Topological transition of a non-Markovian dissipative quantum walk
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Topological transition of a non-Markovian dissipative quantum walk. / Ricottone, A.; Rudner, M. S.; Coish, W. A.
I: Physical Review A - Atomic, Molecular, and Optical Physics, Bind 102, Nr. 1, 012215, 07.2020.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Topological transition of a non-Markovian dissipative quantum walk
AU - Ricottone, A.
AU - Rudner, M. S.
AU - Coish, W. A.
PY - 2020/7
Y1 - 2020/7
N2 - We extend non-Hermitian topological quantum walks on a Su-Schrieffer-Heeger (SSH) lattice [Phys. Rev. Lett. 102, 065703 (2009)PRLTAO0031-900710.1103/PhysRevLett.102.065703] to the case of non-Markovian evolution. This non-Markovian 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 non-Markovian 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 low-frequency properties of the reservoir, characterized by a spectral density J(ϵ)|ϵ|α. In particular, we find a robust topological transition for a sub-Ohmic (α<1) and Ohmic (α=1) reservoir, but no topological transition for a super-Ohmic (α>1) reservoir. This behavior is directly related to the well-known localization transition for the spin-boson model. We confirm the presence of non-Markovian dynamics by explicitly evaluating a measure of Markovianity for this model.
AB - We extend non-Hermitian topological quantum walks on a Su-Schrieffer-Heeger (SSH) lattice [Phys. Rev. Lett. 102, 065703 (2009)PRLTAO0031-900710.1103/PhysRevLett.102.065703] to the case of non-Markovian evolution. This non-Markovian 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 non-Markovian 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 low-frequency properties of the reservoir, characterized by a spectral density J(ϵ)|ϵ|α. In particular, we find a robust topological transition for a sub-Ohmic (α<1) and Ohmic (α=1) reservoir, but no topological transition for a super-Ohmic (α>1) reservoir. This behavior is directly related to the well-known localization transition for the spin-boson model. We confirm the presence of non-Markovian dynamics by explicitly evaluating a measure of Markovianity for this model.
UR - http://www.scopus.com/inward/record.url?scp=85088440810&partnerID=8YFLogxK
U2 - 10.1103/PhysRevA.102.012215
DO - 10.1103/PhysRevA.102.012215
M3 - Journal article
AN - SCOPUS:85088440810
VL - 102
JO - Physical Review A - Atomic, Molecular, and Optical Physics
JF - Physical Review A - Atomic, Molecular, and Optical Physics
SN - 1050-2947
IS - 1
M1 - 012215
ER -
ID: 245610892