Lamb shift of interactive electron-hole pairs in spherical semiconductor Quantum Dots

Abstract

The ground state Lamb shift of a semiconductor spherical Quantum Dot is computed in the effective mass approximation. It appears to be significant enough to be detectable for a wide range of small Quantum Dots synthesized in semiconductors. A possible way to observe it, via the Casimir effect, is suggested.

Lamb shift of non-degenerate energy level systems placed between two infinite parallel conducting plates

“…In this work, we have developed a comprehensive computation method to obtain mathematically rigorous results on the Lamb shift for non-degenerate energy levels in semiconductor spherical QDs placed in a Casimir device. A deviation from the Lamb shift in a vacuum, predicted in [22], is revealed. The explicit formula giving this deviation suggests the possibility to fine tune the spectrum of a QD for experimental purposes, by varying the separation distance between the Casimir plates, provided that such micro-mechanical operations are realizable.…”

“…In such systems each non-degenerate energy level is dressed by the quantum zeropoint fluctuations of the electromagnetic field, forbidding the detection of the corresponding bare energy level. Here we can see that equation ( 6) may be used to label the Lamb shift in semiconducting QDs (calculated for the first time in [22]) by each value of d.…”

“…Here we can see that Eq. ( 6) may be used to label the Lamb shift in semiconducting QDs (calculated for the first time in [22]) by each value of d.…”

“…For this simple model, in the strong confinement regime, it is proven that the predicted Lamb shift, in QDs of size experimentally synthetized and used, is of the same order of magnitude as the one in hydrogen-like atoms, at least for judiciously chosen semiconductors, such as for example InAs or GaAs, and then seems to be observable. Since this is the relative modification of the Lamb shift due to the presence of the Casimir device, the method of calculation of the Lamb shift in QDs [22] is not of interest. However, this provides the Bethe IR cut-offs κ * e,h = 7π 3 λ * e,h .…”

“…However, the understanding of the respective role of vacuum fluctuations and radiative field on the energy level shifts between two parallel plates seems to remain ambiguous [21]. In this paper, to pursue investigations into the analogy between semiconductor QDs and real atoms [22], we address the problem of observability of the atomic-like Lamb shift in spherical semiconductor QDs. As the energy levels of an electron-hole pair confined in a spherical semiconductor QD are non-degenerate [23], how would the Lamb shift in QDs appear since the s-and p-levels are both shifted by the Lamb effect, as opposed to real atoms?…”