Peer-Reviewed Journal Details
Mandatory Fields
Kiukas, J.; Ruschhaupt, A.; Schmidt, P.O.; Werner, R.W.
Journal of Physics A: Mathematical and Theoretical
Exact energy–time uncertainty relation for arrival time by absorption
Optional Fields
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 \Delta T \Delta E >= \sqrt{p} \hbar/2 and <T> \Delta E >= 1.37 \sqrt{p} \hbar, 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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