Engineering and Control
of Cold Molecules
N. P. Bigelow
University of Rochester
Why Cold (Polar) Molecules ?
Why Cold (Polar) Molecules ?
Talks from:
Shlyapnikov
Pfau
Burnett
Sengstock
.
.
.
Why Cold (Polar) Molecules ?
Talks from:
Shlyapnikov
Pfau
Burnett
Sengstock
.
.
.
More Reasons Later in Talk
So what about cold molecules?
Hard to find cycling transitions
 Laser cooling of molecules is
hard if not impossible
Doyle approach - Thermalization
with cold helium gas &
magnetic trapping
Dilution Refrigerator
~mK
Paramagnetic molecules
Large samples
Meijer - time and spatially varying E fields
– decelerator –
(à la high-energy in reverse; H. Gould)
accelerate
Meijer - decelerator
(à la high-energy; H. Gould)
decelerate
Here
“Build” the molecules
from a gas of
pre-cooled atoms
via photoassociation
A Quick Review of
Photoassociation
Starting with
Homonuclears
Molecular potentials
Homonuclear
Singly excited state
Ground state
Photoassociation
Singly excited state
photon
600-1000Å
Ground state
Ground state molecule
formation?
Excited state
photon
Sp. emission
Ground state
(transition rate)
(collision rate& pair distribution)*
(excitation rate)*
(survival rate)*(process probability)*
(density2)*(volume)
These factors determine
molecular production rates
Ground state molecule formation
Poor Franck-Condon factors are discouraging
fi0
i 
photon
Sp. emission
f 
In 1997 Pierre Pillet and co-workers
startled the community
by showing the Cs2 ground-state
molecules were produced
in a conventional
optical trap
R-transfer method
Frank-Condon Matching
Why not heteronuclear molecules?
Molecular potentials
Far better Franck-Condon factors….
Singly excited state
Ground state
We might be CLOBBERED by the
pair distribution function
Rhomo/Rhetero = 950/76 ~ 13
(Rhomo/Rhetero = 950/76 ~ 1/10)2 ~ 100 !
The interaction time is also smaller by a factor of ~ 13!
Nevertheless,
several groups
built multispecies MOTs including
Rochester and
Sao Carlos and
Kasevich
Arimondo
Ingusio
Weidemuller
Windholz
DeMille
Stwalley/Gould
Wang/Buell
Ruff
others
Bose-Fermi&Isotopic: Jin,
Salamon, Ertmer, Ketterle,
Hulet, Sengstock…
Sukenik
NaCs
NaK
NaRb
RbCs
KRb
LiCs
LiNa
?
Most “reactive”
We started with Na + Cs
Search for ground state molecules - the detection pathway
20-200 J 9ns 580-589 nm 2 mm2
NaCs formation and detection
Traps
9ns
100J pulse
@
575-600nm
time (s)
-30
0
20
105
Choice of pulsed laser wavelength
575-600 nm was chosen
 To implement a resonant ionization pathway
 It has enough energy to 2-photon ionize
NaCs
 It will NOT resonantly ionize Cs
2500
Flight Zoom
Na+CsTime
Linof Scale
photons
2000
cold Na
Count
1500
Na+Cs
Cs
Na
Cold Cs
1000
Cold NaCs
Thermal
Na
500
Na2
Cs2
0
0
5
10
Time (s)
15
20
Is NaCs formed by the ionizing pulse ?
Traps
Na-push
beam
9ns
Ionizing
Pulse
time (s)
-30 -15
0
20
105
Push –beam experiment
How cold are the
molecules?
We use time-of-flight
from the interaction
zone as our probe
100
NaCs Temp
90
80
70
TNaCs ~ 260 K
0.2 m/s
(kinetic temp)
Count
60
50
40
30
20
10
0
12.6
12.8
13
13.2
Time (s)
13.4
13.6
21
100
500
1000
2000
3000
4000
4500
4980
KNaCs : The rate of formation
 We detect 500 molecules in 10,000 pulses
 Estimate ionization and detection efficiency ~ 10%
 Kinetic model : 90% of NaCs drifts out of the
trapping region between pulses.


Production rate ~ 50 Hz
d [NaCs] / dt = KNaCs [Na][Cs]

KNaCs ~ 7.4 x 10-15 cm3 s-1
Measured depth of the triplet is 137-247 cm-1
Neumann & Pauly Phys. Rev. Lett. 20, 357-359 (1968).
and J. Chem. Phys. 52, 2548-2555 (1970)
We have scanned 0 – 268 cm-1 and found strong ion signals
(includes 5% of singlet potential)
We have a mixture of singlets and triplets
C. Haimberger, J. Kleinert, npb PRA Rapid Comm.
70, 021402 (R) Aug 2004
Coherent Transfer - State Selective
Ro-vibrational ground state (lower dipole moment)
or
Single excited ro-vibrational state
Incoherent transfer results
already at Yale
The most important part
of this part of our work:
C. Haimberger
J. Kleinert
(M. Bhattacharya,
J. Shaffer & W. Chalupczak)
KRb
RbCs
KRb
40,000 molecules/sec !!
Franck-Condon Factors for hetero-pairs
based on long range (dispersion) potentials
Wang & Stwalley, J. Chem Phys.
Cold (Polar) Molecules
and Quantum Information
2500
2000
1500
Count
Na+Cs
Cs
Na
1000
500
0
0
5
10
Time (s)
15
20
Polar Molecules Allow Coupling
Enabling Quantum Information Applications
• Heteronuclear molecules
are highly polarizable
• The dipole-dipole
coupling of the molecules
can be harnessed for
quantum information
applications (see protocols
for EDMs in Quantum
Dots - e.g. Barenco, et al
PRL 82 1060)
Polar Molecules Allow Couplings
Enabling Quantum Information Applications
(based on scheme by Côté, Yellin [Lukin])
1
3
-1
Energy (10 cm )
0
-1
atoms
-2
-3
bound
molecular
states
-4
-5
-6
0
10
20
30
Internuclear Separation (Å)
40
Polar Molecules Allow Coupling
Enabling Quantum Information Applications
1
v , j   v
3
-1
Energy (10 cm )
0
-1
atoms
-2
-3
bound
molecular
states
-4
-5
-6
0
10
20

