Attojoule calorimetry of mesoscopic superconducting loops

We report the first experimental evidence of nontrivial thermal behavior of the simplest mesoscopic system--a superconducting loop. By measuring the specific heat C of an array of 450,000 noninteracting aluminum loops with very high accuracy of approximately 20 fJ/K, we show that the loops go through a periodic sequence of phase transitions (with a period of an integer number of magnetic flux quanta) as the magnetic flux threading each loop is increased. The transitions are well described by the Ginzburg-Landau theory and are accompanied by discontinuities of C of only several thousands of Boltzmann constants kB.