Rydberg atoms part 1 Tobias Thiele

Content References Part 1: Rydberg atoms Part 2: typical (beam) experiments T. Gallagher: Rydberg atoms References

Introduction – What is „Rydberg“? Rydberg atoms are (any) atoms in state with high principal quantum number n. Rydberg atoms are (any) atoms with exaggerated properties equivalent!

Introduction – How was it found? In 1885: Balmer series: Visible absorption wavelengths of H: Other series discovered by Lyman, Brackett, Paschen, ... Summarized by Johannes Rydberg:

Introduction – Generalization In 1885: Balmer series: Visible absorption wavelengths of H: Other series discovered by Lyman, Brackett, Paschen, ... Quantum Defect was found for other atoms:

Introduction – Rydberg atom? Hydrogen Energy follows Rydberg formula: =13.6 eV Energy

Quantum Defect? Energy follows Rydberg formula: Hydrogen n-Hydrogen Energy

Rydberg Atom Theory Rydberg Atom Almost like Hydrogen Core with one positive charge One electron What is the difference? No difference in angular momentum states

Radial parts-Interesting regions W Ion core r Interesting Region For Rydberg Atoms

(Helium) Energy Structure usually measured Only large for low l (s,p,d,f) He level structure is big for s,p Excentric orbits penetrate into core. Large deviation from Coulomb. Large phase shift-> large quantum defect

(Helium) Energy Structure usually measured Only large for low l (s,p,d,f) He level structure is big for s,p

Electric Dipole Moment Electron most of the time far away from core Strong electric dipole: Proportional to transition matrix element We find electric Dipole Moment Cross Section:

Hydrogen Atom in an electric Field Rydberg Atoms very sensitive to electric fields Solve: in parabolic coordinates Energy-Field dependence: Perturbation-Theory

Stark Effect For non-Hydrogenic Atom (e.g. Helium) „Exact“ solution by numeric diagonalization of in undisturbed (standard) basis ( ,l,m) Numerov

Stark Map Hydrogen Levels degenerate Cross perfect Runge-Lenz vector conserved n=11

Stark Map Hydrogen n=13 k=-11 blue n=12 k=11 red n=11

Stark Map Helium Levels not degenerate s-type Do not cross! No coulomb-potential n=11

Stark Map Helium n=13 k=-11 blue n=12 k=11 red n=11

Stark Map Helium Inglis-Teller Limit α n-5 n=13 n=12 n=11

Rydberg Atom in an electric Field When do Rydberg atoms ionize? No field applied Electric Field applied Classical ionization: Valid only for Non-H atoms if F is Increased slowly

Rydberg Atom in an electric Field When do Rydberg atoms ionize? No field applied Electric Field applied Classical ionization: Valid only for Non-H atoms if F is Increased slowly

(Hydrogen) Atom in an electric Field When do Rydberg atoms ionize? No field applied Electric Field applied Quasi-Classical ioniz.: red blue

(Hydrogen) Atom in an electric Field When do Rydberg atoms ionize? No field applied Electric Field applied Quasi-Classical ioniz.: red blue

(Hydrogen) Atom in an electric Field Blue states Red states classic Inglis-Teller

Lifetime From Fermis golden rule Einstein A coefficient for two states

Lifetime From Fermis golden rule Einstein A coefficient for two states For l≈0: Overlap of WF For l≈0: Constant (dominated by decay to GS)

Lifetime From Fermis golden rule Einstein A coefficient for two states For l ≈ n: For l ≈ n: Overlap of WF

Lifetime 7.2 μs 70 ms ms State Stark State 60 p small Circular state 60 l=59 m=59 Statistical mixture Scaling (overlap of ) Lifetime 7.2 μs 70 ms ms

Rydberg atoms part 2 Tobias Thiele

Part 2- Rydberg atoms Typical Experiments: Beam experiments (ultra) cold atoms Vapor cells

