“Welcome to Rydberg-Land” Yan Zhou, David Grimes, Anthony Colombo, Ethan Klein, Tim Barnum, and RWF Department of Chemistry Massachusetts Institute of Technology ISMS June 16,

Rydberg States Series of “identical” electronic states, each with vibration-rotation structure An infinity of infinities All molecules have Rydberg states Boring? Remedy for unemployment of spectroscopists? A lot happens when you scatter an electron off of a cation! Beyond molecular constants. What was once difficult and tedious is now one million times faster and more informative! 2

Two Powerful Weapons Chirped Pulse millimeter-Wave Spectroscopy – Brooks Pate Buffer Gas Cooled Ablation Source – Frank De Lucia, John Doyle, Dave Patterson, Dave DeMille 3

Level Diagram for Optical-Optical-mm Triple Resonance in Ca 4

2 Lasers/Ionization vs. 2 Lasers+CP/FID Old 1 GHz Resolution Scan: n*=10-20, 823 cm -1, 25,000 resolution elements 100 hours for 20:1 S:B Active volume: 0.01 cm 3 BaX Single Rydberg state number density: 10 5 /cm 3 Transition moment: ~10 D Sequential scan: detect ions New 50 kHz Resolution 20 GHz, 400,000 resolution elements: 400k/25k=16 10 sec for 20:1 S:B Advantage: 16x36k=600k 300 cm /cm 3 Advantage: 30kx100=3,000,000 >1000 D Multiplexed FID detection 5

Some Ideas and Tricks n*-scaling (effective principal quantum number) Repeated (n, n+1) patterns Rotation-electronic resonance: broken patterns 2-D laser + mm-wave spectroscopy Ramped pulsed electric field ionization Stark demolition Up vs. down Polarization to determine ΔN Superradiance Photon echo 6

In Rydberg-Land Rydberg Equation is the Law! – We Observe Differences in Energy n-Scaling and Repetition – Everything scales as – Almost everything in (n,n+1) almost always appears scaled in (n+m,n+1+m) Energy Transfer: Ion-Core Rydberg Electron? Resonance! We can select each mechanism. 7

Two Flavors of Rydberg States Core-Nonpenetrating (integer n*): long range probe of ion-core multipole moments (μ,Q,O) and polarizability (α,γ) – Huge |Δn*|<1 transition moments, long lifetimes – Inside-out ligand field theory – Algebraic formulas: splittings  μ,Q,O,α,γ of ion Jeff Kay, J. Chem. Phys. 128, , (2008). Core-Penetrating (non-integer n*): hard collisions of e - with ion-core – Series terminus (lowest n*) state encodes intra-core dynamics 8

What are Core Nonpenetrating States? 9 N+N+ N Λ (ℓ) N+N+ N ℓ Centrifugal barrier prevents overlap with the core Nonradiative decay mechanisms (autoionization, predissociation) scale as overlap with the core (proportional to n -3, exponentially decreasing with ℓ). Rotation and orbital angular momentum recouple as n, ℓ and N increase. Evolution from Hund’s case b to case d. ℓRℓR

F–F– M 2+ x r c.m Å for CaF + f should be nonpenetrating Penetrating vs. Nonpenetrating Rydberg Orbitals 10

Weapon 1: Chirped Pulse millimeter- Wave Multiplexed direct detection of transitions: Free Induction Decay No high-voltage ion- or UV-VIS photon-detection systems 20 GHz bandwidth, 50 kHz resolution (0.4 million resolution elements in a single chirped pulse). 20:1 S:B in 10 s (100 chirps) Reliable relative intensities: ~5% accuracy Easily recognizable patterns of transitions Small departures from expected patterns at predicted resonances Manipulation by user-designed chirped pulse or pulse sequence GHz 11

FID During a Chirp 12

detector generator Weapon 2: Buffer gas cooled ablation source Ne 20K 4K 40K ablation laser pump lasers 90% Ni mesh Volume: 3cm x 3cm x 20 cm ~ 200cm 3 Number of molecules in a single Rydberg state: 10 9 Beam velocity: 150m/s, Doppler broadening reduced by 10 13

20 GHz Chirp in GHz Region Want to sample transitions in the Δn=1 region 14

15 12 cm -1 n=41n=42n=43n=44 n= GHz

Tricks for Organizing Rydberg Spectra Especially the CNP States Ramped pulsed field ionization Up vs. down transition from phase of FID Stark demolition in ~1 V/cm electric field – Destroys FID from 2-level system with one CNP R,P vs. Q from RzRzRz vs RzRzQz lab frame polarization of transition sequence: determines Size of quadrupole splitting: determines 16

Approximately locating n*~43 17 t n* ~

Which way is up? 40.88f 41.73d 33.67s 34.13p Time/μs Time/ns 18

Calcium Atoms Fitted Phase Difference: FID-mmW Pulse 1.08(2) π0.04(1) π 34.13p – 33.67s41.73f – 40.88d Single frequency excitationsUncertainties in () are the 95% confidence intervals 19 UP DOWN

Stark Demolition Core Penetrating (CP) Rydberg states are not sensitive to a weak electric field Core Nonpenetrating (CNP) Rydberg states are very sensitive to a weak electric field CNP states are located at integer n* – Best way to locate a series of integer-n* states Differential Stark Demolition – Quadrupole splitting of CNP states depends on – Spectroscopic black hole ( ) vs. outliers

Stark demolition 21 CNP CP CP or CNP 1V/cm CNP, l>4 FID no FID CP CNP CP ~10MHz 36.04

