What is the difference between the DC and AC Stark effects?

The DC Stark effect is the shift in a static electric field, governed by the static polarizability. The AC Stark effect is the shift in an oscillating field, governed by the frequency-dependent dynamic polarizability, and is the mechanism behind optical dipole trapping.

Why are Rydberg atoms so sensitive to electric fields?

Rydberg atoms have very large orbits and hence enormous polarizabilities and dipole moments, so even modest electric fields produce large Stark shifts and can ionize them, which is the basis of state-selective field ionization detection.

The Stark Effect

The Stark effect is the shift and splitting of atomic energy levels and spectral lines produced by an external electric field.

Definition

The Stark effect is the change in atomic energy levels caused by an external electric field through the interaction of the field with the atom's permanent or induced electric dipole moment; it is linear in the field for states with degenerate opposite-parity components and quadratic otherwise.

Scope

This topic covers the response of atoms to applied electric fields: the linear Stark effect that occurs in hydrogen's degenerate levels, the quadratic Stark effect proportional to atomic polarizability that dominates in most atoms, the strong sensitivity of high Rydberg states to fields, and the AC (dynamic) Stark shift produced by oscillating optical fields. It treats how these shifts are calculated by perturbation theory.

Core questions

How does an electric field shift and split atomic energy levels?
Why is the effect linear in hydrogen but quadratic in most other atoms?
How does the Stark shift depend on atomic polarizability?
What is the AC Stark shift produced by an oscillating field?

Key concepts

Electric dipole interaction
Linear versus quadratic Stark effect
Static and dynamic polarizability
Stark shift of Rydberg states
AC Stark (light) shift
Field ionization

Key theories

Linear and quadratic Stark effect: First-order perturbation theory gives a non-zero linear shift only for degenerate opposite-parity states, as in hydrogen; otherwise the leading effect is second order, a quadratic shift proportional to the static polarizability of the level.
AC Stark (light) shift: An oscillating electric field, such as that of a laser, shifts atomic levels through their dynamic polarizability; this light shift underlies optical dipole traps and is a key systematic effect in optical atomic clocks.

Clinical relevance

Stark shifts enable electric-field control of atoms: the AC Stark shift provides the trapping potential of optical dipole traps and optical lattices, must be carefully compensated as a systematic in optical clocks, and the extreme field sensitivity of Rydberg atoms makes them effective field sensors and a resource for quantum technology.

History

Stark discovered the splitting of hydrogen lines in an electric field in 1913, and the linear effect was an early triumph of both the old quantum theory (Epstein, Schwarzschild) and of Schrödinger's wave mechanics. The quadratic effect and, much later, the AC Stark shift driven by laser fields extended the phenomenon to atom trapping and precision metrology.

Key figures

Johannes Stark
Erwin Schrödinger
Paul Epstein

Seminal works

stark1914
bransden2003

Frequently asked questions

What is the difference between the DC and AC Stark effects?: The DC Stark effect is the shift in a static electric field, governed by the static polarizability. The AC Stark effect is the shift in an oscillating field, governed by the frequency-dependent dynamic polarizability, and is the mechanism behind optical dipole trapping.
Why are Rydberg atoms so sensitive to electric fields?: Rydberg atoms have very large orbits and hence enormous polarizabilities and dipole moments, so even modest electric fields produce large Stark shifts and can ionize them, which is the basis of state-selective field ionization detection.