Open Quantum Systems

This chapter explores open quantum systems, shedding light on their behavior. As a concrete illustration of such systems, we meticulously examine the interaction between a two-level atom and the reservoir consisting of free space modes. We employ the Born-Markov approximation to tackle the Weisskopf-Wigner problem of the relaxation of a two-level atom within this reservoir. Within the Schrödinger picture, we introduce a pivotal concept: the density matrix. Through its introduction, we derive the von Neumann equation describing the time evolution of this matrix. Furthermore, we unveil the Lindblad equation and demonstrate its practical application in addressing radiation phenomena. We also derive Fermi’s golden rule, a fundamental expression in quantum mechanics, and discuss its scope and limitations. Lastly, we derive the operator Heisenberg-Langevin equations, deploying them to describe the dynamic behavior of a two-level atom under the influence of an external field. These equations also guide us in unraveling the spectrum of such a system, providing a comprehensive insight into its behavior.