"Population switching" is a phenomenon involving a steep filling of a narrow level in a quantum dot at the expense of a wide one as a common gate voltage is varied. This effect has been discussed in several contexts, including charge sensing by means of a current-carrying quantum point contact (QPC), as well as in relation with lapses of the transmission phase of a quantum dot.
Is the switching involved abrupt, in which case one is facing a first order quantum phase transition?
Mapping this problem onto a two-species Coulomb gas representation, we demonstrate that it is equivalent to an orbital Kondo model, and find that the switching is steep but not abrupt; however, when one tries to measure this behavior by electrostatically coupling one of the levels to a charge detecting QPC, one may render the switching abrupt. We show that this quantum phase transition is triggered by a change in physics from a Mahan exciton controlled dynamics to an Anderson orthogonality catastrophe controlled dynamics. Including the spin degree of freedom may lead to a realization of the SU(4) Kondo effect, as well as to quantum criticality of the two-impurity-Kondo type.