Excitation of Ultracold Molecules to “Trilobite-like” Long-range Molecular Rydberg States M. A....

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 Foundationand 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

2 4 6 8 10 12 14

0

5000

10000

15000

20000

25000

30000

35000

1 3+g

2+g

2 3g

Rb+2

5s+4D

5s+5P1/2

5s+5s

2 3+g

a 3+u

R(Å)

Ene

rgy(

cm-1)

J. Lozeille, et al., Eur. Phys. J. D. 39, 261 (2006).

1) PA in a MOT to form bound excited-state Rb2*.

2) Radiative stabilization into the metastable triplet state, a 3Σu

+

3) Efficient detection using pulsed laser REMPI through the 2 1Σu

+ state.

Photoassociative formation and detectionof Rb2 in the a 3Su

+ state

PA

REMPI

Experimental Scheme

MOT beams to windowson y,z axes

Trap laser

Repumplaser

CO2 laser

Channeltron

PA laser

Detection Laser

Typically 5106 atoms,density 1011 cm–3,at ≈140 mK

MOT

for optional optical trapping

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 Franck-Condon factors.

For the Rydberg experiment, nearly pure v = 35 is used.

Excitation of long-range Rydberg moleculesfrom a 3Su

+, v=35

5s + np

5s + 5sa 3Su+,

Topics


a 3Su+ state.




4. Future prospects

3. Rydberg-Rydberg “Macrodimers” bound at very long range (Côté, us, Shaffer, others).

4. Ion-pair “heavy Rydberg” states. For very high v, vibrational structure ap-proaches a Rydberg series (Ubachs, Merkt, McCormack, Kirrander, ...).

Four classes of Rydberg molecules

1. Ordinary Rydberg states of molecules. A single highly excited electron interacts with the ionic core.

2. Ground-state atoms bound to Rydberg atoms: “Trilobites” and similar states (Greene, Pfau, ...).

Rb2+

Rb+

Rb-

Rb+ Rb+Cn/Rn

Rb+ Rb

Figure is from V. Bendkowsky, B. Butscher, J. Nipper, J. P. Shaffer, R. Löw, and T. Pfau. Nature 458, 1005 (2009).

Bonding mechanism for 5s + ns

2

.( ) 2 ( ) ( ) .s RydV R a k R In the “Fermi-Greene” mean-field model,

Vibrational wave functions for 5s + 35s

Figure is from V. Bendkowsky, B. Butscher, J. Nipper, J. P. Shaffer, R. Löw, and T. Pfau. Nature 458, 1005 (2009).

The ground-state atom can be well-localized as shown for v = 0, or broadly distributed between wells, as for v = 1.

• 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)

1 2

.min

2 1( ) 2 ( ) ( )

4

n

s RydV R a k R

23.( ) 6 ( ( )) ( )p RydV R a k R

Bonding for 1

• Trilobite state with extensive high- contributions is extremely dipolar.

• Not yet directly observed.

Previous observations of Rydberg-induced bonding

5s+ns “trilobite-like” states:

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.

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).

5s + 35s

5s + 36s

5s + 37s

Prior observation via collisional satellites

Theory: Hamilton, Greene, and Sadeghpour, J. Phys. B 35, L199 (2002).

Experiment: Greene, Hamilton, Crowell, Vadla, and Niemax, Phys. Rev. Lett. 97, 233002 (2006).

5s+np “butterfly” states:

• Calculated n=30 wave function gives the name.

Rb+

Rb

• At n = 9–12, collisional broadening “satellites” in heat-pipe spectra have profiles that match the long-range potential wells.

Topics


a 3Su+ state.




4. Future prospects

Excitation of long-range Rydberg moleculesfrom a 3Su

+, v=35

5s + np

5s + 5sa 3Su+,

A transitional case: 5s +7p

-200 -100 0 100 2000.1

1

10

100

1000

0

10

20

30

Our spectrum

(cm-1)

Niemax collisional"satellite" spectrum

* *

Cs impuritylines 6S - 9PJ

*

Rb

2+ io

ns/la

ser

shot

k R (

1038

cm5 ) *

7p

• 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.

0 20 40 6027000

27500

28000

28500

1g

1g

3g

3g

3g

3g

5s+7p

Ene

rgy

(cm

-1)

R (a0)

to 5s+6d

from A.R. Allouche, unpublished (2012)

1C. H. Greene, E. L. Hamilton, H. Crowell, C. Vadla, and K. Niemax, Phys. Rev. Lett. 97, 233002 (2006).

2M. A. Bellos, R. Carollo, J. Banerjee, E. E. Eyler, P. L. Gould, and W. C. Stwalley, arXiv:1303.3420.

40 100 200

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.

1M. A. 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).

40 100 200

The 5s +12p “butterfly” state


40 100 200


40 100 200


The 5s + 9p “butterfly” state

40 100 200

Zooming in for excitation near 32 a0

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).

Correspondence of spectra to potentials

Signals for n=9,10

These large signals are observed only in the Rb2

+ detection channel.

Pulse energy is too low for photoionization states must autoionize.

0 5 10 15 20 25 30 35

Rb2+ ion signal (ions)

**

20 30 40 50 60

-150

-100

-50

0

50

100

R (a0)

v fro

m

9p (cm-

1 )

inital state prob. density

to 9p

to 8d

9p atomic resonance

0 5 10 15 20 25 30

* *

Rb2

+ ion signal (ions)

20 30 40 50 60

-150

-100

-50

0

50

100

to 10p

to 7f, 7g

to 9d

R (a0)

v fro

m

10p (cm-

1 )


10p

Continuation to n=11, 12

0 5 10 15

Rb2+ ion signal (ions)

* *

20 30 40 50 60-100

-50

0

50

100

to 9f,9g

to 12p

to 11d

to 13s

inital state prob. density R (a0)

v f

rom

12

p (

cm-1 )

0 5 10 15 20 25 30

* *

Rb2

+ ion signal (ions)

20 30 40 50 60

-150

-100

-50

0

50

100

to 11p

to 8f, 8g

to 10d

R (a0)

v fro

m 11p

(cm

-1)


Topics


a 3Su+ state.




4. Future prospects

Future prospects

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.

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.

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 Undergrads

David Rahmlow 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, [email protected].

Excitation of Ultracold Molecules to “Trilobite-like” Long-range Molecular Rydberg States M. A....

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