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- 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?

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?