Ultracold Molecules

Introductory course onUltracold quantum gases

July 10-12, Innsbruck

Steven Knoop

Why ultracold molecules ?• Ultracold chemistry

– Control with external fields

• High resolution spectroscopy– Example: time variation me/mp

• Molecular BEC– “Superchemistry”– Dipolar quantum gases

• Quantum processing

F+H2(ν=0,j=0)->HF(ν’)+H

1 mK 1 K

s

p

Atoms: simple level structure

S1/2

2P1/2

2P3/2

Atoms: simple level structure

S1/2

2P1/2

2P3/2

Closed opticaltransitionmakes lasercooling work !

alkali, earth-alkali,metastable noble gases,few exotic species

Atoms: simple level structure

From atoms to molecules

rU(r)

+ rot. structure+ hyperfine structure

many vib.levels

many vib.levels

rU(r)

many decay channels:laser cooling fails

From atoms to molecules

slowing and cooling of molecules

Buffer gas coolingJ. Doyle et al.

molecules withlarge magnetic dipole moment

Stark decelerationG. Meijer et al.

polar molecules

slowing and cooling of molecules

Buffer gas coolingJ. Doyle et al.

molecules withlarge magnetic dipole moment

Stark decelerationG. Meijer et al.

polar molecules

mK…K

Starting from ultracold atoms:

free atoms

laser 1

laser 2

s+s

s+p

controlled photo-associationtwo-color

photo-associationone-color

laser

s+s

s+p

low molecule numbers, low densities

photo-association

molecules @ few nKmolecular quantum gas

atomic quantum gas

Herbig et al., Science 301, 1510 (2003)

Feshbach molecules

Starting from ultracold atoms:Feshbach association

Ultracold Feshbach molecules

• Ultracold atomic gases • Feshbach resonances

• Very basic two-body physics, molecular structure• Feshbach resonance (molecular view)• Feshbach association• Properties of Feshbach molecules• Fermion composed Feshbach molecules• Towards ultracold ground-state molecules NEW

Two-body potential

r

U(r)incident or scattering channel

r

Attractive potential: van der Waals force ~ -1/r6

Repulsive potential: Coulomb force

some molecular physics

Vibrational states

Rotational states

1+11+22+2

Hyperfine states

~ 100 THz

~ 3300 cm-1 (wavenumbers) / ~ 0.4 eV

1+11+22+2

~ 1 GHz

Zeeman effect

F=2

F=1

Magnetic field

Energy

Hyperfine splitting

mF

2

1

0

-1

-2

-1

0

1

7Li, 23Na, 39K, 41K, 87Rb

(2,1)+(2,1)

mF210-1

-2

-10

1(1,1)+(1,1)

B

E

B

E

(magnetically induced)Feshbach resonance

Feshbach resonance

F=2

F=1

Feshbach resonance

two atoms

B

E

molecule

binding energy

Feshbach resonance: a closer look

avoided crossing

scat

terin

g le

ngth

B0

entrance doors into the ultracold molecular world

Adiabatic magnetic field ramp

two atoms

B

E

molecule

• Imaging: fast magnetic field backramp

• Separation: e.g. magnetic field gradient

dissociation

Adiabatic magnetic field ramp

two atoms

B

E

molecule

• Imaging: fast magnetic field backramp

• Separation: e.g. magnetic field gradient

Purification

B

E

• resonant laser light / microwave pulse

making Feshbach molecules from BECs

CsCs22

Innsbruck, Science 301, 1510 (2003)

NaNa22

MIT, PRL 91, 210402 (2003)

MPQ, PRL 92, 020406 (2004)

8787RbRb22

Properties Feshbach molecules

• single rovibrational quantum state

- highly excited vibrational state (ν=-1)

- rotationally cold s-wave (ℓ=0) even ℓ (BB)odd ℓ (FF)all ℓ (BB’,BF,FF’)

• weakly bound (kHz-MHz-GHz)

Properties Feshbach molecules• atom-molecule, molecule-molecule collisions

relaxation to lower vibrational states

Properties Feshbach molecules

MIT, PRL 92, 180402 (2003)

