Measuring Entropy of Exotic Particles

In recent years many candidate setups have been proposed to support exotic quasi-particles, such as Majorana fermions (MFs), which may be relevant for quantum computing, but whether these particles have been observed experimentally is currently a topic of a vivid debate. Entropy measurements can unambiguously separate these quasi-particles from other, simpler excitations. The entropy of a MFs is, for example, log2/2 (in units of the Boltzman constant), a fractional value that cannot be attributed to a localized excitation. However, standard entropy measurements applicable to bulk systems cannot be utilized in measuring the additional entropy of a mesoscopic device, which may be due to less than a single electron in the device. In this talk I will describe recent theoretical and experimental progress in performing such measurements, either using thermopower and/or using the Maxwell relations [1,2]. Particular examples will be single and double quantum dots in the Coulomb blockade regime. Lastly I will show how the formalism has been generalized to deduce the entropy from conductance measurements, and, applying it to a setup where two and three-channel Kondo physics have been observed, yields the fractional entropy of a single MF and a single Fibonacci anyon [3].  Lastly I will discuss the backaction of the measurement and discuss the possibility of measuring entanglement entropy [4].

[1]    Direct entropy measurement in a mesoscopic quantum system, N. Hartman, et al.,  Nature Physics 14, 1083 (2018).
[2]    How to measure the entropy of a mesoscopic system via thermoelectric transport, Y. Kleeorin et al., Nature Comm. 10 , 5801 (2019)
[3]    Fractional Entropy of Multichannel Kondo Systems from Conductance-Charge Relations, C. Han et al., Phys. Rev. Lett. 128, 146803 (2022).
[4]    Realistic protocol to measure entanglement at finite temperatures, C. Han, Y. Meir and E. Sela, Phys. Rev. Lett., 130, 136201 (2023).