Entropy of a double quantum dot

TL;DR

This paper investigates entropy changes in a double quantum dot system using charge sensing, revealing how occupation states and quantum effects influence entropy in both independent and coupled regimes, with implications for complex quantum systems.

Contribution

It introduces a method to measure entropy in a double quantum dot, analyzing both independent and molecular regimes, and clarifies the effects of Pauli blockade and nonequilibrium dynamics.

Findings

Single-electron occupation increases entropy by $k_B \, ext{log} 2$

Charge transitions in the molecular regime affect measured entropy

Pauli blockade impacts entropy signals but is distinguishable via rate models

Abstract

We use charge sensing to detect entropy changes in a double quantum dot defined by electrostatic gating of a GaAs/AlGaAs heterostructure. This system can be tuned to be two separate systems, like two independent, artificial atoms, or a single coherent system, like a molecule. We study entropy changes in both regimes due to changes in the occupation of the system. First we recover the single-dot result for each dot, that the occupation of the dot by a single electron corresponds to an increase in the entropy of $k_{\mathrm{B}} \log 2$. Next we examine two different charge transitions in the "molecular" regime, and how it reveals itself in terms of the measured entropy. We also uncover a realization of Pauli blockade that clutters the entropy signal. By applying a rate equation model, we demonstrate the effect's nonequilibrium origins and exclude it from the analysis of the system's entropy. Understanding these experiments in this simplest coupled system enables the study of the entropy in other, more complicated coupled quantum systems, such as ones with topological or highly entangled ground states.