Coherent controlof ultracold molecules

Christiane P. Koch

Institut fur Theoretische Physik, Freie Universitat Berlin

Basics on Quantum Control Summer School, CargeseAugust 21, 2008

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

introduction 1:ultracold molecules

what means ultracold?

ultracold: T ≤ 100µK a single quantum state(or very few)

Bose-

Einstein

condensation

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

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)

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

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

introduction 2:coherent control

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)〉?

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

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

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

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

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

control in time domainTannor & Rice

spatially localizedwavepackets

manipulation of phase, variation of ∆t

Baumert, Grosser, Thalweiser, Gerber, PRL 67, 3753 (1991)

control in time domainTannor & Rice

spatially localizedwavepackets

manipulation of phase, variation of ∆t

Baumert, Grosser, Thalweiser, Gerber, PRL 67, 3753 (1991)

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

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

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

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

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

example 1:

making ultracold moleculeswith laser light

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

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)

1 can we find an optical analogon of magneticFeshbach resonances?

2 what about coherent photoassociation?

3 how do we get ’true’ molecules?

optical Feshbach resonances

d

2 atoms at the same site of an optical lattice

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)

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

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

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

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

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

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

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?

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

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

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!

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!

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!

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!

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

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

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

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

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

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

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)

’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)

’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)

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

why is making molecules possible?

0 50 100 150 200 250internuclear distance [ units of Bohr radii ]

1 / R3 E

b = 1 cm

-1

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

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)

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)

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)

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)

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)

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

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

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

example 2:

laser induced resonance

or

shaping the potentialenergy surfaces

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

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)

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)

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)

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)

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)

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)

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)

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)

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

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?

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?

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

+

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

+

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

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

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

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

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

field-induced resonant couplingin collaboration with R. Moszynski

ener

gy

internuclear distance R

pump

dump

coupling

wavepacket motion

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

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

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

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

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 ]

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

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

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+

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+

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

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

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

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

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

example 3:

quantum informationwith ultracold molecules

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)

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)

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)

coherent control: shielding

cancel dipole-dipole interaction with external field control in

rotational Hamiltonian

coherent control: shielding

cancel dipole-dipole interaction with external field control in

rotational Hamiltonian

coherent control: shielding

cancel dipole-dipole interaction with external field control in

rotational Hamiltonian

example 4:

vibrational cooling ofultracold molecules

vibrational cooling – theory

vibrational cooling – theory

vibrational cooling – theory

vibrational cooling – theory

the cooling target

dark ground state

maximum excitation

solutions

vibrational cooling – theory

the cooling target

dark ground state

maximum excitation

solutions

vibrational cooling – theory

the cooling target

dark ground state

maximum excitation

solutions

vibrational cooling – theory

the cooling target

dark ground state

maximum excitation

solutions

cooling = maintaining adark ground state

vibrational cooling – exp.

vibrational cooling – exp.

a crude way of maintaing a dark ground state . . .

vibrational cooling – exp.

. . . but it works!

summary

pump-dump photoassociation: initial state &timescales

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

summary

pump-dump photoassociation: initial state &timescales

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

summary

pump-dump photoassociation: initial state &timescales

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

summary

pump-dump photoassociation: initial state &timescales

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

summary

pump-dump photoassociation: initial state &timescales

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