Population switching and charge sensing in quantum dots: A case for a quantum phase transition

A broad and a narrow level of a quantum dot connected to two external leads may swap their respective occupancies as a function of an external gate voltage. By mapping this problem onto a multi-flavored Coulomb-gas we show that such population switching is not abrupt. However, trying to measure it by adding a third electrostatically coupled lead may render this switching an abrupt first order quantum phase transition. This is related to the interplay of the Mahan mechanism versus the Anderson orthogonality catastrophe, in similitude to the Fermi edge singularity. A concrete setup for experimental observation of this effect is also suggested.