Theoretical constraints on simulating non-Markovian topological quantum walks in synthetic dimensions*

Topologically protected quantities are robust to symmetry-preserving perturbations that don’t close an energy gap. However, every realistic system is coupled to an environment that may break those symmetries and thus break the topological protection. A significant recent effort has been focussed on the non-Hermitian description of open systems in this context [1]. When considering Hermitian system-bath models, where the bath is included in the model, new behavior can become apparent. This is the case in the non-Markovian topological quantum walks, introduced in Ref. [2]. In this model, a walker can evolve on an SSH-chain with quantum baths attached to every other site. The mean displacement of the walker before leaving the bath is quantized and equal to the topological invariant of the SSH model for sub-ohmic baths. For super-ohmic baths, however, this quantization breaks down. We will discuss theoretical constraints on reproducing this effect experimentally with a finite bath and how to implement the resulting model in synthetic dimensions [3].

[1] N. Okuma and M. Sato, “Non-Hermitian Topological Phenomena: A Review,” Annu. Rev. Condens. Matter Phys., vol. 14, no. 1, pp. 83–107, 2023, doi: 10.1146/annurev-conmatphys-040521-033133.

[2] A. Ricottone, M. S. Rudner, and W. A. Coish, “Topological transition of a non-Markovian dissipative quantum walk,” Phys. Rev. A, vol. 102, no. 1, p. 012215, Jul. 2020, doi: 10.1103/PhysRevA.102.012215.

[3] F. Pellerin, R. Houvenaghel, W. A. Coish, I. Carusotto, and P. St-Jean, “Wavefunction tomography of topological dimer chains with long-range couplings.” arXiv, Jul. 03, 2023. doi: 10.48550/arXiv.2307.01283.