Topological transition of a nonMarkovian dissipative quantum walk
Abstract
We extend nonHermitian topological quantum walks on a SuSchriefferHeeger (SSH) lattice [Phys. Rev. Lett. 102, 065703 (2009), 10.1103/PhysRevLett.102.065703] to the case of nonMarkovian evolution. This nonMarkovian model is established by coupling each unit cell in the SSH lattice to a reservoir formed by a quasicontinuum of levels. We find a topological transition in this model even in the case of nonMarkovian evolution where the walker may visit the reservoir and return to the SSH lattice at a later time. The existence of a topological transition does, however, depend on the lowfrequency properties of the reservoir, characterized by a spectral density J (ɛ ) ∝ɛ^{ α} . In particular, we find a robust topological transition for a subOhmic (α <1 ) and Ohmic (α =1 ) reservoir, but no topological transition for a superOhmic (α >1 ) reservoir. This behavior is directly related to the wellknown localization transition for the spinboson model. We confirm the presence of nonMarkovian dynamics by explicitly evaluating a measure of Markovianity for this model.
 Publication:

Physical Review A
 Pub Date:
 July 2020
 DOI:
 10.1103/PhysRevA.102.012215
 arXiv:
 arXiv:2003.00350
 Bibcode:
 2020PhRvA.102a2215R
 Keywords:

 Quantum Physics;
 Condensed Matter  Mesoscale and Nanoscale Physics
 EPrint:
 10 pages, 4 figures