Spontaneous emission is ultimately responsible for most of the light we see all around us; it is so ubiquitous that there are many names given to what is essentially the same process.
If atoms (or molecules) are excited by some means other than heating, the spontaneous emission is called luminescence.
And there are different forms of luminescence depending on how excited atoms are produced (electroluminescence, chemiluminescence etc.).
If the excitation is effected by the absorption of radiation the spontaneous emission is called fluorescence.
Sometimes molecules have a metastable level and continue to fluoresce long after the exciting radiation is turned off; this is called phosphorescence.
Spontaneous emission cannot be explained by classical electromagnetic theory and is fundamentally a quantum process.
[5] Contemporary physicists, when asked to give a physical explanation for spontaneous emission, generally invoke the zero-point energy of the electromagnetic field.
[6][7] In 1963, the Jaynes–Cummings model[8] was developed describing the system of a two-level atom interacting with a quantized field mode (i.e. the vacuum) within an optical cavity.
It gave the nonintuitive prediction that the rate of spontaneous emission could be controlled depending on the boundary conditions of the surrounding vacuum field.
, it may spontaneously decay to a lower lying level (e.g., the ground state) with energy
An energy level diagram illustrating the process of spontaneous emission is shown below:
: Spontaneous transitions were not explainable within the framework of the Schrödinger equation, in which the electronic energy levels were quantized, but the electromagnetic field was not.
Spontaneous emission in free space depends upon vacuum fluctuations to get started.
That is, the electromagnetic field has infinitely more degrees of freedom, corresponding to the different directions in which the photon can be emitted.
In the presence of electromagnetic vacuum modes, the combined atom-vacuum system is explained by the superposition of the wavefunctions of the excited state atom with no photon and the ground state atom with a single emitted photon: where
[4] To solve for the transition amplitude, one needs to average over (integrate over) all the vacuum modes, since one must consider the probabilities that the emitted photon occupies various parts of phase space equally.
The "spontaneously" emitted photon has infinite different modes to propagate into, thus the probability of the atom re-absorbing the photon and returning to the original state is negligible, making the atomic decay practically irreversible.
Such irreversible time evolution of the atom-vacuum system is responsible for the apparent spontaneous decay of an excited atom.
If one were to keep track of all the vacuum modes, the combined atom-vacuum system would undergo unitary time evolution, making the decay process reversible.
The theory of the spontaneous emission under the QED framework was first calculated by Victor Weisskopf and Eugene Wigner in 1930 in a landmark paper.
[12][13][14] The Weisskopf-Wigner calculation remains the standard approach to spontaneous radiation emission in atomic and molecular physics.
[15] Dirac had also developed the same calculation a couple of years prior to the paper by Wigner and Weisskopf.
In a homogeneous medium, such as free space, the rate of spontaneous emission in the dipole approximation is given by: where
The above equation clearly shows that the rate of spontaneous emission in free space increases proportionally to
In contrast with atoms, which have a discrete emission spectrum, quantum dots can be tuned continuously by changing their size.
-frequency dependence of the spontaneous emission rate as described by Fermi's golden rule.
Meta-stable states form a very important feature that is exploited in the construction of lasers.
Specifically, since electrons decay slowly from them, they can be deliberately piled up in this state without too much loss and then stimulated emission can be used to boost an optical signal.
If emission leaves a system in an excited state, additional transitions can occur, leading to atomic radiative cascade.
[19] These correlations were used by John Clauser[20]: 880 [21]: 592 and Alain Aspect[22] in work that contributed to their 2022 Nobel prize in physics.