Excitation of Ultracold Molecules to
“Trilobite-like” Long-range Molecular
Rydberg States
M. A. Bellos, R. Carollo, J. Banerjee, E. E. Eyler,
P. L. Gould, and W. C. Stwalley
Physics Department, University of Connecticut
Supported by the National Science Foundation
and the Air Force Office of Scientific Research (MURI)
Topics
1. Introduction to cold molecules and photoassociation
• Production and detection of Rb2 in the metastable
a 3Su+ state.
• State-selective production of high-v levels.
2. Long-range “trilobite-like” Rydberg molecules
• Bonding mechanism.
• Existing experiments.
3. Direct excitation of cold molecules
• Excitation at long range near the 5s + np asymptotes.
• Comparison with calculated potentials and prior work.
4. Future prospects
Photoassociative formation and detection
of Rb2 in the a 3Su+ state
+
Rb2
35000
Energy(cm-1)
30000
2 3 g
25000
1) PA in a MOT to form
bound excited-state Rb2*.
2 +
Sg
REMPI
5s+4D
1 3+g
20000
15000
2 3S+g
5s+5P1/2
2) Radiative stabilization
into the metastable triplet
state, a 3Σ+u
10000
PA
5000
5s+5s
0
a
2
3 +
Su
4
6
8
10
12
3) Efficient detection using
pulsed laser REMPI through
the 2 1Σ+u state.
14
R(Å)
J. Lozeille, et al., Eur. Phys. J. D. 39, 261 (2006).
Experimental Scheme
CO2 laser
for optional optical trapping
MOT
Typically 5106 atoms,
density 1011 cm–3,
at ≈140 m K
Trap laser
Repump
laser
Channeltron
Detection Laser
MOT beams to windows
on y,z axes
PA laser
REMPI spectrum from a, v = 35–36
In this example, a very clean
spectrum to the 2 3Sg+ state is
observed.
The entire spectrum from 14000–
17000 cm–1 was analyzed in a
UConn/Pisa/Orsay collaboration:
Lozeille, et al., Eur. Phys. J. D 39,
261 (2006).
Vibrationally selected a-state Rb2
By choosing the PA level in
the 0g- (5s + 5p1/2) state, the
vibrational level(s) populated
by radiative decay can be
selected.
These zoomed-in REMPI
spectrum show the specificity
and adjustability due to
narrowly-peaked FranckCondon factors.
For the Rydberg experiment,
nearly pure v = 35 is used.
Excitation of long-range Rydberg molecules
from a 3Su+, v =35
5s + np
a 3Su+,
5s + 5s
Topics
1. Introduction to cold molecules and photoassociation
• Production and detection of Rb2 in the metastable
a 3Su+ state.
• State-selective production of high-v levels.
2. Long-range “trilobite-like” Rydberg molecules
• Bonding mechanism.
• Existing experiments.
3. Direct excitation of cold molecules
• Excitation at long range near the 5s + np asymptotes.
• Comparison with calculated potentials and prior work.
4. Future prospects
Four classes of Rydberg molecules
1. Ordinary Rydberg states of
3.
molecules. A single highly excited
electron interacts with the ionic core.
Rb2+
2. Ground-state atoms bound to
Rydberg atoms: “Trilobites” and
similar states (Greene, Pfau, ...).
Rydberg-Rydberg “Macrodimers”
bound at very long range (Côté, us,
Shaffer, others).
Rb+
Cn/Rn
4. Ion-pair “heavy Rydberg” states. For
very high v, vibrational structure approaches a Rydberg series (Ubachs,
Merkt, McCormack, Kirrander, ...).
Rb+
Rb+
Rb
Rb+
Rb-
Bonding mechanism for 5s + ns
2
In the “Fermi-Greene” mean-field model,V ( R)  2 as (k )  Ryd . ( R) .
Figure is from V. Bendkowsky, B. Butscher, J. Nipper, J. P. Shaffer, R. Löw, and T. Pfau. Nature 458, 1005 (2009).
Vibrational wave functions for 5s + 35s
The ground-state atom can be well-localized as shown for
v = 0, or broadly distributed between wells, as for v = 1.
Figure is from V. Bendkowsky, B. Butscher, J. Nipper, J. P. Shaffer, R. Löw, and T. Pfau. Nature 458, 1005 (2009).
Bonding for   1
2
2 1
V ( R)  2 as (k ) 
 Ryd . ( R)
 min 4
n 1
• Trilobite state with extensive high-
contributions is extremely dipolar.
