Introduction to Rydberg Atoms: Background What is a Rydberg Atom? A Rydberg atom is an atom in a principle quantum number state, n, that is larger than the valence n of a particular atom. Rydberg atoms have many exotic properties that have made them a contemporary research topic since the 1880’s.

Rydberg atom physics has tracked atomic and quantum physics research for over a century!

Tom Gallagher First Observations of Rydberg Transitions

The Balmer series was the first observation of Rydberg states in an experiment. Rydberg states are typically defined (loosely) as states that involve principal quantum numbers that are greater than n for the ground state. Development of Rydberg Atom Physics

• At First, Rydberg atoms played a role in the development of quantum mechanics – explanation of the atom and spectroscopy.

Bohr was able to relate the Rydberg constant to the physical constants that describe the properties of the electron – mass and charge.

109721.6 109728.64 109734. 69 109735. 77 109736.61 109736.86 Rydberg Atoms were Studied to Learn About Atomic Properties • Relatively low resolution spectroscopy could be used to study how electric and magnetic fields affected atoms. - Stark shifts - Diamagnetic shifts - Collisions

Exaggerated properties used to investigate phenomena that are otherwise difficult to observe in valence states. Development of Narrow Bandwidth Lasers The development of narrow bandwidth lasers, namely dye lasers, allowed individual Rydberg states to be addressed. • details of Stark shifts • wavepacket dynamics • field ionization • chaos • magnetic fields • electric and magnetic fields • collisions • plasmas • cavity QED • …. Laser Cooled and Trapped Samples Laser Cooling and Trapping has allowed experimentalists to overcome the Doppler effect and reach ultrahigh spectral resolution. • Rydberg atom interactions • preparation of collective states • novel molecular states • many-body interactions • precision measurement • electric field sensing • plasmas • quantum information • anti-Hydrogen • …. Alkali Rydberg Atoms - Background Alkali Rydberg Atoms- Energies Hydrogen – Radial Wavefunctions

Probability densities vs. electronic radial coordinate Alkali Rydberg Atoms- Model Potential Alkali Rydberg Atoms-Wavefunctions Alkali Rydberg Atoms-Quantum Defect Rubidium Alkali Rydberg Atoms-Quantum Defect

T.F. Gallagher, Rydberg Atoms, Cambridge (1994). Alkali Rydberg Atoms - Scaling Alkali Rydberg Atoms - Magnitudes

• These values are extreme compared to ground state atoms.

• The scaling with n allows one to control the properties of the atom.

• The lifetimes are long enough to make these features useful. Alkali Rydberg Atoms - Excitation Alkali Rydberg Atoms – Transition Dipole Moments

Potassium There is a strong dependence on the radial integral as n changes.

Quantum defects matter here.

The angular integral is important, mostly for selection rules.

Hydrogen Normalization of wavefunction changes as n-3/2.

T.F. Gallagher, Rydberg Atoms, Cambridge (1994). Alkali Rydberg Atoms – Transition Strength

Potassium Hydrogen

The transition strength to Rydberg states generally decreases as n-3 because of the scaling with the dipole moment – you need more laser power to achieve the same coupling strength (Rabi frequency goes as n-3/2) as n increases. Alkali Rydberg Atoms-Decay • Spontaneous emission.

• Blackbody induced emission.

• Blackbody induced absorption. - includes ionization.

• Collisions. Alkali Rydberg Atoms-Decay

The lifetimes of the Rydberg atoms change with n.

Different l states have different lifetimes – l changes selection rules and multiplicity.

The change with n is due to how the A coefficient scales with  and the nodal structure T.F. Gallagher, Rydberg Atoms, Cambridge (1994). of the wave functions for allowed transitions Alkali Rydberg Atoms – Spontaneous Emission Alkali Rydberg Atoms – Spontaneous Emission Alkali Rydberg Atoms – Spontaneous Emission Alkali Rydberg Atoms – Spontaneous Emission

∗ )

T.F. Gallagher, Rydberg Atoms, Cambridge (1994). These scaling laws come from experimental measurements, although they can be reproduced by careful calculations.

These values are good at 0K where blackbody radiation effects can be neglected. Alkali Rydberg Atoms- Blackbody Effects

T.F. Gallagher, Rydberg Atoms, Cambridge (1994). The fact that there are thermal photons in field modes that are resonant with Rydberg atom transitions means that we have to consider that stimulated processes (Einstein B coefficient) can lead to atomic decay and excitation. There is also absorption that can ionize the Rydberg atom. Alkali Rydberg Atoms – Temperature Spencer et al., PRA 26, 1490 (1982).

In T.F. Gallagher, Rydberg Atoms, Cambridge (1994). Alkali Rydberg Atoms – Blackbody Radiation Alkali Rydberg Atoms – Blackbody Radiation Alkali Rydberg Atoms - Decay

Blackbody radiation can have a large effect on Rydberg atom lifetimes – this is a stimulated emission effect – Einstein B coefficient.

Rb

=

= Beterov et al., PRA 79, 052504 (2009) Beterov et al., PRA 75, 052720 (2007) Alkali Rydberg Atoms- Blackbody Shifts Alkali Rydberg Atoms – Blackbody Shifts Alkali Rydberg Atoms – Stark Shifts Alkali Rydberg Atoms - Hydrogen Alkali Rydberg Atoms - Hydrogen Alkali Rydberg Atoms - Hydrogen

• Manifold splits into 3 sub-levels – 2 degenerate.

• States behave as if it has a permanent electric dipole moment – 3eEa0 • The new states no longer have definite parity • The hydrogenic states of alkali atoms are degenerate and therefore have linear Stark shifts Alkali Rydberg Atoms- Low l Alkalis Alkali Rydberg Atoms – Low l Alkalis Alkali Rydberg Atoms – Stark Shifts Hydrogen

It is useful to compare and contrast Cs and H Stark states.

Cesium

T.F. Gallagher, Rydberg Atoms, Cambridge (1994). Cesium Alkali Rydberg Atoms – Stark Shifts Zimmerman et al., PRA 20, 2251 (1979). Avoided Crossing Appear Alkali Rydberg Atoms- Detection T.F. Gallagher, Rydberg 1 Atoms, Cambridge (1994).

Saddle point

Alkalis and Hydrogen differ in some important ways. • ‘normal’ ionization • ‘tunnel’ ionization Alkali Rydberg Atoms – Field Ionization Hydrogen

No avoided crossings in Hydrogen

T.F. Gallagher, Rydberg Atoms, Cambridge (1994). E. Luc Koenig and A. Bachelier, J. Phys. B 13, 1743 (1980). Alkali Rydberg Atoms – Field Ionization Li • Similar story to H • Some differences crossings two flavors of ionization

T.F. Gallagher, Rydberg Atoms, Cambridge (1994). Littmann et al., PRL 37, 486 (1976). Alkali Rydberg Atoms – Pulsed Field Ionization T.F. Gallagher, Rydberg Atoms, Cambridge (1994). Field ionization is an important way to detect Rydberg atoms.

Adiabatic vs. Diabatic ionization. Alkali Rydberg Atoms – Field Ionization

• Diabatic Behavior gives different thresholds • Adiabatic preserves zero field state ordering • Mixed behavior can occur Jeys et al., PRL 44, 390 (1980). T.F. Gallagher, Rydberg Atoms, Cambridge (1994). Alkali Rydberg Atoms - EIT EIT with Rydberg atoms Alkali Rydberg Atoms - EIT Alkali Rydberg Atoms – Magnetic Fields