22 ℓ = 5 ℓ = 4 ℓ = 3 ℓRℓR Hund’s case d: N is rigorous, N + is pattern- forming Quadrupole splitting pattern Black holeOutliers ℓ ≤ n-1

Differential Stark Demolition 23 CNP CP CP or CNP 1V/cm CNP l>4 FID no FID CP Different electric field strengths (<1V/cm) will distinguish between small (outlier states) and very small (black hole) quantum defects. Differential Stark Demolition

Polarization 24 C2ΠC2Π X2Σ+X2Σ+ ~20100 cm -1 ~18600 cm -1 n~43, l =3 n-1, l +1 n+1, l +1

Molecular system - BaF C2ΠC2Π X2Σ+X2Σ+ ~20100 cm -1 ~18600 cm -1 IP 0 =38745 cm -1 n~43, l =3 n-1, l +1 n+1, l +1 v + =0, N + D 0 =48200 cm -1 v + =1 v + =2 200 new transitions / hour Laser resolution: 1 GHz mmW resolution: 50 kHz 25

Organize transitions in 2D spectrum (1) Rydberg formula (2) Up/down transitions (3) Stark demolition – CP or CNP Δn=1 CP CNP 26

Ok, Now What? Electronic structure of a cation Mechanisms for exchange of energy and angular momentum between electron and ion Many-Molecule interactions: superradiance Preparation of cations in a single quantum state Slowing and trapping of neutral molecules 27

Resonance Exchange electron kinetic energy and angular momentum for nuclear rotation angular momentum Conserve angular momentum Conserve energy 28

“Stroboscopic effect:” Resonances Dipole n*,l,N + +1  n*+1,l+1,N + Quadrupole n*,l,N + +2  n*+1,l+2,N + N+N+ n* N+N+ n* Select n* and N + to be near a resonance. Select for either dipole- or quadrupole-mediated interaction mechanism. Look for departures from normal n*,n*+1 pattern at ~1 kHz precision. 29

π/2π 20 ns, 6 V/m 2.2 μs Time/μs 10 ns, 6 V/m Inhomogeneity (Doppler) dominated, 1/πT 2 ´ = 150 kHz Measure homogeneous decay rate. Multi-Pulse (photon-echo) experiments 30

Superradiance in Ba 6s 2 1 S 0 6snp 1 P 1 n = 30 – – 98 GHz 1 S 0 or 1 D 2 ~42000 cm -1 75kHz 150kHz 4MHz 1MHz (a) (b) (c) (a)Highest resolution in a low density gas (b)Superradiance in the time-domain (c)Superradiance and frequency shift in the frequency-domain 31

mmW multi-step population transfer 32 CP, l=3 CNP, l=4 mmW 1 mmW 2 CNP, l=5 Blind search: A pulse sequence with 3 or more 20 GHz chirps No increase in the search time mmW multiple resonances

Ladder climbing 33 57d–54f 56g–54f 56g–54h artifact 57d 54f 56g 54h Laser

Stepwise Excitation to High- (n, ) (n+1, +1),(n+1, +1) (n, +2),(n, +2) (n+1, +3) Transition sequence straddles with decreasing oscillation No possibility of unwanted transitions 34

35 n n+1 (+1) (+2) (+3)

36 ΔνΔν +1→ +2→ +1+2→ +3

Pure Electronic Transitions in Molecules Are No more Difficult than in Atoms Atomic electronic transitions initially studied by the Kleppner group Millimeter-wave resolution (100 kHz) For n*=43 – Sequential scan (not multiplexed): (20GHz / 100kHz) x 1s = 60 hours! A few seconds for CPmmW spectra Molecular spectra simplified by CNP propensity rules! Data analysis: for n*=43, N<10, l<6: 360 states! Units: MHz 37 OR

Global model 38 Valence state (v, N) Core-penetrating Rydberg state (v, N) = Σ(v+, N+, l) Core-nonpenetrating Rydberg state (v+, N+, l) laser mmW Completely coupled Partially decoupled Several ion states Completely decoupled One ion state Physics Well controlled system Chemistry Ion-electron interactions Multichannel collision Electron probes ion molecular ion Global model Larger molecules? CP states are complicated CP states have short lifetime

Spectroscopists are born not made 39 My vision for Rydberg spectroscopy is that the tedium of long scans, the crossword puzzle aspect of assignments, and the robotic collection of archival molecular constants, will be replaced by speed, accuracy, and new classes of structure/dynamics mechanism-based patterns.

Upcoming Rydberg talks RE04 – Buffer gas cooled molecule source for CPmmW spectroscopy – Tim Barnum RE05 – Direct observation of Rydberg-Rydberg transitions via CPmmW spectroscopy – Yan Zhou RE06 – Toward the use of Rydberg states for vibration-rotation state-selective production of molecular ions RE07 – Selective population of core nonpenetrating molecular Rydberg states – David Grimes 40

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Kepler Period = 13 ps Rotational Period = 13 ps Kepler Period = 26 ps Rotational Period = 13 ps N+N+ 'p' Π Series; N = 3 Stroboscopic Effects 42

Pattern-Forming Quantum Number N Determined From Combination Differences Plot E ROT - BN(N+1) vs. N Slope is -2Bℓ R ; Determines N + Anomalous B eff ℓ-Uncoupling Case (b) Case (d) 43

Physical Basis for n* -3 Scaling (1), varies by < 1.5% ≈ constant; r node n*-independent, n* ≥ 6 1 st radial node at Inside core KE varies < 3% n* = 6  n* = 44

= Physical Basis for n* -3 Scaling (2) = = Kepler period: Inner lobe amplitude ~ n*  3/2 45