Two-level system in a thermal bath

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SUMMARY

The discussion focuses on calculating population transfer in a two-level quantum system immersed in a thermal bath, characterized by a resonant frequency ##\omega_0## and a mean frequency ##<\omega>## defined by the equation ##<\omega> = \sigma_\omega = \frac{\pi^2}{6}\frac{k_B T}{\hbar}##. The assumption is made that the difference between ##\omega_0## and ##<\omega>## is negligible compared to ##\omega_0##. The participants explore methods to quantify the population transfer to the excited state under perturbative conditions, where only a small fraction of the population transitions from the ground state.

PREREQUISITES
  • Understanding of quantum mechanics, specifically two-level systems.
  • Familiarity with thermal baths and their impact on quantum states.
  • Knowledge of perturbation theory in quantum mechanics.
  • Basic grasp of statistical mechanics, particularly the relationship between temperature and frequency.
NEXT STEPS
  • Study the derivation of population transfer equations in two-level systems.
  • Explore the role of thermal baths in quantum state transitions.
  • Learn about perturbation theory applications in quantum mechanics.
  • Investigate the effects of temperature on quantum systems using statistical mechanics.
USEFUL FOR

Quantum physicists, researchers in quantum mechanics, and students studying thermal effects on quantum systems will benefit from this discussion.

Malamala
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Hello! I have a 2-level system, with the resonant frequency ##\omega_0## in a thermal bath, by which I mean that I have photons with mean frequency and standard deviation of frequency at a temperature ##T## given by:

$$<\omega> = \sigma_\omega = \frac{\pi^2}{6}\frac{k_B T}{\hbar}$$
I can assume that ##|\omega_0 - <\omega>| << \omega_0##. If I start in the ground state and I assume I am in the perturbative regime (i.e. only a very small population gets transferred to the excited state), how can I calculate the population transfer to the excited state as a function of time?
 

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