Non-radiative density matrix EOM

In summary, the dissipative term of the equation of motion for the density matrix in a 3 level system coupled with 2 lasers can be written as a sum involving the rates of transitions between different states. This term is important for understanding how the system dissipates energy and can be found in equation 4.4 of the provided article.
  • #1
luxiaolei
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Dear all, Could anyone please explain to me for a 3 level syste, coupled with 2 lasers, what is the equation describing the disspative term of the equation of motion of the density matrix? I am looking for a non-radiative decay, namely the overall population should conserved.

I have found this article, on equation 4.4, it looks like answered my question, but very confused with the notation it used.

http://www.diss.fu-berlin.de/diss/servlets/MCRFileNodeServlet/FUDISS_derivate_000000003495/4_4_dynamics.pdf?hosts=

thank you so much in advance.
 
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  • #2
The equation you are looking for is the dissipative term of the equation of motion for the density matrix. This term describes how the system dissipates energy, and can be written as:\rho_{ij} \dot{=} \sum_k \left( \Gamma_{ikj} \rho_{kk} - \frac{1}{2} \left( \Gamma_{ijk} + \Gamma_{jik} \right) \rho_{ij} \right),where \Gamma_{ijk} is the rate at which the transition from state i to state j occurs due to the interaction with state k. This term is typically used to describe non-radiative decay, meaning that the total population is conserved.
 

1. What is the "Non-radiative density matrix EOM"?

The Non-radiative density matrix EOM (Equation of Motion) is a mathematical framework used in quantum physics to describe the evolution of a multi-electron system in the presence of non-radiative (or non-dissipative) interactions. It is used to calculate the time-dependent behavior of the system's density matrix, which contains information about the probabilities of different quantum states of the system.

2. What are non-radiative interactions?

Non-radiative interactions refer to any type of interaction between particles that do not involve the emission or absorption of electromagnetic radiation (such as light). Examples of non-radiative interactions include Coulombic interactions between charged particles and exchange interactions between particles with spin.

3. What is the importance of the Non-radiative density matrix EOM in scientific research?

The Non-radiative density matrix EOM is an important tool in understanding and predicting the behavior of complex quantum systems, particularly those involving multiple interacting particles. It is used in various fields of research, including quantum chemistry, condensed matter physics, and materials science.

4. How is the Non-radiative density matrix EOM different from the Radiative density matrix EOM?

The Radiative density matrix EOM is a similar mathematical framework, but it includes interactions involving the emission and absorption of electromagnetic radiation. The Non-radiative density matrix EOM only considers interactions that do not involve radiation, making it more suitable for systems that do not exhibit significant radiative behavior.

5. Are there any limitations to the Non-radiative density matrix EOM?

Like any mathematical model, the Non-radiative density matrix EOM has its limitations. It assumes that the system is in a state of thermal equilibrium, and it does not account for the effects of external perturbations or quantum measurement. Additionally, it becomes significantly more complex when applied to systems with a large number of particles or when higher-order interactions are considered.

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