Abstract
Conventionally, the effect of measurements on a quantum system is assumed to introduce decoherence, which renders the system classical-like. We consider here a microscopic meter, that is, an auxiliary essentially quantum system whose state is measured repeatedly, and show that it can be employed to induce transitions from classical states into inherently quantumlike states. The meter state is assumed to be lost in the environment and we derive a non-Markovian master equation for the dynamic system in the case of nondemolition coupling to the meter; this equation can be cast in the form of an $({N}_{a})$th-order differential equation in time, where ${N}_{a}$ is the dimension of the meter basis. We apply the approach to a harmonic oscillator coupled to a spin-$\frac{1}{2}$ meter and demonstrate how it can be used to engineer effective Hamiltonian evolution, subject to decoherence induced by the projective meter measurements.
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