Measurement-assisted Landau-Zener transitions

Abstract

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 non-selective 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.Comment: 17 pages, 7 figure

Quantum dynamics intervened by repeated nonselective measurements

“…With the use of one nonselective measurement the transition rate can be diminished at least to one half [8]. We conjecture that with the use of N nonselective measurements the minimal transition probability in the regime ǫ ≫ ∆ 2 diminishes as O( 1 N ).…”

“…It is Eq. (3), which is usually referred to as nonselective measurement in the literature [6][7][8]. In what follows, we also focus on nonselective measurement channels Λ of the form (3).…”

Flows in non-equilibrium quantum systems and quantum photosynthesis

“…Substituting these expressions into the equations for the diagonal part of the density matrix, we obtain the system of linear equations for the stationary state Eigenvalues of this matrix are 0, λ ± (s), where λ ± (s) are deformations of λ ± given by (23). Comparison of this system of equations and the system (13), (14, (15) implies the following proposition.…”

Minimal Time Generation of Density Matrices for a Two-Level Quantum System Driven by Coherent and Incoherent Controls

“…Coherent control drives essentially the Hamiltonian aspects of the dynamics, and is typically realized by a shaped laser pulse [1][2][3][4][5]. Incoherent control drives non-Hamiltonian, i.e., dissipative aspects of the dynamics, and can be realized by reservoir engineering [15], measurement apparatus [6,16], etc.…”