# How can a photon "stimulate emission" if it really does (Einstein coefficients)

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• freetheparticle
In summary: If the atom is in the ground state, then this photon has a frequency that matches the atom's ground state vibration. However, if the atom is in an excited state, then the photon has a frequency that matches the excited state vibration. The atom absorbs this photon, and its energy is transferred to the atom in an excited state, changing its state back to the ground state.
freetheparticle
Einstein coefficients tell us that there is some probability for an atom to go from E_1 to E_2 given by the coefficient of absorption. This is fine, but why is there only one coefficient (absorption) going from E_1 to E_2 and two for the transition E_2 to E_1? Spontaneous emission makes sense but I can't wrap my head around stimulated emission. How can a photon "stimulate emission" if it doesn't come into existence until it is emitted by the particle?

freetheparticle said:
How can a photon "stimulate emission" if it doesn't come into existence until it is emitted by the particle?

Stimulated emission means there are already photons present in the same state as the photon to be emitted by the particle. It is those photons that are already present that stimulate the emission.

Demystifier, vanhees71 and bhobba
PeterDonis said:
Stimulated emission means there are already photons present in the same state as the photon to be emitted by the particle. It is those photons that are already present that stimulate the emission.
Okay, but how does an external photon cause the particle to emit a photon of the same state? I don't see how it can encourage the particle to radiate a different photon.

freetheparticle said:
how does an external photon cause the particle to emit a photon of the same state?

Because of Bose-Einstein statistics: for bosons (photons are bosons), if there is already a particle present in a given state, the amplitude for another particle to transition to that state is increased.

bhobba
freetheparticle said:
Einstein coefficients tell us that there is some probability for an atom to go from E_1 to E_2 given by the coefficient of absorption. This is fine, but why is there only one coefficient (absorption) going from E_1 to E_2 and two for the transition E_2 to E_1? Spontaneous emission makes sense but I can't wrap my head around stimulated emission. How can a photon "stimulate emission" if it doesn't come into existence until it is emitted by the particle?
There cannot be something like "spontaneous absorption", because you cannot absorb a photon that is not present to begin with!

bhobba
I think Einstein first deduced the existence of stimulated emission by thermodynamical arguments, i.e. a system of a photon gas and atoms would never reach thermal equilibrium if only absorption and spontaneous emission took place.

It would reach thermal equilibrium, but not the right Planck distribution (i.e., a Bose-Einstein distribution for a gas of massless bosons with no conserved charge/particle-number) but something like a classical Boltzmann distribution for the em. field, which leads to the UV catastrophe.

hilbert2
I find it much easier to understand the processes of absorption and emission by thinking of fields and charged particle distributions.

Consider an electron distribution in the ground state of an atom (let's say an S-type wavefunction). To simplify, this has a charge distribution that is separated from the excited state charge distribution (let's say a P-type wavefunction), exactly by a time varying electric field that is the oscilliation of the EM field of the photon at the resonance frequency of the atom. Put in another way, the electric field of the light pulls the charged electrons in such a way as to create a new shape, and since the new shape (P wavefunction) is also stable/constructively interferring, it can be excited. This is absorption.

Stimulated emission can simply be explained as the reverse: a photons electric field with the same frequency but the opposite phase must be able to pull the electron distribution shape back to the original, so the atom de-excites, i.e. emits energy.

Spontaneous emission is the one which is tricky to explain, since this requires the vacuum field to act as catalyst to change the wavefunction of the atom, and can obviously only happen as emission, since there is no energy to allow absorption.

vanhees71 and BvU
freetheparticle said:
Einstein coefficients tell us that there is some probability for an atom to go from E_1 to E_2 given by the coefficient of absorption. This is fine, but why is there only one coefficient (absorption) going from E_1 to E_2 and two for the transition E_2 to E_1? Spontaneous emission makes sense but I can't wrap my head around stimulated emission. How can a photon "stimulate emission" if it doesn't come into existence until it is emitted by the particle?
Actually, spontaneous emission is harder to explain. It goes into the realm of Quantum Field Theory because that's the most fundamental level theory. It is the interaction of a charged particle with the electromagnetic field at the ground state. The total energy of such vacuum field is well defined, but are fluctuating and this is what the charged particle is interacting with.

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freetheparticle said:
Okay, but how does an external photon cause the particle to emit a photon of the same state? I don't see how it can encourage the particle to radiate a different photon.
Here is a semi-classical intuitive picture. The external photon has a frequency ##\omega##, so it stimulates the electron to oscillate with the frequency ##\omega-\omega_e##, where ##\omega_e=E_e/\hbar## is the electron's frequency before the stimulation. This oscillation of the electron creates the radiation from the electron, which manifests as emittion of a new photon.

HAYAO said:
Actually, in terms of Quantum Field Theory, spontaneous emission is harder to explain. It is the interaction of a charged particle with the electromagnetic field at the ground state. The total energy of such vacuum field is well defined, but are fluctuating and this is what the charged particle is interacting with.
To the contrary, only with QFT you can explain spontaneous emission. In fact, spontaneous emission is the most simple phenomenon which indicates that the quantization of the em. field is necessary to describe all phenomena (including black-body radiation), while all tree-level results for scattering (including Compton scattering and the photoelectric effect) are consistent with semi-classical (relativistic) QT (treating only the charged particles as "quantized" and keeping the em. field classical).

weirdoguy, HAYAO and BvU
vanhees71 said:
To the contrary, only with QFT you can explain spontaneous emission. In fact, spontaneous emission is the most simple phenomenon which indicates that the quantization of the em. field is necessary to describe all phenomena (including black-body radiation), while all tree-level results for scattering (including Compton scattering and the photoelectric effect) are consistent with semi-classical (relativistic) QT (treating only the charged particles as "quantized" and keeping the em. field classical).
Oh yes, of course. I made a grammatical mistake.

## 1. How can a photon stimulate emission?

According to Einstein's theory of spontaneous and stimulated emission, a photon can stimulate the emission of another photon by interacting with an excited atom or molecule. This interaction causes the excited atom or molecule to release its stored energy in the form of a photon, resulting in stimulated emission.

## 2. What are Einstein coefficients?

Einstein coefficients are numerical values that describe the probability of an atom or molecule undergoing spontaneous or stimulated emission. These coefficients were first introduced by Albert Einstein in his theory of radiation, and they are used to calculate the rate of stimulated emission in a given system.

## 3. How do Einstein coefficients relate to stimulated emission?

Einstein coefficients play a crucial role in the process of stimulated emission. The coefficient for stimulated emission represents the probability of an excited atom or molecule undergoing stimulated emission when it is interacting with a photon of the correct energy. This probability is dependent on the number of photons present and the properties of the excited atom or molecule.

## 4. Can a photon stimulate emission in any type of material?

Yes, a photon can stimulate emission in any material that contains atoms or molecules capable of being excited. This includes gases, liquids, and solids. However, the efficiency of stimulated emission may vary depending on the properties of the material, such as its density and composition.

## 5. What are the practical applications of stimulated emission?

Stimulated emission has many practical applications, including in laser technology, optical amplifiers, and quantum computing. Lasers, in particular, rely on stimulated emission to produce a highly coherent and powerful beam of light. Optical amplifiers, on the other hand, use stimulated emission to amplify weak signals in optical communication systems.

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