Teaching the environment to control quantum systems

A nonequilibrium, generally time-dependent, environment whose form is deduced by optimal learning control is shown to provide a means for incoherent manipulation of quantum systems. Incoherent control by the environment (ICE) can serve to steer a system from an initial state to a target state, either mixed or in some cases pure, by exploiting dissipative dynamics. Implementing ICE with either incoherent radiation or a gas as the control is explicitly considered, and the environmental control is characterized by its distribution function. Simulated learning control experiments are performed with simple illustrations to find the shape of the optimal nonequilibrium distribution function that best affects the posed dynamical objectives.

Figure 1

The Planck density of black body radiation (upper curve) and the density (un-normalized) of nonequilibrium radiation composed of three nearly monochromatic sources (lower curve).

Figure 2

Results of ICE simulations with tailored incoherent radiation as the control for target states (a) ${\rho }^{\mathrm{T}}=\mathrm{diag}(0.3,0.3,0.2,0.2)$, (b) ${\rho }^{\mathrm{T}}=\mathrm{diag}(0.3,0.2,0.3,0.2)$, and (c) ${\rho }^{\mathrm{T}}=\mathrm{diag}(0.4,0.1,0.4,0.1)$. Each case shows the objective function vs GA generation, the optimal spectral distribution vs frequency, and the evolution of the diagonal matrix elements of the density matrix for the optimal distribution. In the plots for the objective function the upper curve is the average value for the objective function and the lower one is the best value in each generation.

Figure 3

Results of ICE simulations with a surrounding nonequilibrium gas as the control for target states (a) ${\rho }^{\mathrm{T}}=\mathrm{diag}(0.3,0.3,0.2,0.2)$, (b) ${\rho }^{\mathrm{T}}=\mathrm{diag}(0.3,0.2,0.3,0.2)$, and (c) ${\rho }^{\mathrm{T}}=\mathrm{diag}(0.4,0.1,0.4,0.1)$. Each case shows the objective function vs GA generation, the optimal distribution vs momentum, and the evolution of the diagonal elements of the density matrix for the optimal distribution. In the plots for the objective function the upper curve is the average value for the objective function and the lower one is the best value in each generation.