Effect of Environment Initial State on Non-Markovianity of a Spin Coupled to a XY Spin Chain
September 25th, 2019 JULIAN ROOS Max Planck Institute for Quantum Optics

The subject of open quantum systems (OQS) focuses on the description of quantum systems coupled to a (typically much larger) environment. Instead of solving the generally non-accessible time evolution of the total system, one tries to obtain an effective reduced description which involves the degrees of freedom of the OQS only. In this context, the distinction between Markovian and non-Markovian dynamics is a central theme.

The same OQS perspective can be applied to study the dynamics of a subsystem in a closed many-body quantum system, where the rest of the system plays the role of environment, and the long time evolution of the full system is out of reach due to build-up of entanglement. This is interesting because the computation of local observables requires only to know the state of a (small) subsystem. However, the standard derivation to obtain a Markovian reduced description is based on weak coupling and a separation of time scales between open system and environment; two conditions that are generally not fulfilled in the quantum many-body setup. It is thus interesting to analyse whether there are cases in which the dynamics still admits a reduced description in this setting, and, in case such a description exists, whether it is Markovian.

We explore these questions in the particular case of a spin (the OQS) coupled to a XY spin chain. Describing the spin chain in terms of free fermions, we find that whilst initially populating few fermionic modes (e.g. using a low temperature thermal state) induces a number of non-Markovian phenomena not present in the vacuum case, increasing temperature gradually removes non-Markovianity until at high temperature the spin dynamics are captured by a Markovian reduced description. This applies even in scenarios that strongly violate the conditions mentioned above. The Markovianity of high temperature setups is not completely general. If the spin is coupled to the first site of the chain, any non-Markovianity of the vacuum case survives at all temperatures. Whilst some of the above cases are analytically tractable, in general we solve the dynamics numerically using matrix product states.

Seminar, September 25, 2019, 11:00. ICFO’s Seminar Room

Hosted by Prof. Maciej Lewenstein