Pseudomodes as an effective description of memory: Non-Markovian dynamics of two-state systems in structured reservoirs

We investigate the non-Markovian dynamics of two-state systems in structured reservoirs. We establish a connection between two theoretical quantum approaches, the pseudomodes [B. M. Garraway, Phys. Rev. A 55, 2290 (1997)] and the recently developed non-Markovian quantum jump method [J. Piilo et al., Phys. Rev. Lett. 100, 180402 (2008)]. This connection provides a clear physical picture of how the structured reservoir affects the system dynamics, suggesting the role of the pseudomodes as effective description of environmental memory.

Figure 1

Diagrammatic representation of the atom-pseudomode dynamics. (a) Atom interacting with a Lorentzian structured reservoir: the atom interacts with a single pseudomode which leaks into a Markovian reservoir. (b) Atom in a “simple” photonic band gap: we see a more complex memory architecture, the second pseudomode acts as a memory for the atom, while the first pseudomode acts as a memory for the first one.

Figure 2

The solid line is the decay rate for a two-level atom in a Lorentzian structured reservoir. The dashed line is the compensated rate of change of the pseudomode population $d{\left|b_1\left(t\right)\right|}^2/dt+\Gamma {\left|b_1\left(t\right)\right|}^2$. The units for the rates on the vertical and horizontal axis are ${\gamma }_0$ and $1/{\gamma }_0$ with ${\gamma }_0=4{\Omega }_0^2/\Gamma$ Markovian decay rate of the atom. We have taken the values $\Gamma =0.6{\gamma }_0$, ${\Omega }_0=\sqrt{0.15}{\gamma }_0$, and ${\omega }_c-{\omega }_0=4\Gamma$.