34
WSO
45
10 200
10
20
30
SO
cou
plin
g [ cm
-1 ]
![Page 88: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/88.jpg)
choice of coupling laserI = 3.5× 108 W/cm2 −3.2× 109 W/cm2
ω2 = 11351 cm−1 (881 nm) y target X1Σ+g level: v ′′ = 1
-10 0 10time [ ns ]
0
25
50
E(t) [ M
V/
m ]
coupling
du
mp
pu
mp
ener
gy
internuclear distance R
pump
dump
coupling
wavepacket motion
10 ns pulse isconstant on
timescale of 100 ps
feasible & robust
CPK & Moszynski, submitted
![Page 89: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/89.jpg)
choice of coupling laserI = 3.5× 108 W/cm2 −3.2× 109 W/cm2
ω2 = 11351 cm−1 (881 nm) y target X1Σ+g level: v ′′ = 1
-10 0 10time [ ns ]
0
25
50
E(t) [ M
V/
m ]
coupling
du
mp
pu
mp
ener
gy
internuclear distance R
pump
dump
coupling
wavepacket motion
10 ns pulse isconstant on
timescale of 100 ps
feasible & robustCPK & Moszynski, submitted
![Page 90: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/90.jpg)
dynamics w/ induced res. coupling
photoassociation (pump) pulse
0 20 40 60 80 100 120 140 1600
5
x 10−5
B1Σu+
0 20 40 60 80 100 120 140 1600
1
2
x 10−4
(1)1Πg
0 20 40 60 80 100 120 140 1600
5
x 10−5
Intramolecular distance [ a0 ]
X1Σg+
![Page 91: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/91.jpg)
dynamics w/ induced res. coupling
stabilization (dump) pulse
0 20 40 60 80 100 120 140 1600
0.05
0.1B1Σ
u+
t = 93.0 ps
0 20 40 60 80 100 120 140 1600
0.1
0.2(1)1Π
g
0 20 40 60 80 100 120 140 1600
1
2x 10
−3
Intramolecular distance [ a0 ]
X1Σg+
![Page 92: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/92.jpg)
how many molecules?
10 100 1000 10000pulse energy [ nJ ]
1×10-6
1×10-4
1×10-2
tran
sfer
pro
bab
ilit
y
Ic = 5.6 x 10
9 W/cm
2
10 100 1000 10000pulse energy [ nJ ]
1×10-6
1×10-5
1×10-4
1×10-3
1×10-2
tran
sfer
pro
bab
ilit
y
Ic = 3.2 x 10
9 W/cm
2
Ic = 1.4 x 10
9 W/cm
2
typical MOT conditions: Nmol = 12.5, 10 kHz rep.rate: 1 mol/ms
accumulate molecules over many pump-dump cycles
employ dissipation to achieve
unidirectionality
collisional decay to v = 0 within 1 ms if
ρ ∼ 10−13 cm−3
can be improved: flux enhancement & speed up of decay
![Page 93: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/93.jpg)
how many molecules?
10 100 1000 10000pulse energy [ nJ ]
1×10-6
1×10-4
1×10-2
tran
sfer
pro
bab
ilit
y
Ic = 5.6 x 10
9 W/cm
2
10 100 1000 10000pulse energy [ nJ ]
1×10-6
1×10-5
1×10-4
1×10-3
1×10-2
tran
sfer
pro
bab
ilit
y
Ic = 3.2 x 10
9 W/cm
2
Ic = 1.4 x 10
9 W/cm
2
typical MOT conditions: Nmol = 12.5, 10 kHz rep.rate: 1 mol/ms
accumulate molecules over many pump-dump cycles
employ dissipation to achieve
unidirectionality
collisional decay to v = 0 within 1 ms if
ρ ∼ 10−13 cm−3
can be improved: flux enhancement & speed up of decay
![Page 94: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/94.jpg)
how many molecules?
