Quantum evolution in the stroboscopic limit of repeated measurements

Abstract

We consider a quantum system dynamics caused by successive selective and non-selective measurements of the probe coupled to the system. For the finite measurement rate ${\tau }^{-1}$ and the system-probe interaction strength $\gamma$ we derive analytical evolution equations in the stroboscopic limit $\tau \to 0$ and ${\gamma }^2\tau =\mathrm{const}$, which can be considered as a deviation from the Zeno subspace dynamics on a longer timescale $T\sim ({\gamma }^2\tau {)}^{-1}\gg {\gamma }^{-1}$. Non-linear quantum dynamics is analyzed for selective stroboscopic projective measurements of an arbitrary rank. Non-selective measurements are shown to induce the semigroup dynamics of the system-probe aggregate. Both non-linear and decoherent effects become significant at the timescale $T\sim ({\gamma }^2\tau {)}^{-1}$, which is illustrated by a number of examples.

arXiv comment9 pages, 7 figures, published version

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