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A broad and a narrow level of a quantum dot connected to two external leadsmay swap their respective occupancies as a function of an external gatevoltage. By mapping this problem onto a multi-flavored Coulomb-gas we show thatsuch population switching is not abrupt. However, trying to measure it byadding a third electrostatically coupled lead may render this switching anabrupt first order quantum phase transition. This is related to the interplayof the Mahan mechanism versus the Anderson orthogonality catastrophe, insimilitude to the Fermi edge singularity. A concrete setup for experimentalobservation of this effect is also suggested.

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