1. 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)

2. Topics 1.Introduction to cold molecules and photoassociation Production and detection of Rb 2 in the metastable a 3  u + 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

3. R(Å)R(Å) Energy(cm -1 ) J. Lozeille, et al., Eur. Phys. J. D. 39, 261 (2006). 1) PA in a MOT to form bound excited-state Rb 2 *. 2) Radiative stabilization into the metastable triplet state, a 3 Σ u + 3) Efficient detection using pulsed laser REMPI through the 2 1 Σ u + state. Photoassociative formation and detection of Rb 2 in the a 3  u + state PA REMPI

4. Experimental Scheme Typically 5  10 6 atoms, density 10 11 cm –3, at ≈140  K MOT for optional optical trapping

5. REMPI spectrum from a, v =35–36 In this example, a very clean spectrum to the 2 3  g + 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).

6. Vibrationally selected a -state Rb 2 By choosing the PA level in the 0 g - (5s+5p 1/2 ) 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.

7. Excitation of long-range Rydberg molecules from a 3  u +, v =35 5s + np 5s + 5s a 3u+,a 3u+,

8. Topics 1.Introduction to cold molecules and photoassociation Production and detection of Rb 2 in the metastable a 3  u + 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

9. 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,...). Rb 2 + Rb + Rb - Rb + Cn/RnCn/Rn Rb

10. 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 In the “Fermi-Greene” mean-field model,

11. 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.

12. 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) Bonding for  1 Trilobite state with extensive high- contributions is extremely dipolar. Not yet directly observed.

13. 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

14. 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.

15. Topics 1.Introduction to cold molecules and photoassociation Production and detection of Rb 2 in the metastable a 3  u + 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

16. Excitation of long-range Rydberg molecules from a 3  u +, v =35 5s + np 5s + 5s a 3u+,a 3u+,

17. A transitional case: 5s +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. 1 M. A. Bellos, R. Carollo, J. Banerjee, E. E. Eyler, P. L. Gould, and W. C. Stwalley, arXiv:1303.3420.

18. 1 C. H. Greene, E. L. Hamilton, H. Crowell, C. Vadla, and K. Niemax, Phys. Rev. Lett. 97, 233002 (2006). 2 M. 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.

19. 1 M. A. Bellos, R. Carollo, J. Banerjee, E. E. Eyler, P. L. Gould, and W. C. Stwalley, arXiv:1303.3420. 2 C. 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

20. 1 M. A. Bellos, R. Carollo, J. Banerjee, E. E. Eyler, P. L. Gould, and W. C. Stwalley, arXiv:1303.3420. 2 C. H. Greene, E. L. Hamilton, H. Crowell, C. Vadla, and K. Niemax, Phys. Rev. Lett. 97, 233002 (2006). 40 100 200 The 5s +11p “butterfly” state

21. 40 100 200 1 M. A. Bellos, R. Carollo, J. Banerjee, E. E. Eyler, P. L. Gould, and W. C. Stwalley, arXiv:1303.3420. 2 C. H. Greene, E. L. Hamilton, H. Crowell, C. Vadla, and K. Niemax, Phys. Rev. Lett. 97, 233002 (2006). The 5s +10p “butterfly” state

22. 40 100 200 1 M. A. Bellos, R. Carollo, J. Banerjee, E. E. Eyler, P. L. Gould, and W. C. Stwalley, arXiv:1303.3420. 2 C. H. Greene, E. L. Hamilton, H. Crowell, C. Vadla, and K. Niemax, Phys. Rev. Lett. 97, 233002 (2006). The 5s + 9p “butterfly” state

23. 40 100 200 Zooming in for excitation near 32 a 0

24. Left panels: zoomed-in potentials from previous slide. Bottom panel: Vibrational wave function of the initial a 3  u +, 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

25. Signals for n=9,10 These large signals are observed only in the Rb 2 + detection channel. Pulse energy is too low for photoionization  states must autoionize. 9p atomic resonance 10p

26. Continuation to n=11, 12

27. Topics 1.Introduction to cold molecules and photoassociation Production and detection of Rb 2 in the metastable a 3  u + 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

28. 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.

29. Summary Cold Rb 2 can be produced via in the metastable a 3  u + 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

30. Contributors Postdoc Grad StudentsUndergrads David RahmlowYe HuangMichael Rosenkrantz Hyewon PechkisKevin 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.