• Not yet directly observed.
V ( R)  6 (a p (k ))  Ryd . ( R)
3
2
• Butterfly state for p-wave near
5s+nl, at large n.
• Deeply bound for Rb due to a
large p-wave shape resonance.
C. H. Greene, A. S. Dickinson, and H. R. Sadeghpour , Phys. Rev. Lett. 85, 2458 (2000);
E. L Hamilton, C. H. Greene and H. R. Sadeghpour, J. Phys. B 35 L199 (2002)
Previous observations of Rydberginduced bonding
5s+ns “trilobite-like” states:
5s + 35s
5s + 36s
5s + 37s
Stuttgart: Bendkowsky, Butscher, Nipper,
Shaffer, Löw, and Pfau, Nature 458, 1005
(2009), several other papers.
Oklahoma: Tallant, et al., Phys. Rev. Lett. 109,
173202 (2012).
Seen in direct PA excitation near 5s + ns
in very cold, very dense trapped Rb,
with n =31–39.
At these n values, there are just a few
bound vibrational levels, 10–30 MHz
below the atomic Rydberg line.
Prior observation via collisional satellites
5s+np “butterfly” states:
Rb
Rb+
• Calculated n=30 wave function gives
the name.
• At n = 9–12, collisional broadening
“satellites” in heat-pipe spectra have
profiles that match the long-range
potential wells.
Theory: Hamilton, Greene, and Sadeghpour, J. Phys.
B 35, L199 (2002).
Experiment: Greene, Hamilton, Crowell, Vadla, and
Niemax, Phys. Rev. Lett. 97, 233002 (2006).
Topics
1. Introduction to cold molecules and photoassociation
• Production and detection of Rb2 in the metastable
a 3Su+ state.
• State-selective production of high-v levels.
2. Long-range “trilobite-like” Rydberg molecules
• Bonding mechanism.
• Existing experiments.
3. Direct excitation of cold molecules
• Excitation at long range near the 5s + np asymptotes.
• Comparison with calculated potentials and prior work.
4. Future prospects
Excitation of long-range Rydberg molecules
from a 3Su+, v =35
5s + np
a 3Su+,
5s + 5s
A transitional case: 5s +7p
* *
1000
28500
30
7p
to 5s+6d
Cs impurity
1
g
Niemax collisional
"satellite" spectrum
*
5
28000
kR (10 cm )
5s+7p
38
Energy (cm-1)
Sg
100 lines 6S - 9PJ
3
1
g
3
Sg
3
g
27500
20
10
10
*
1
Our spectrum
+
Sg
Rb2 ions/laser shot
3
from A.R. Allouche, unpublished (2012)
27000
0
20
40
R (a0)
60
0
0.1
-200
-100
0
100
200
 (cm )
-1
• The well-resolved vibrational lines seem to be a mix of levels from the
covalent short-range potential and shallow wells from Rydberg binding.
• Similar overall structure to the broad resonances in prior heat-pipe spectra.
• Resolution is limited by the pulsed laser, and can be greatly improved.
1M. A.
Bellos, R. Carollo, J. Banerjee, E. E. Eyler, P. L. Gould, and W. C. Stwalley, arXiv:1303.3420.
Calculated potentials for n = 9-12
Top panel: Calculations from
Greene, et al.1 using Coulomb’
Green’s function method.
Bottom panel: Squared gradients
of Rydberg electronic wave
functions,2 calculated by
Numerov integration.
1C.
H. Greene, E. L. Hamilton, H. Crowell, C. Vadla, and K. Niemax,
Phys. Rev. Lett. 97, 233002 (2006).
40
100
200
2M. A.
Bellos, R. Carollo, J. Banerjee, E. E. Eyler, P. L. Gould, and W.
C. Stwalley, arXiv:1303.3420.
The 5s +12p “butterfly” state
1M. A.
40
100
200
Bellos, R. Carollo, J. Banerjee, E. E. Eyler, P. L. Gould, and W. C.
Stwalley, arXiv:1303.3420.
2C. H. Greene, E. L. Hamilton, H. Crowell, C. Vadla, and K. Niemax, Phys.
Rev. Lett. 97, 233002 (2006).
The 5s +11p “butterfly” state
1M. A.
40
100
200
Bellos, R. Carollo, J. Banerjee, E. E. Eyler, P. L. Gould, and W. C.
Stwalley, arXiv:1303.3420.
