Measuring the entropy of a single spin
Entropy measurements offer a powerful tool for identifying the underlying microscopic character of electronic states. Such measurements are typically based on bulk properties that are straightforward to observe in macroscopic samples, but exceedingly difficult to access in mesoscopic systems that may consist of just a few electrons or quasiparticles. Taking advantage of a well-known Maxwell relation, we realize a protocol for entropy-to-charge conversation in a gate-defined GaAs quantum dot that enables an entropy measurement of the first three quantum states in the dot. The entropy of a single spin (k_B ln2) is measured with a few percent accuracy, as is the entropy arising at the magnetic field-driven singlet-triplet crossing for two electrons. Future prospects for identifying more exotic quantum states such as 2-channel Kondo states, non-Abelian Moore-Read quasiparticles, and Majorana quasiparticles in semiconductors will be discussed.