Notes on dissipation

How to consider the dissipation in quantum system, especially the cavity QED system? In my research, two different methods were used: master equation and quantum jump.

Let’s consider the main dissipation in the cavity QED system firstly. There are two channels the system lossing its coherence, the spontaneous emission of atoms and the cavity loss. The root of spontaneous emission is the coupling between atoms and the modes other than cavity modes. The state information losses during spontaneous emission. The coupling between cavity field and the atoms vibration located in the cavity wall lead to cavity loss.

The master equation method includes the dissipation via adding spontaneous emission and cavity loss items in the equation. To solve the equation, we should express the equation in the computational basis and solve the matrix equaition. This is not a easy task.

The quantum jump approach bases on the principle of quantum mechanics that the quantum system is probalisitic. During the evolution, for a single atom, it could jump and could not jump. If we focus on the latter condition, we can get the probability that the system doesn’t decay. Conditional Hamiltonian is defined to calculate this probability. This method is suit for the system contains a few atoms and cavity modes.