Absorption and emission spectrum in quantum optics

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• Cedric Chia
In summary, resonance fluorescence is a phenomenon where light is emitted from a quantum dot, atom, or defect center when an electric field is applied. 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.

Cedric Chia

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?

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.

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.

yucheng

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