Cavity-QED systems

Goal: large g, small G Couple atoms to cavities Realize Jaynes-Cummings Hamiltonian Single atom(dipole) - coupling to cavity: 𝑔= 𝑑 𝐹 0 ℏ = 𝜔 0 𝑑 2 2 𝜖 0 ℏ 𝑉 Reduce mode volume Increase resonance frequency Increase dipole moment

Coupling Rydberg atoms Couple atoms to cavities Realize Jaynes-Cummings Hamiltonian Single atom(dipole) - coupling to cavity: Scaling with excitation state n? 𝑔= 𝑑 𝐹 0 ℏ = 𝜔 0 𝑑 2 2 𝜖 0 ℏ 𝑉 =2 𝜋 43.768 𝑘𝐻𝑧 S. Haroche (Rydberg in microwave cavity) ∝𝑛 2 𝑔= 𝑑 𝐹 0 ℏ = 𝜔 0 𝑑 2 2 𝜖 0 ℏ 𝑉 ≈2 𝜋 6∗ 10 11 𝑛 −4 ∝𝑛 −3 ∝𝑛 9

Advantages microwave regime for strong coupling g>> G,k Coupling to ground state of cavity l~0.01 m (microwave, possible) for n=50 l ~10-7 m (optical, n. possible), Typical mode volume: 1mm *(50 mm)2 Linewidth: G ~ 10 Hz (microwave) G ~ MHz (optical)

Summary coupling strength Microwave: Optical: What about G? Optical G6p~ 2.5 MHz Rydberg G50p~300 kHz, G50,50~100 Hz h=𝑔/Gnp ∝ 1/n, h=𝑔/Gn,n-1 ∝ n 𝑔~2𝜋 40 𝑘𝐻𝑧, κ ~2𝜋 10 𝐻𝑧 frequency limited Mode volume limited 𝑔~2𝜋 5 𝑀𝐻𝑧, κ ~2𝜋 1 𝑀𝐻𝑧 n-4 Optimal n when g >> G ~ κ n-3 n-5

Cavity-QED from groundstates to Rydberg-states Hopefully we in future! BEC in cavity Single atoms in optical cavities Haroche

Cavity-QED systems Combine best of both worlds - Hybrid

Hybrid system for optical to microwave conversion

ETH physics Rydberg experiment Creation of a cold supersonic beam of Helium. Speed: 1700m/s, pulsed: 25Hz, temperature atoms=100mK

ETH physics Rydberg experiment Excite electrons to the 2s-state, (to overcome very strong binding energy in the xuv range) by means of a discharge – like a lightning.

ETH physics Rydberg experiment Actual experiment consists of 5 electrodes. Between the first 2 the atoms get excited to Rydberg states up to Ionization limit with a dye laser.

Dye/Yag laser system

Dye/Yag laser system Experiment

Dye/Yag laser system Experiment Nd:Yag laser (600 mJ/pp, 10 ns pulse length, Power -> 10ns of MW!!) Provides energy for dye laser

Dye/Yag laser system Dye laser with DCM dye: Dye is excited by Yag and fluoresces. A cavity creates light with 624 nm wavelength. This is then frequency doubled to 312 nm. Experiment Nd:Yag laser (600 mJ/pp, 10 ns pulse length, Power -> 10ns of MW!!) Provides energy for dye laser

Dye laser cuvette Nd:Yag pump laser Frequency doubling DCM dye

ETH physics Rydberg experiment Detection: 1.2 kV/cm electric field applied in 50 ns. Rydberg atoms ionize and electrons are detected at the MCP detector (single particle multiplier) .

Results TOF 100ns

Results TOF 100ns Inglis-Teller limit

Results TOF 100ns Adiabatic Ionization- rate ~ 70% (fitted)

Pure diabatic Ionization- rate: Results TOF 100ns Adiabatic Ionization- rate ~ 70% (fitted) Pure diabatic Ionization- rate:

Pure diabatic Ionization- rate: Results TOF 100ns Adiabatic Ionization- rate ~ 70% (fitted) Pure diabatic Ionization- rate: saturation From ground state

Results TOF 15 ms From ground state lifetime

Rabi oscillations over a distance of 1.5 mm between Rydberg states