High-resolution Spectroscopy of Long- range Molecular Rydberg States of 85 Rb 2 Ryan Carollo, Edward E. Eyler, Yoann Bruneau Phillip L. Gould, and W. C. Stwalley Department of Physics, University of Connecticut Supported by the National Science Foundation and the Air Force Office of Scientific Research (MURI)

Topics 1.Introduction to long-range Rydberg molecules Bonding mechanisms. Ground state-Rydberg bonds at high and low. Access by direct photoassociation of cold atoms. 2.Direct excitation of cold molecules Production and detection of high- v Rb 2 in the metastable a 3  u + state. Survey scans near the 5s+np asymptotes. Initial results from high-resolution spectroscopy. 3.Plans for KRb Two interacting series of long-range states. Proposed experimental scheme.

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 categories 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 (GSR bonds): “Trilobites,” “butterflies,” etc. (Greene, Pfau, Shaffer, us,...). Rb 2 + Rb + Rb - Rb + Cn/RnCn/Rn Rb

Molecular 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). In the “Fermi-Greene” mean-field model, Wave functions can be quite distributed, as for v=1 here. Numerous transitions have been observed by Pfau, Shaffer, et al.

Butterfly state for p-wave near 5s+nl, with n > 6. 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. Recently observed by Shaffer group.

Prior observation for 5s + np in Rb Theory: Hamilton, Greene, and Sadeghpour, J. Phys. B 35, L199 (2002). Experiment: Greene, Hamilton, Crowell, Vadla, and Niemax, Phys. Rev. Lett. 97, (2006). 5s+np “butterfly” states: Rb + Rb Calculated n=30 wave function gives the name. In Cs 2, Shaffer group recently observed 6s + np resonances for n ≈ 30. For Rb with n=9–12, heat-pipe spectra show collisional broadening “satellites”.

Topics 1.Introduction to long-range Rydberg molecules Bonding mechanisms. Ground state-Rydberg bonds at high and low. Access by direct photoassociation of cold atoms. 2.Direct excitation of cold molecules Production and detection of high- v Rb 2 in the metastable a 3  u + state. Survey scans near the 5s+np asymptotes. Initial results from high-resolution spectroscopy. 3.Plans for KRb Two interacting series of long-range states. Proposed experimental scheme.

Three questions 1.Is direct bound-bound excitation feasible? High-v levels of cold molecules appear ideal. 2.Structure and dynamics of p-wave “butterfly” states Not observed until our work (and now Shaffer’s) 3.Transition from covalent to long-range bonding In Rb 2, 5s+7p is the lowest threshold supporting a long-range potential minimum Has two sets of vibrational levels with differing character

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

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

REMPI spectrum from a, v =35–36 Here, a very clean spectrum to the 2 3  g + state is observed. The a state vibrational distribution can be adjusted by choice of the PA transition. The entire spectrum from 14000– cm –1 was analyzed in a UConn/Pisa/Orsay collaboration: Lozeille, et al., Eur. Phys. J. D 39, 261 (2006).

Excitation of long-range Rydberg molecules from a 3  u +, v =35 Nd:YAG-pumped dye laser produces 5 ns pulses with ~6 GHz bandwidth. n=7–12 have been surveyed. Newest work: n=7 with 100 MHz resolution, using a pulse-amplified cw laser.

A transitional case: 5s +7p Resolution is limited by the pulsed laser in this survey scan. Similar overall structure to the broad resonances in prior heat-pipe spectra. More details later. M. A. Bellos, R. Carollo, J. Banerjee, E. E. Eyler, P. L. Gould, and W. C. Stwalley, Phys. Rev. Lett. 111, (2013).

1 C. H. Greene, E. L. Hamilton, H. Crowell, C. Vadla, and K. Niemax, Phys. Rev. Lett. 97, (2006). 2 M. A. Bellos, R. Carollo, J. Banerjee, E. E. Eyler, P. L. Gould, and W. C. Stwalley, arXiv: 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.

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

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

Survey scan for 5s+7p Full potential curve allows comparison with predicted vibra- tional structure. Details are unreli- able because spin- orbit interaction was not included.

Outer-well vibrational levels Characteristic level spacing of the outer well is evident. 10p

High-resolution spectra (2015) Surprisingly, inner- well levels are much more intense than outer-well GSR levels. Only a few selected spectra available so far.

Internal substructure is from the a state Large spacing is the a- state vibrational interval. Small spacings do not vary from one state to another, but agrees with atomic hfs interval.  Surprisingly, a-state hfs at high v simply mirrors atomic hfs. No previous obser- vations are known.

Topics 1.Introduction to long-range Rydberg molecules Bonding mechanisms. Ground state-Rydberg bonds at high and low. Access by direct photoassociation of cold atoms. 2.Direct excitation of cold molecules Production and detection of high- v Rb 2 in the metastable a 3  u + state. Survey scans near the 5s+np asymptotes. Initial results from high-resolution spectroscopy. 3.Plans for KRb Two interacting series of long-range states. Proposed experimental scheme.

Two GSR electronic configurations K+K+ Rb Rb + K K is predicted to have a similar e – scattering length to Rb, but its Rydberg quantum defects differ somewhat.  Both configurations support long-range molecules, probably with observable interactions.

Excitation scheme for KRb Potentials for K + Rb* should be similar in shape to Rb 2. PA in heteronuclear species generally allows larger detunings.

KRb Franck-Condon factors To form v=28 in the a state, PA to 2(0 – ) with v ~ 170 gives a 12% branching ratio. Franck-Condon factors from v=28 to long-range “butterfly” states are very favorable.

Summary Bound-bound transitions allow R-selective excitation of exotic “butterfly” states and other “trilobite-like” bonds. Survey scans and limited high-resolution spectra have been obtained starting with the a 3  u + state of Rb 2, with v=35 and 36. Transition from covalent to “GSR” bond can be clearly seen for 5s+7p. Similar experiments in KRb will soon be underway. Rb + Rb

Contributors Postdocs Grad StudentsUndergrads David RahmlowYe HuangMichael Rosenkrantz Yoann BruneauHyewon PechkisKevin Wei Ryan CarolloMichael Cantera Michael BellosCameron Vickers Jayita Banerjee

Other extensions 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, especially 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. Two-photon cw excitation can provide <1 MHz.

Signals for n=11, 12