Exact energy-time uncertainty relation for arrival time by absorption

Jukka Kiukas*, Andreas Ruschhaupt, Piet O. Schmidt, Reinhard F. Werner

*Awdur cyfatebol y gwaith hwn

Allbwn ymchwil: Cyfraniad at gyfnodolynErthygladolygiad gan gymheiriaid


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 particles 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 ΔTΔE ≥ √ ph 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.

Iaith wreiddiolSaesneg
Rhif yr erthygl185301
CyfnodolynJournal of Physics A: Mathematical and Theoretical
Rhif cyhoeddi18
Dynodwyr Gwrthrych Digidol (DOIs)
StatwsCyhoeddwyd - 19 Ebr 2012
Cyhoeddwyd yn allanolIe

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