We present the first measurements of thermal signatures of the Little-Parks
effect using a highly sensitive nanocalorimeter. Small variations of the heat
capacity C_p of 2.5 millions of non interacting micrometer-sized
superconducting rings threaded by a magnetic flux Φ have been measured by
attojoule calorimetry. This non-invasive method allows the measurement of
thermodynamic properties -- and hence the probing of the energy levels -- of
nanosystems without perturbing them electrically. It is observed that C_p is
strongly influenced by the fluxoid quantization (Little-Parks effect) near the
critical temperature T_c. The jump of C_p at the superconducting phase
transition is an oscillating function of Φ with a period Φ_0=h/2e,
the magnetic flux quantum, which is in agreement with the Ginzburg-Landau
theory of superconductivity.Comment: To be published in Physical Review B, Rapid Communication