Embedding Dissipation and Decoherence in Unitary Evolution Schemes

Dissipation and decoherence, and the evolution from pure to mixed states in quantum physics, are handled through master equations for the density matrix. By embedding elements of this matrix in a higher-dimensional Liouville-Bloch equation, the methods of unitary integration are adapted to solve for the density matrix as a function of time, including the nonunitary effects of dissipation and decoherence. The input requires only solutions of classical, initial value time-dependent equations. Results are illustrated for a damped, driven two-level system.

Figure 1

${\rho }_{22}(t)$ for an oscillating driving field with $J/\omega =3$, $A/\omega =45$, and damping values (a) $\Gamma /\omega =0$, (b) $\Gamma /\omega =0.35$, and (c) $\Gamma /\omega =5$.

Figure 2

As in Fig. 1, for ${\rho }_{12}(t)$ with (a) $\Gamma /\omega =0$ and (b) $\Gamma /\omega =0.35$. The entropy $S$ for $\Gamma /\omega =0.29$ is shown in (c).