Goldilocks cooling: Demonstrating the quantum Mpemba effect in a two-level system

Sammanfattning

This thesis investigates the quantum Mpemba effect, where an initially hotter system cools down faster than an initially colder one. This was demonstrated in a qubit system coupled to two environments. A thermal state is chosen as the initial state and then left to freely equilibrate. It was shown that the initial thermal state can be chosen in a way to accelerate the resulting relaxation process. The Liouvillian dynamics were analyzed and, by eliminating the contribution of the slowest decaying eigenmode (SDM) corresponding to accelerated relaxation dynamics, the effect was demonstrated. All states with vanishing SDM contributions were considered and found to belong to a plane in the Bloch sphere corresponding to a reduced state space. A thermal state could be shown to exist in this subspace, which is the Mpemba state that relaxes the fastest. The numerical relaxation dynamics were computed and the accelerated behavior of the Mpemba state verified. The fidelity of the Mpemba state also exhibits a steeper decay, consistent with the faster-decaying modes. The results were found to only strongly affect the solution in regions close to the steady state.