• atom-molecule, molecule-molecule collisions

relaxation to lower vibrational states

atom-molecule

molecule-molecule

Adiabatic magnetic field ramp

two atoms

B

E

molecule

Properties Feshbach molecules

MIT, PRL 92, 180402 (2003)

• atom-molecule, molecule-molecule collisions

relaxation to lower vibrational stateslimited lifetime

atom-molecule

molecule-molecule

Properties Feshbach molecules

MIT, PRL 92, 180402 (2003)

• atom-molecule, molecule-molecule collisions

relaxation to lower vibrational stateslimited lifetime

optical lattice

(one molecule per lattice site)

atom-molecule

molecule-molecule

E/(∆µ∆B)

a/a bg

(B-B0)/∆B

∆B

Εb

Scattering length

Binding energy

Properties Feshbach molecules

a/2Quantum halo state

66LiLi22

Halo dimers out of fermions• Pauli blocking

• atom-dimer and dimer-dimer relaxation suppressed for large a

trap depth

• forming Feshbach molecules by three-body recombination

molecular BEC gallery (2003-2004)

MIT, Ketterle et al.66LiLi22

ENS Paris, Salomon et al.

66LiLi22

Rice, Hulet et al.

66LiLi22

Innsbruck, Grimm et al.

66LiLi22

JILA, Jin et al.4040KK22

Overview Feshbach molecules

23Na2 (s-wave)

85Rb2 (s-wave)

87Rb2 (s-, d-wave)

133Cs2 (s-, d-, g-, l-wave)

85Rb87Rb (s-wave)

6Li2 (s-wave)40K2 (s-wave)

6Li2 (p-wave)40K2 (p-wave)

Fuchs et al, PRA 2008

Gaebler et al, PRL 2007

Thompson et al, PRL 2005

Dürr et al, PRL 2004Volz et al, PRA 2005

Xu et al, PRL 2003

Herbig et al, Science 2003Mark et al, PRA 2007

Regal et al, Nature 2003

Strecker et al, PRL 2003Jochim et al, PRL 2003Cubizolles et al, PRL 2003Zwierlein et al, PRL 2003

Ospelkaus et al, PRL 2006Papp & Wieman, PRL 2006

hom

onuc

lear

hete

ronu

clea

r

bosons fermions

40K87Rb (s-wave)

boson+boson boson+fermion fermion+fermion

6Li40K 7Li87Rb 6Li87Rb

In the (near) future ?

6Li23Na 87Rb133Cs41K87Rb39K87Rb

52Cr2

Recent development

Recipe

make Feshbach moleculescoherent two-photon transfer

(STIRAP)

S+P

Towards ultracold dense gas of ground-state molecules

r

S+S

X1Σg+: singlet

a3Σu-: triplet

~ 100 THz

~10 THz

ν=0, J=0

ν=-1

ν=-2

Innsbruck, Cs2, ν=155 -> ν=73 (32 THz) Danzl et al, Science (published online: 10 July 2008)

ν=155

ν=73

JILA, KRb, ν=-1 -> ν=-3 (10 GHz)Ospelkaus et al, Nature Physics (published online: 22 June 2008)

Heteronuclear molecules: towards dipolar quantum gas !

Innsbruck, Rb2, ν=-1 -> ν=-2 (0.6 GHz)Winkler et al, PRL 98, 043201 (2007)

Quantum gas of chemically bound molecules !

ν=-1

ν=-2

Innsbruck, Cs2, ν=155 -> ν=73 (32 THz) Danzl et al, Science (published online: 10 July 2008)

ν=155

ν=73

JILA, KRb, ν=-1 -> ν=-3 (10 GHz)Ospelkaus et al, Nature Physics (published online: 22 June 2008)

Heteronuclear molecules: towards dipolar quantum gas !

Innsbruck, Rb2, ν=-1 -> ν=-2 (0.6 GHz)Winkler et al, PRL 98, 043201 (2007)

triplet ν=0 ground state(6 THz)

STAY TUNED !!!triplet ν=0 ground state

(7 THz)

Quantum gas of chemically bound molecules !