Maybe it's due to the fact that orbitals of emitter atoms are more ionized-type when charge density increased but the atomic structure haven't been changed to the direction of neutrality enough without emission stimulations...

So are you saying that the electric field magnitude enhances the transition dipole moment of the emitter? Essentially a larger field leads to a more 'polarized' orbital? Something along those lines? That may be true, but the emission rate is normally expressed as a function of both the transition dipole moment and the electric field.

Thanks for the answer Esa!

Thanks guys. I know quite a bit more than I did a few days ago. Glad I asked.

In the review article: https://www.nature.com/articles/nphoton.2015.103

The first expression they use for the modified emission rate is proportional to (u12*E)^2. Here u12 is the transition dipole moment and E is the local electric field. This seems like the square of the dipolar energy associated with the transition.

Is it useful/true to think about this term meaning that the electric field (via dipolar energy associated with the transition) is perturbing the two level system and allows for the transition?

Also, one of my fellow students said that increasing the electric field also increases the photonic density of states (PDOS). I thought these were two separate effects? Is the electric field related to the PDOS?

So I bit the bullet and read the pertinent chapters from a quantum optics textbook (Knight and Gerry).

I believe that I understand the effect, just posting here for any people that come later with the same question.

The way that I understand it is that quantum mechanically, the electric field acts to mix the two states that are involved with the emission of light (the excited and ground state). This mixing can be enhanced by applying a larger electric field with the only caveat being that the polarization of the electric field needs to match the transition dipole moment associated with the electronic transition.

The reason that this effect does not disappear when the applied electric field goes to zero is that electromagnetic fields exhibit zero point fluctuations (zero point energy). Even with no photons present (minimum value of E) there is still a finite probability for the transition to occur due to the fluctuations. The reason that it is polarization independent is that the fluctuations can be thought of as occurring in all spatial directions.

Maybe I missed some subtleties, but I think that is the main point.

The expression for the energy density allows a fairly simple way to generalize this. The corresponding expressions are

ElectricEnergyDensity = E^2/(4 pi e0) where E is in Volts/meter

MagneticEnergyDensity = B^2/(mu0) where B is in Tesla

GravitationalEnergyDensity = g^2/(8 pi G) where g is in meters/second^2

muo is 4 pi * 10^-7 Newton second^2/Coulomb^2

eo is 1/(muo C^2) Farad/meter

At the earth's surface the equivalent magnetic field is about 380 Tesla, the electric field about 1.14 * 10^11 volts/meter. The laser intensity about 1.72 * 10^19 Watts/meter^2.

A version of the Purcell effect (enhanced emission) will be important in the laser vacuum experiments where all these fields can be calibrated against each other. The time varying gravitational potential and time varying gravitational potential gradient effects should be easily observable. And the magnetic and electric effects as well. I am hoping to check the gravitational energy density expression, because I think that 8 should be a 4. And to calibrate the global magnetic and gravitational observing networks against a pure vacuum experiment.

I mention this because enhanced emission can come about in a wide variety of ways. And most are dynamic. The static field effects can be related to the time dilation equation that is used for GPS time corrections. It is mostly used with only the gravitational potential and the velocity potential terms, but magnetic and electric potentials can be added when the energy density of those fields is comparable to, or exceeds, the gravitational energy density.

Because it is a dynamic effect, one can enhance or slow down pretty much any reaction with the proper combination of fields. Since our technology still cannot reach some of the levels required, the low energy experiments can set bound on the form of the relationships, the practical application for things like laser and flourescent enhancement, shot noise, chemical and nuclear reaction rate enhancement. I am a bit tired, so I cannot rattle off another dozen things I have looked into. But just wanted to comment about some things that seem to be coming together.

The only other thing that fits in somewhere is Mossbauer. If you model the reactions precisely, the recoil energy accounting, and magnetic dipole orientation measurement has to be precise. And it helps me to remember that every mixture of high frequencies - no matter how high - will have beat frequencies. I am mainly interested in frequencies below 1 Hz down to picoHertz and many of the fine differences are at that level or smaller.

I monitor global communities and see many connections being formed. Someone, somewhere, has looked at all of these things. If you cannot find what you want by focusing on the electric energy density, then go and look at the magnetic, gravitational, laser, nuclear and other energy density papers. They are mostly all saying the same thing, but in different units and scales. Enhancement and acceleration are universal processes that cut across all fields. Control of nuclear reactions by the proper shaped and timed fields would be a good thing to make into an engineering discipline, not just a bunch of scattered theories and hunches.

I liked all your comments. You would make a great group. If only ResearchGate would provide decent tools for sharing models and data and detailed comparisons, not just "ink on paper".

Richard Collins, The Internet Foundation