Controlled dephasing of an electron interferometer with a path detector at equilibrium

Controlled dephasing of electrons, via 'which path' detection, involves, in general, coupling a coherent system to a current driven noise source. However, here, we present a case in which a nearly isolated electron puddle at thermal equilibrium strongly affects the coherence of a nearby electronic interferometer. Moreover, for certain average electron occupations of the puddle, the interferometer exhibits complete dephasing. This robust phenomenon stems from the Friedel Sum Rule, which relates a system's occupation with its scattering phases. The interferometer opens a peeping window into physics of the isolated electron puddle, which cannot be accessed otherwise.