Decoherence and Relaxation in Quantum Spin Clusters
Equilibration and eventually thermalization in closed quantum systems under unitary time evolution is a fascinating and focused topic in modern many-body physics, and it is as well the central theme of this research collaboration. Already rather early in the 1990s, the practical consequences of internal thermalization were employed by us to study, e.g., the appearance of the nuclear liquid-gas transition in nuclear fragmentation reactions.
This project is going to focus on the related, but different aspect of internal decoherence in finite-size closed quantum systems under unitary time evolution. As in the cases of thermalization the key to an understanding is a sharp definition of the employed notion of decoherence. We will mainly investigate the Hahn echo decoherence, but will also study and compare with other experimentally relevant definitions such as free induction decay.
Two major setups shall be studied in this project. The first consists of only electronic spins that are driven by external field protocols. Our aim is to study the dynamics of the system using realistic interactions between the electronic spins that contain dipolar interactions, which we assume to be very relevant for the decoherence process. The second setup considers small electronic spin systems that are coupled to small nuclear spin systems. This introduces different energy scales into the problem. Not only is the nuclear spin bath small, also the band of energy eigenvalues of the bath is small compared to the interaction strength with the system. The system-bath dynamics is non-Markovian. It constitutes a generalization of the central spin model towards a central multi-qubit model. Again, realistic interactions will be used.
We aim at a better understanding of several issues: 1. How can internal decoherence be defined and understood? 2. What is the role of conserved quantities? 3. Which role is played by realistic (symmetry breaking) interactions such as the dipolar interaction? 4. Is there equilibration free decoherence? 5. Are there systems and scenarios under which coherence is preserved? The last question is of utmost importance for any quantum computing scheme.