Optimal shape of STIRAP pulses for large dissipation at the intermediate level

Abstract

We study the problem of maximizing population transfer efficiency in the STIRAP system for the case where the dissipation rate of the intermediate state is much higher than the maximum amplitude of the control fields. Under this assumption, the original three-level system can be reduced to a couple of equations involving the initial and target states only. We find the control fields which maximize the population transfer to the target state for a given duration T , without using any penalty involving the population of the lossy intermediate state, but under the constraint that the sum of the intensities of the pump and Stokes pulses is constant, so the total field has constant amplitude and the only control parameter is the mixing angle of the two fields. In the optimal solution the mixing angle changes in the bang-singular-bang manner, where the initial and final bangs correspond to equal instantaneous rotations, while the intermediate singular arc to a linear change with time. We show that the optimal angle of the initial and final rotations is the unique solution of a transcendental equation where duration T appears as a parameter, while the optimal slope of the intermediate linear change as well as the optimal transfer efficiency is expressed as functions of this optimal angle. The corresponding optimal solution recovers the counterintuitive pulse-sequence, with nonzero pump and Stokes fields at the boundaries. We also show with numerical simulations that transfer efficiency values close to the optimal derived using the approximate system can also be obtained with the original STIRAP system using dissipation rates comparable to the maximum control amplitude.

On the optimality of optical pumping for a closed Λ-system with large decay rates of the intermediate excited state

“…We also showed numerically that optical pumping remains optimal when the decay rate to the target state is larger than that to the initial state or the two rates are not very different from each other. The current methodology can also be extended to open systems, as we did in our recent work [38] for an open Λ-system with large decay in the intermediate level. An STIRAP-like optimal pulse-sequence was derived, with both pump and Stokes fields active.…”

Optimal Pulse Design for Dissipative-Stimulated Raman Exact Passage

“…where u p and u s are the pump and Stokes controls, respectively (corresponding to half of the traditional Rabi frequencies), with the lossy upper state |2 , via the dissipation rate Γ. Instead of analyzing such a complicated lossy system requiring specific adaptation of the cost [22], large dissipation [23], or assumption on the controls [24], we consider an alternative procedure to treat approximately but accurately the problem in the situation of interest having a relatively low dissipation rate without adapting the cost, nor restricting the controls. From the unlossy system H ≡ H Γ=0 , the effects of the loss are taken into account at the second order perturbation theory from the knowledge of the state amplitude of state |2 (in absence of dissipation):…”

Optimal shortcuts of stimulated Raman adiabatic passage in the presence of dissipation

“…We also discuss how the optimal solution can be further integrated with shortcuts to adiabaticity, as well as how the formulation of the problem in the transformed basis can take advantage of the spins-to-springs mapping. Note that in our recent work [43], we solved the same problem for the special case where dissipation is much larger than the amplitude of the applied fields, so that the intermediate state |2falsefalse⟩ can be adiabatically eliminated from the equations, leading to a simpler two-dimensional problem. Here, in contrast, we solve the full three-dimensional optimal control problem.…”