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Journal of Experimental and Theoretical Physics

On the photon arrival-time-energy uncertainty relation

S. N. Molotkov

Published Jan 1, 2009• 1 citation
Publisher

Abstract

A lower bound is obtained for the photon arrival-time-energy uncertainty relation.
DOI
10.1134/s106377610901004x

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We prove an uncertainty relation for energy and arrival time, where the arrival of a particle at a detector is modeled by an absorbing term added to the Hamiltonian. In this well-known scheme the probability for the particle's arrival at the counter is identified with the loss of normalization for an initial wave packet. Under the sole assumption that the absorbing term vanishes on the initial wavefunction, we show that and , where 〈 T 〉 denotes the mean arrival time and p is the probability for the particle to be eventually absorbed. Nearly minimal uncertainty can be achieved in a two-level system, and we propose a trapped ion experiment to realize this situation.
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