PT symmetric non-unitary quantum walks with higher topological numbers

Hideaki Obuse (Hokkaido University)

Recently, a non-Hermitian Hamiltonian, especially, possessing parity and time-reversal symmetry(PT symmetry), has attracted great attention because of its novel properties, such as, reality of eigenenergy, exceptional points, and so on[1]. While PT symmetric systems have been realized in various classical optical experiments, only few experiments can perform non-Hermitian quantum systems with PT symmetry. Among them, an approach by using a quantum walk defined by a time-evolution operator provides a feasible and systematic way to study such open quantum systems. In the previous work, topological phases and the edge states of a PT symmetric non-unitary quantum walk, whose topological number is one, have been studied theoretically[2] and confirmed experimentally[3].

In the present work, we theoretically and experimentally study a PT symmetric non-unitary quantum walk with higher topological numbers[4,5]. We confirm the validity of the bulk-edge correspondence and further study the multiple edge states originating from the higher topological numbers.

[1] C. M. Bender and S. Boettcher, Phys. Rev. Lett. 80, 5243 (1998).
[2] K. Mochizuki, D. Kim, and H. Obuse, Phys. Rev. A 93, 062116 (2016).
[3] L. Xiao, X. Zhan, Z. H. Bian, K. K. Wang, X. Zhang, X. P. Wang, J. Li, K. Mochizuki, D. Kim, N. Kawakami, W. Yi, H. Obuse, B. C. Sanders, and P. Xue, Nat. Phys. 13, 1117 (2017).
[4] L. Xiao, X. Qiu, K. Wang, Z. Bian, X. Zhan, H. Obuse, B. C. Sanders, W. Yi, and P. Xue, Phys. Rev. A 98, 063847 (2018). 
[5] M. Kawasaki, K. Mochizuki, N. Kawakami, and H. Obuse, arXiv:1905.11098.