10 100 1000 10000pulse energy [ nJ ]
1×10-6
1×10-4
1×10-2
tran
sfer
pro
bab
ilit
y
Ic = 5.6 x 10
9 W/cm
2
10 100 1000 10000pulse energy [ nJ ]
1×10-6
1×10-5
1×10-4
1×10-3
1×10-2
tran
sfer
pro
bab
ilit
y
Ic = 3.2 x 10
9 W/cm
2
Ic = 1.4 x 10
9 W/cm
2
typical MOT conditions: Nmol = 12.5, 10 kHz rep.rate: 1 mol/ms
accumulate molecules over many pump-dump cycles
employ dissipation to achieve
unidirectionality
collisional decay to v = 0 within 1 ms if
ρ ∼ 10−13 cm−3
can be improved: flux enhancement & speed up of decay
![Page 95: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/95.jpg)
field-induced resonant coupling’shaping’ the potentials
ener
gy
internuclear distance R
pump
dump
coupling
wavepacket motion
-10 0 10time [ ns ]
0
25
50coupling
du
mp
pu
mpa b
c
qualitative & substantial change of dynamics
implementing resonance phenomenon of coldmolecules via coherent control
![Page 96: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/96.jpg)
acknowledgements
people
work on alkalis
Francoise Masnou-Seeuws & ElianeLuc-Koenig, Orsay (France)
Ronnie Kosloff, Jerusalem (Israel)
work on Ca2
Robert Moszynski, Warsaw (Poland)
funding
Deutsche Forschungsgemeinschaft
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example 3:
quantum informationwith ultracold molecules
![Page 98: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/98.jpg)
quantum information= squaring the circle
particles with no
interaction
little decoherence
controlled
interaction
two-qubit gates
scalability
polar molecules in periodic arrangementspolar molecules = dipole-dipole interaction
in a static electric field
DeMille, PRL 88, 067901 (2002)
electrostatic trap on a chip
Cote, Nat. Phys. 2, 583 (2006)
![Page 99: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/99.jpg)
quantum information= squaring the circle
particles with no
interaction
little decoherence
controlled
interaction
two-qubit gates
scalability
polar molecules in periodic arrangementspolar molecules = dipole-dipole interaction
in a static electric field
DeMille, PRL 88, 067901 (2002)
electrostatic trap on a chip
Cote, Nat. Phys. 2, 583 (2006)
![Page 100: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/100.jpg)
quantum information= squaring the circle
particles with no
interaction
little decoherence
controlled
interaction
two-qubit gates
scalability
polar molecules in periodic arrangementspolar molecules = dipole-dipole interaction
in a static electric field
DeMille, PRL 88, 067901 (2002)
electrostatic trap on a chip
Cote, Nat. Phys. 2, 583 (2006)
![Page 101: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/101.jpg)
coherent control: shielding
cancel dipole-dipole interaction with external field control in
rotational Hamiltonian
![Page 102: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/102.jpg)
coherent control: shielding
cancel dipole-dipole interaction with external field control in
rotational Hamiltonian
![Page 103: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/103.jpg)
coherent control: shielding
cancel dipole-dipole interaction with external field control in
rotational Hamiltonian
![Page 104: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/104.jpg)
example 4:
vibrational cooling ofultracold molecules
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vibrational cooling – theory
![Page 106: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/106.jpg)
vibrational cooling – theory
![Page 107: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/107.jpg)
vibrational cooling – theory
![Page 108: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/108.jpg)
vibrational cooling – theory
the cooling target
dark ground state
maximum excitation
solutions
![Page 109: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/109.jpg)
vibrational cooling – theory
the cooling target
dark ground state
maximum excitation
solutions
![Page 110: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/110.jpg)
vibrational cooling – theory
the cooling target
dark ground state
maximum excitation
solutions
![Page 111: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/111.jpg)
vibrational cooling – theory
the cooling target
dark ground state
maximum excitation
solutions
cooling = maintaining adark ground state
![Page 112: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/112.jpg)
vibrational cooling – exp.
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vibrational cooling – exp.
a crude way of maintaing a dark ground state . . .
![Page 114: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/114.jpg)
vibrational cooling – exp.
. . . but it works!
![Page 115: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/115.jpg)
summary
pump-dump photoassociation: initial state ×cales
shaping the potentials 1: mimic resonantcoupling with an external field
shaping the potentials 2: shield moleculesfrom each other by manipulation with ac or dcelectric fields
vibrational cooling: maintain a dark targetstate
ultracold & ultrafast = pretty cool
![Page 116: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/116.jpg)
summary
pump-dump photoassociation: initial state ×cales
shaping the potentials 1: mimic resonantcoupling with an external field
shaping the potentials 2: shield moleculesfrom each other by manipulation with ac or dcelectric fields
vibrational cooling: maintain a dark targetstate
ultracold & ultrafast = pretty cool
![Page 117: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/117.jpg)
summary
pump-dump photoassociation: initial state ×cales
shaping the potentials 1: mimic resonantcoupling with an external field
shaping the potentials 2: shield moleculesfrom each other by manipulation with ac or dcelectric fields
vibrational cooling: maintain a dark targetstate
ultracold & ultrafast = pretty cool
![Page 118: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/118.jpg)
summary
pump-dump photoassociation: initial state ×cales
shaping the potentials 1: mimic resonantcoupling with an external field
shaping the potentials 2: shield moleculesfrom each other by manipulation with ac or dcelectric fields
vibrational cooling: maintain a dark targetstate
ultracold & ultrafast = pretty cool
![Page 119: Coherent control of ultracold molecules [1ex]Brumer & Shapiro E i w 1 E f w 1 w 3 w 1 Shapiro & Brumer: Principles of Quantum Control of Molecular Processes. Wiley 2003 Tannor & Rice](https://reader035.vdocument.in/reader035/viewer/2022071509/612a20f211c01c7b7355b202/html5/thumbnails/119.jpg)
summary
pump-dump photoassociation: initial state ×cales
shaping the potentials 1: mimic resonantcoupling with an external field
shaping the potentials 2: shield moleculesfrom each other by manipulation with ac or dcelectric fields
vibrational cooling: maintain a dark targetstate
ultracold & ultrafast = pretty cool