2C. H. Greene, E. L. Hamilton, H. Crowell, C. Vadla, and K. Niemax, Phys.
Rev. Lett. 97, 233002 (2006).
The 5s +10p “butterfly” state
1M. A.
40
100
200
Bellos, R. Carollo, J. Banerjee, E. E. Eyler, P. L. Gould, and W. C.
Stwalley, arXiv:1303.3420.
2C. H. Greene, E. L. Hamilton, H. Crowell, C. Vadla, and K. Niemax, Phys.
Rev. Lett. 97, 233002 (2006).
The 5s + 9p “butterfly” state
1M. A.
40
100
200
Bellos, R. Carollo, J. Banerjee, E. E. Eyler, P. L. Gould, and W. C.
Stwalley, arXiv:1303.3420.
2C. H. Greene, E. L. Hamilton, H. Crowell, C. Vadla, and K. Niemax, Phys.
Rev. Lett. 97, 233002 (2006).
Zooming in for excitation near 32 a0
40
100
200
Correspondence of spectra to potentials
Left panels: zoomed-in potentials from
previous slide.
Bottom panel: Vibrational wave function
of the initial a 3Su+, v = 35 state used for
uv laser excitation.
Right panel: Molecular ion signal,
detected by time-of-flight mass
spectroscopy (enlargements follow).
Signals for n = 9,10
100
to 8d
9p atomic resonance
-1
v from 9p (cm )
50
0
**
to 9p
These large signals
are observed only
in the Rb2+
detection channel.
-50
-100
-150
20
30
inital state prob. density
40
R (a0)
50
60
15
10
5
0
20
25
30
35
+
Rb2 ion signal (ions)
Pulse energy is too
low for
photoionization
 states must
autoionize.
100
to 9d
-1
v from 10p (cm )
50
10p
to 10p
0
*
*
-50
-100
to 7f, 7g
-150
20
30
inital state prob. density
40
R (a0)
50
60
0
5
10
+
15
20
Rb2 ion signal (ions)
25
30
Continuation to n =11, 12
100
to 10d
-1
v from 11p (cm )
50
0
to 11p
*
*
-50
to 8f, 8g
-100
-150
20
30
inital state prob. density
40
R (a0)
50
60
0
5
10
+
15
20
25
30
Rb2 ion signal (ions)
100
-1
v from 12p (cm )
to 13s
50
to 11d
0
*
to 12p
-50
*
to 9f,9g
-100
20
30
inital state prob. density
40
R (a0)
50
60
0
5
+
10
Rb2 ion signal (ions)
15
Topics
1. Introduction to cold molecules and photoassociation
• Production and detection of Rb2 in the metastable
a 3Su+ state.
• State-selective production of high-v levels.
2. Long-range “trilobite-like” Rydberg molecules
• Bonding mechanism.
• Existing experiments.
3. Direct excitation of cold molecules
• Excitation at long range near the 5s + np asymptotes.
• Comparison with calculated potentials and prior work.
4. Future prospects
Future prospects
High-resolution spectra:
• Bound-bound excitation has no density dependence; allows complete
freedom from collisions and interactions with nearby atoms.
• A pulse-amplified laser will immediately improve resolution from 20
GHz to 50 MHz. Two-photon cw excitation can provide <1 MHz.
Dynamics:
• Lifetimes? Decay pathways?
• Does the ion-pair limit just below the
5s + 8p neutral atom limit affect the
decay rates for n > 7?
Other states:
• Can easily extend to higher n, other ’s.
• Other molecules: KRb?
• Start with Feshbach molecules for
excitation at very long range.
Summary
• Cold Rb2 can be produced via in the metastable a 3Su+
state with v≈ 35.
• Allows excitation of exotic “butterfly” states and other
“trilobite-like” bonds, using bound-bound transitions
for the first time.
• Next: high-resolution study of vibrational structure,
dynamics.
• For progress on an alternative approach to cold
molecules, come to talk RD01, “Methods for
Manipulating CaF Using Optical Polychromatic Forces
Rb
Rb+
Contributors
Postdoc
Grad Students
David Rahmlow
Undergrads
Ye Huang
Michael Rosenkrantz
Hyewon Pechkis
Kevin Wei
Ryan Carollo
Michael Bellos
Jayita Banerjee
And one of you??
A postdoctoral position for ultracold molecule research is
available starting any time after August 1. Send inquiries or
applications to Ed Eyler, eyler@phys.uconn.edu.