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arXiv:0902.2596 · Physical Review A

Control of quantum dynamics by optimized measurements

Feng Shuang, Mianlai Zhou, Alexander Nikolaevich Pechen, Re-Bing Wu, Ofer M. Shir, HERSCHEL A. RABITZ

Published Dec 29, 2008• 39 citations
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Abstract

Quantum measurements are considered for optimal control of quantum dynamics with instantaneous and continuous observations utilized to manipulate population transfer. With an optimal set of measurements, the highest yield in a two-level system can be obtained. An analytical solution is given for the problem of population transfer by measurement-assisted coherent control in a three-level system with dynamical symmetry. The anti-Zeno effect is recovered in the controlled processes. Demonstrations show that suitable observations can be powerful tools in the manipulation of quantum dynamics.

DOI
10.1103/physreva.78.063422

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Quantum measurements are considered for optimal control of quantum dynamics with instantaneous and continuous observations utilized to manipulate population transfer. With an optimal set of measurements, the highest yield in a two-level system can be obtained. An analytical solution is given for the problem of population transfer by measurement-assisted coherent control in a three-level system with dynamical symmetry. The anti-Zeno effect is recovered in the controlled processes. Demonstrations show that suitable observations can be powerful tools in the manipulation of quantum dynamics.
This paper explores the utility of instantaneous and continuous observations in the optimal control of quantum dynamics. Simulations of the processes are performed on several multilevel quantum systems with the goal of population transfer. Optimal control fields are shown to be capable of cooperating or fighting with observations to achieve a good yield, and the nature of the observations may be optimized to more effectively control the quantum dynamics. Quantum observations also can break dynamical symmetries to increase the controllability of a quantum system. The quantum Zeno and anti-Zeno effects induced by observations are the key operating principles in these processes. The results indicate that quantum observations can be effective tools in the control of quantum dynamics.
A general scheme is presented for controlling quantum systems using evolution driven by nonselective von Neumann measurements, with or without an additional tailored electromagnetic field. As an example, a two-level quantum system controlled by nonselective quantum measurements is considered. The control goal is to find optimal system observables such that consecutive nonselective measurement of these observables transforms the system from a given initial state into a state which maximizes the expected value of a target operator (the objective). A complete analytical solution is found including explicit expressions for the optimal measured observables and for the maximal objective value given any target operator, any initial system density matrix, and any number of measurements. As an illustration, upper bounds on measurement-induced population transfer between the ground and the excited states for any number of measurements are found. The anti-Zeno effect is recovered in the limit of an infinite number of measurements. In this limit the system becomes completely controllable. The results establish the degree of control attainable by a finite number of measurements.
This paper explores the manipulation between eigenstates in a two-level system by a sequence of instantaneous projective measurements. Three cases of the manipulations are studied: the manipulation of optimal measurement-based control; the optimal measurement-based manipulation with the effect of free evolution of system; and the external control fields being used to compensate for the effect caused by the free evolution. Numerical simulations are conducted to verify the results obtained from the theoretically analytical solutions. The optimal parameters for each manipulation case are obtained. The experimental results indicate that the external control fields can make the optimal measurement-based control more effective.
Nonselective quantum measurements, i.e., measurements without reading the results, are often considered as a resource for manipulating quantum systems. In this work, we investigate optimal acceleration of the Landau-Zener (LZ) transitions by nonselective quantum measurements. We use the measurements of a population of a diabatic state of the LZ system at certain time instants as control and find the optimal time instants which maximize the LZ transition. We find surprising nonmonotonic behavior of the maximal transition probability with increase of the coupling parameter when the number of measurements is large. This transition probability gives an optimal approximation to the fundamental quantum Zeno effect (which corresponds to continuous measurements) by a fixed number of discrete measurements. The difficulty for the analysis is that the transition probability as a function of time instants has a huge number of local maxima. We resolve this problem both analytically by asymptotic analysis and numerically by the development of efficient algorithms mainly based on the dynamic programming. The proposed numerical methods can be applied, besides this problem, to a wide class of measurement-based optimal control problems.
We study quantum system dynamics driven by continuous laser fields under the measurement process. In order to take into account the system transition due to the measurement, we define the superoperator which eliminates the coherence relevant to the measured quantum states. We clarify that the dynamics of the measured states is frozen in the frequent measurement limit, while the space spanned by unmeasured states is isolated from the original system. We also derive the effective Liouvillian which governs incoherent population dynamics under the condition, in which measurements are frequently applied. We apply the formulation to two-level and Lambda-type three-level systems and clarify how the quantum measurements hinder the coherent population dynamics driven by the continuous laser fields in practical examples. Analysis on the laser field amplitude dependency of the final distribution in the t-->infinity limit suggests the possibility of the measurement-assisted quantum control.
Quantum systems with dynamical symmetries have conserved quantities that are preserved under coherent control. Therefore, such systems cannot be completely controlled by means of only coherent control. In particular, for such systems, the maximum transition probability between some pairs of states over all coherent controls can be less than one. However, incoherent control can break this dynamical symmetry and increase the maximum attainable transition probability. The simplest example of such a situation occurs in a three-level quantum system with dynamical symmetry, for which the maximum probability of transition between the ground and intermediate states using only coherent control is 1/2, whereas it is about 0.687 using coherent control assisted by incoherent control implemented through the non-selective measurement of the ground state, as was previously analytically computed. In this work, we study and completely characterize all critical points of the kinematic quantum control landscape for this measurement-assisted transition probability, which is considered as a function of the kinematic control parameters (Euler angles). The measurement-driven control used in this work is different from both quantum feedback and Zeno-type control. We show that all critical points are global maxima, global minima, saddle points or second-order traps. For comparison, we study the transition probability between the ground and highest excited states, as well as the case when both these transition probabilities are assisted by incoherent control implemented through the measurement of the intermediate state.