Atomic electron transition



In atomic physics and chemistry, an atomic electron transition (also called an atomic transition, quantum jump, or quantum leap) is an electron changing from one energy level to another within an atom or artificial atom. The time scale of a quantum jump has not been measured experimentally. However, the Franck–Condon principle binds the upper limit of this parameter to the order of attoseconds.

Electrons jumping to energy levels of smaller n emit electromagnetic radiation in the form of a photon. Electrons can also absorb passing photons, which drives a quantum jump to a level of higher n. The larger the energy separation between the electron's initial and final state, the shorter the photons' wavelength.

History
Danish physicist Niels Bohr first theorized that electrons can perform quantum jumps in 1913. Soon after, James Franck and Gustav Ludwig Hertz proved experimentally that atoms have quantized energy states.

The observability of quantum jumps was predicted by Hans Dehmelt in 1975, and they were first observed using trapped ions of barium at University of Hamburg and mercury at NIST in 1986.

Theory
An atom interacts with the oscillating electric field:

with amplitude $$|\textbf{E}_0|$$, angular frequency $$\omega$$, and polarization vector $$\hat{\textbf{e}}_\mathrm{rad}$$. Note that the actual phase is $$ (\omega t - \textbf{k} \cdot \textbf{r}) $$. However, in many cases, the variation of $$ \textbf{k} \cdot \textbf{r} $$ is small over the atom (or equivalently, the radiation wavelength is much greater than the size of an atom) and this term can be ignored. This is called the dipole approximation. The atom can also interact with the oscillating magnetic field produced by the radiation, although much more weakly.

The Hamiltonian for this interaction, analogous to the energy of a classical dipole in an electric field, is $$ H_I = e \textbf{r} \cdot \textbf{E}(t) $$. The stimulated transition rate can be calculated using time-dependent perturbation theory; however, the result can be summarized using Fermi's golden rule: $$ Rate \propto |eE_0|^2 \times | \lang 2 | \textbf{r} \cdot \hat{\textbf{e}}_\mathrm{rad} |1 \rang |^2 $$ The dipole matrix element can be decomposed into the product of the radial integral and the angular integral. The angular integral is zero unless the selection rules for the atomic transition are satisfied.

Recent discoveries
In 2019, it was demonstrated in an experiment with a superconducting artificial atom consisting of two strongly-hybridized transmon qubits placed inside a readout resonator cavity at 15 mK, that the evolution of some jumps is continuous, coherent, deterministic, and reversible. On the other hand, other quantum jumps are inherently unpredictable.