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Chin. Phys. B, 2021, Vol. 30(2): 020506    DOI: 10.1088/1674-1056/abd765
Special Issue: SPECIAL TOPIC — Quantum computation and quantum simulation
SPECIAL TOPIC—Quantum computation and quantum simulation Prev   Next  

Quantum dynamics on a lossy non-Hermitian lattice

Li Wang(王利)1,†, Qing Liu(刘青)1, and Yunbo Zhang(张云波)2
1 Institute of Theoretical Physics, State Key Laboratory of Quantum Optics and Quantum Optics Devices, Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan 030006, China; 2 Key Laboratory of Optical Field Manipulation of Zhejiang Province and Physics Department of Zhejiang Sci-Tech University, Hangzhou 310018, China
Abstract  We investigate quantum dynamics of a quantum walker on a finite bipartite non-Hermitian lattice, in which the particle can leak out with certain rate whenever it visits one of the two sublattices. Quantum walker initially located on one of the non-leaky sites will finally totally disappear after a length of evolution time and the distribution of decay probability on each unit cell is obtained. In one regime, the resultant distribution shows an expected decreasing behavior as the distance from the initial site increases. However, in the other regime, we find that the resultant distribution of local decay probability is very counterintuitive, in which a relatively high population of decay probability appears on the edge unit cell which is the farthest from the starting point of the quantum walker. We then analyze the energy spectrum of the non-Hermitian lattice with pure loss, and find that the intriguing behavior of the resultant decay probability distribution is intimately related to the existence and specific property of the edge states, which are topologically protected and can be well predicted by the non-Bloch winding number. The exotic dynamics may be observed experimentally with arrays of coupled resonator optical waveguides.
Keywords:  quantum walk      non-Hermitian lattice      dissipations      edge states  
Received:  19 November 2020      Revised:  14 December 2020      Accepted manuscript online:  30 December 2020
PACS:  05.40.Fb (Random walks and Levy flights)  
  03.65.Vf (Phases: geometric; dynamic or topological)  
  42.82.Et (Waveguides, couplers, and arrays)  
Fund: Project supported by the National Natural Science Foundation of China (Grant Nos. 11404199 and 11674201), Natural Science Foundation of Shanxi Province, China (Grant No. 1331KSC), Natural Science Foundation for Youths of Shanxi Province, China (Grant No. 2015021012), and Research Initiation Funds from SXU (Grant No. 216533801001).
Corresponding Authors:  Corresponding author. E-mail: liwangiphy@sxu.edu.cn   

Cite this article: 

Li Wang(王利), Qing Liu(刘青), and Yunbo Zhang(张云波) Quantum dynamics on a lossy non-Hermitian lattice 2021 Chin. Phys. B 30 020506

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