A Absorption and emission spectrum in quantum optics

Cedric Chia
Messages
21
Reaction score
1
TL;DR Summary
Absorption spectrum for a quantum dot
The emission spectrum or resonance fluorescence for a quantum dot, atom or defect center are discussed in many quantum optics textbook, for example see "Quantum Optics" by Marlan O. Scully and M. Suhail Zubairy Chapter 10 , "Quantum Optics" by D. F. Walls and Gerard J. Milburn Chapter 10 and "Quantum Optics" by Raymond Chiao and John Garrison Chapter 14.

In these textbooks, the formula for resonance fluorescence is given by:
$$
\alpha(\omega)=Re\int_0^{\infty}dt\left<E^{(-)}(t)E^{(+)}(t+\tau)\right>e^{i\omega\tau}
$$
where one usually relates the electric field operator with the atomic raising/lowering operator:
$$
\left<E^{(+)}(t)\right>\propto\left<\sigma\right>
$$

But what about the formula for absorption spectrum? Where can I find discussion on the absorption spectrum? And what if I have a system coupled to local vibrational modes (a polaron), how would that change the formula of emission and absorption spectrum?
 
Physics news on Phys.org
I know very little about quantum dots, but I do remember a review paper on spectral line shapes: van Vleck J H and Huber D L 1977, Rev. Mod. Phys. 49, 939-959. Both, absorption coefficients and emissivities can be expressed in terms of Fourier transforms of the dipole moment auto-correlation function, or more generally, of the current density fluctuations.
 
  • Like
Likes yucheng and Cedric Chia
WernerQH said:
spectral line shapes: van Vleck J H and Huber D L 1977, Rev. Mod. Phys. 49, 939-959. Both, absorption coefficients and emissivities can be expressed in terms of Fourier transforms of the dipole moment auto-correlation function, or more generally, of the current density fluctuations.
Is this not found in spectroscopy texts/monographs (or at least rather quantum mechanical ones as opposed to semiclassical)?
 
That's a very general basic principle. In linear-response theory the response function is given in terms of the (retarded) autocorrelation function of the source. It's also known as the Green-Kubo formula.
 
Not an expert in QM. AFAIK, Schrödinger's equation is quite different from the classical wave equation. The former is an equation for the dynamics of the state of a (quantum?) system, the latter is an equation for the dynamics of a (classical) degree of freedom. As a matter of fact, Schrödinger's equation is first order in time derivatives, while the classical wave equation is second order. But, AFAIK, Schrödinger's equation is a wave equation; only its interpretation makes it non-classical...
I am not sure if this falls under classical physics or quantum physics or somewhere else (so feel free to put it in the right section), but is there any micro state of the universe one can think of which if evolved under the current laws of nature, inevitably results in outcomes such as a table levitating? That example is just a random one I decided to choose but I'm really asking about any event that would seem like a "miracle" to the ordinary person (i.e. any event that doesn't seem to...
Back
Top