30
40
v , j   1
Internuclear Separation (Å)
v, j  0
•Start with two molecules in same state
Ai  0
Bi  0


Polar Molecules Allow Coupling
Enabling Quantum Information Applications
1
v , j   v
3
-1
Energy (10 cm )
0
-1
atoms
-2
-3
bound
molecular
states
-4
-5
-6
0
10
20

30
40
v , j   1
Internuclear Separation (Å)
v, j  0
•Start with two molecules in same state
Ai  0
Bi  0
•Use Raman pulses - create superposition
A  a0 0  a1 1


B  b0 0  b1 1
Polar Molecules Allow Coupling
Enabling Quantum Information Applications
1
v , j   v
3
-1
Energy (10 cm )
0
-1
atoms
-2
-3
bound
molecular
states
-4
-5
-6
0
10
20

30
40
v , j   1
Internuclear Separation (Å)
v, j  0
Two-molecule state:

AB  c 00 00  c11 11  c 01 01  c10 10

Polar Molecules Allow Coupling
Enabling Quantum Information Applications
Now excite  to the state 
v , j   v
(large dipole moment)

v , j   1
v, j  0


Polar Molecules Allow Coupling
Enabling Quantum Information Applications
Now excite  to the state , wait an
Interaction time  then de-excite back to 1
v , j   v
(large dipole moment)
AB  c00 00  ei c11 11  c01 01  c10 10 
v , j   1
v, j  0
Phase gate, CNOT gates etc. possible


“Dipole blockade and quantum information processing using mesoscopic
Atomic ensembles”, Lukin, Fleischhauer, Côté, Duan, Jaksch, Cirac and Zoller
PRL 87 037901
A specific qubit platform
Each atom sees a local field that
couples it to its neighbors and
permits selective addressing
E a  E ext (xa )  E int (xa )
The coupling cannot be switched off
but instead can be compensated
using echo-type refocussing
techniques of NMR.
What is needed is a source of cold
molecules
D. DeMille, PRL 88, 067901
Molecules and “Chips”
Atom Chip
+-- polarization
Y
IS~1-3 A
SiO2(250nm)
x
Z
Cu(1mm)
Ag(50nm)
Si(1mm)
IB~15-20 A
z
y
z0
B=B0y
Our 1st Generation
Atom Chips
5 mm
y
x
20 mm
10 mm
1 mm
h=1-5 m
Cross-section:
2 mm
w=250 m
Current density:
J~ 106 A/cm2
Cold Atomic
Mixtures-on-a-chip
Trap
Image of Trap
Imaging of sample
Atom chip surface
Rb-Cs
Holmes, Tscherneck,
Quinto-su and Bigelow
2nd Generation
Chips
P. Quinto-Su, M. Tschernek, M. Holmes and N. P. Bigelow, On-chip detection of
laser-cooled atoms, Optics Express, 12, 5098 (2004).
•Collaboration with Corning, Inc.
•<100 atom sensitivity
3rd Generation
Chips: Molecule Chips
WHY OPTICS and MOLECULES ON THE CHIP?
Optical Fiber
Probe/readout/control laser
WHY OPTICS and MOLECULES ON THE CHIP?
4th Generation
Chips
3 cm
Higher current
Capability
Heroines and Heroes
of this part of the work:
Michaela Tscherneck
Michael Holmes
Pedro Quinto-Su
C. Haimberger
J. Kleinert
Vortex Lattice
in a Coupled
Atom-Molecule
Condensate
(non-polar molecules)
Single component atomic BEC - Triangular vortex lattice
Ω is rotation frequency
Atom-Molecule BEC (homo-nuclear)
Mean-field model
• Three scattering constants ga, gm and gam
• Coherent constant 
• Two Gross-Pitaevskii equations
Atom-Molecule BEC – Energies
– Two key types of interaction between atoms and molecules
• Coherent coupling
• Interspecies scattering
Atom-Molecule BEC - rotating
(nv)m = 2(nv)a
Vortex density of molecular condensate is
twice that of the atomic condensate
Vortex Lattice
in a Coupled Atom-Molecule Condensate
(non-polar molecules)
Sungjong Woo
Department of Physics & Astronomy
University of Rochester
Q-Han Park
Department of Physics
Korea University
Summary
We can create cold diatomic polar molecules
We can create them and manipulate them on “chips”
There are interesting new aspects of
degenerate systems involving molecules
Summary
We can create cold diatomic polar molecules
We can create them and manipulate them on “chips”
There are interesting new aspects of
degenerate systems involving molecules
Can you calculate your Archimedes factor?