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Atomic electron transition

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From Wikipedia, the free encyclopedia

Change of an electron between energy levels within an atom

An electron in aBohr model atom, moving fromquantum leveln = 3 ton = 2 and releasing aphoton. The energy of an electron is determined by its orbit around the atom, The n = 0 orbit, commonly referred to as theground state, has the lowest energy of all states in the system.

Inatomic physics andchemistry, anatomic electron transition (also called an atomic transition, quantum jump, or quantum leap) is anelectron changing from oneenergy level to another within anatom^[1] orartificial atom.^[2] The time scale of a quantum jump has not been measured experimentally. However, theFranck–Condon principle binds the upper limit of this parameter to the order ofattoseconds.^[3]

Electrons canrelax into states of lower energy by emittingelectromagnetic radiation in the form of a photon. Electrons can also absorb passing photons, whichexcites the electron into a state of higher energy. The larger the energy separation between the electron's initial and final state, the shorter the photons'wavelength.^[4]

History

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Danish physicistNiels Bohr first theorized that electrons can perform quantum jumps in 1913.^[5] Soon after,James Franck andGustav Ludwig Hertz proved experimentally that atoms have quantized energy states.^[6]

The observability of quantum jumps was predicted byHans Dehmelt in 1975, and they were first observed usingtrapped ions ofbarium atUniversity of Hamburg andmercury atNIST in 1986.^[4]

Theory

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An atom interacts with the oscillatingelectric field:

E(t)=|{\textbf {E}}_{0}|Re(e^{-i{\omega }t}{\hat {\textbf {e}}}_{\mathrm {rad} })

with amplitude $|{\textbf {E}}_{0}|$ , angular frequency $\omega$ , and polarization vector ${\hat {\textbf {e}}}_{\mathrm {rad} }$ .^[7] 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 oscillatingmagnetic 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 usingtime-dependent perturbation theory; however, the result can be summarized usingFermi's golden rule: $Rate\propto |eE_{0}|^{2}\times |\langle 2|{\textbf {r}}\cdot {\hat {\textbf {e}}}_{\mathrm {rad} }|1\rangle |^{2}$ The dipole matrix element can be decomposed into the product of the radial integral and the angular integral. The angular integral is zero unless theselection rules for the atomic transition are satisfied.

Recent discoveries

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In 2019, it was demonstrated in an experiment with a superconductingartificial atom consisting of two strongly-hybridizedtransmon qubits placed inside a readout resonator cavity at 15 mK, that the evolution of some jumps is continuous, coherent, deterministic, and reversible.^[8] On the other hand, other quantum jumps are inherently unpredictable.^[9]