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- Title
General tracking control of arbitrary N-level quantum systems using piecewise time-independent potentials.
- Authors
Delben, G.; Luz, M.
- Abstract
Here we propose a tracking quantum control protocol for arbitrary N-level systems. The goal is to make the expected value of an observable $${\mathcal O}$$ to follow a predetermined trajectory S( t). For so, we drive the quantum state $$|\varPsi (t) \rangle $$ evolution through an external potential V which depends on $$M_V$$ tunable parameters (e.g., the amplitude and phase (thus $$M_V = 2$$ ) of a laser field in the dipolar condition). At instants $$t_n$$ , these parameters can be rapidly switched to specific values and then kept constant during time intervals $$\Delta t$$ . The method determines which sets of parameters values can result in $$\langle \varPsi (t) | {\mathcal O} |\varPsi (t) \rangle = S(t)$$ . It is numerically robust (no intrinsic divergences) and relatively fast since we need to solve only nonlinear algebraic (instead of a system of coupled nonlinear differential) equations to obtain the parameters at the successive $$\Delta t$$ 's. For a given S( t), the required minimum $$M_V = M_{\min }$$ 'degrees of freedom' of V attaining the control is a good figure of merit of the problem difficulty. For instance, the control cannot be unconditionally realizable if $$M_{\min } > 2$$ and V is due to a laser field (the usual context in real applications). As it is discussed and exemplified, in these cases a possible procedure is to relax the control in certain problematic (but short) time intervals. Finally, when existing the approach can systematically access distinct possible solutions, thereby allowing a relatively simple way to search for the best implementation conditions. Illustrations for 3-, 4-, and 5-level systems and some comparisons with calculations in the literature are presented.
- Subjects
QUANTUM mechanics; TRAJECTORIES (Mechanics); TRACKING control systems; QUANTUM states; QUANTUM theory
- Publication
Quantum Information Processing, 2016, Vol 15, Issue 5, p1955
- ISSN
1570-0755
- Publication type
Article
- DOI
10.1007/s11128-016-1241-z