Influence of measurement on the lifetime and the linewidth of unstable systems

Abstract

We investigate the quantum Zeno effect in the case of electron tunneling out of a quantum dot in the presence of continuous monitoring by a detector. It is shown that the Schrödinger equation for the whole system can be reduced to Bloch-type rate equations describing the combined time-development of the detector and the measured system. Using these equations we find that continuous measurement of the unstable system does not affect its exponential decay to a reservoir with a constant density of states. The width of the energy distribution of the tunneling electron, however, is not equal to the inverse life-time -it increases due to the decoherence generated by the detector. We extend the analysis to the case of a reservoir described by an energy dependent density of states, and we show that continuous measurement of such quantum systems affects both the exponential decay rate and the energy distribution. The decay does not always slow down, but might be accelerated. The energy distribution of the tunneling electron may reveal the lines invisible before the measurement.

Weak-coupling approximations in non-Markovian transport

“…Our model has an exact correspondence with an effective wide band two level Fano-Anderson model 25 with Hamiltonian (13) with a left and a right dot state, d L and d R , and a couplingT C between them. Each lead couples only to its adjacent dot.…”

“…tron in lead a ∈ {R, L} with momentum k. We choose a Lorentzian-shaped right tunneling rate, like in 25,26 :…”

“…Consequently, to explore effects beyond the common BornMarkov-approximation, one would study higher-order perturbation theory in the contact coupling (e.g. 22,23,24 ) and/or allow for energy-dependent tunneling rates, i.e., go beyond the wide-band approximation 14,25,26,27,28,29 . In this work we choose the latter whilst analyzing perturbative approaches in lowest-order tunnel coupling only.…”

Systematic perturbation theory for dynamical coarse-graining

“…In the interaction picture, the annihilation and creation operators transform according to b k (t) = e +iHBt b k e −iHBt = e −iω k t b k and the hermitian conjugate, respectively. The second order correlation function then evaluates to (36) where the bosonic occupation number is given by n(ω) = 1 e βω −1 .…”

Non-Markovian decoherence theory for a double-dot charge qubit

“…Here we shall use a Lorentzian spectral density that has been used in the study of the influence of a measuring lead on a single dot [49] and molecular wires coupling to electron reservoirs [50]. The Lorentzian spectral density we used here has a form:…”