Simulating a Quantum Dot Thermometer using Feynman's Vector Model for Two-Level Systems

Measuring temperature at the nanoscale is a significant challenge in fields such as quantum computing and biomedicine. Quantum dots, whose optical properties vary with temperature, can help address this problem. In this study, we address this challenge by simulating a quantum dot thermometer. The approach models the dot as a two-level system and uses Feynman's geometric model, where the quantum state is represented as a vector. As the system interacts with its thermal environment, this vector changes, gradually reaching equilibrium; tracking this evolution reveals the system's behavior. Ultimately, the final population difference between the two levels, predicted by the Boltzmann distribution, indicates the temperature.

To implement this approach, we built the simulation in Python and utilized NumPy and SciPy to solve the primary differential equation governing thermal relaxation. Once the simulation was run, it provided a calibration curve that relates the equilibrium value of r₃ to various temperatures. Therefore, by measuring the population difference, the local temperature can be found. This method offers a straightforward and visual approach to understanding the function of a quantum sensing device.