Experimental verification of generalized eigenstate thermalization hypothesis in an integrable system

Qin-Qin Wang; Si-Jing Tao; Wei-Wei Pan; Zhe Chen; Geng Chen; Kai Sun; Jin-Shi Xu; Xiao-Ye Xu; Yong-Jian Han; Chuan-Feng Li; Guang-Can Guo

doi:10.1038/s41377-022-00887-5

Experimental verification of generalized eigenstate thermalization hypothesis in an integrable system

Light Sci Appl. 2022 Jun 28;11(1):194. doi: 10.1038/s41377-022-00887-5.

Authors

Qin-Qin Wang^#^{1

2

3}, Si-Jing Tao^#^{1

2

3}, Wei-Wei Pan^{1

2

3}, Zhe Chen^{1

2

3}, Geng Chen^{1

2

3}, Kai Sun^{1

2

3}, Jin-Shi Xu^{1

2

3}, Xiao-Ye Xu^{4

5

6}, Yong-Jian Han^{7

8

9}, Chuan-Feng Li^{10

11

12}, Guang-Can Guo^{1

2

3}

Affiliations

¹ CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China.
² CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, China.
³ Hefei National Laboratory, University of Science and Technology of China, Hefei, 230088, China.
⁴ CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China. xuxiaoye@ustc.edu.cn.
⁵ CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, China. xuxiaoye@ustc.edu.cn.
⁶ Hefei National Laboratory, University of Science and Technology of China, Hefei, 230088, China. xuxiaoye@ustc.edu.cn.
⁷ CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China. smhan@ustc.edu.cn.
⁸ CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, China. smhan@ustc.edu.cn.
⁹ Hefei National Laboratory, University of Science and Technology of China, Hefei, 230088, China. smhan@ustc.edu.cn.
¹⁰ CAS Key Laboratory of Quantum Information, University of Science and Technology of China, Hefei, 230026, China. cfli@ustc.edu.cn.
¹¹ CAS Center for Excellence in Quantum Information and Quantum Physics, University of Science and Technology of China, Hefei, 230026, China. cfli@ustc.edu.cn.
¹² Hefei National Laboratory, University of Science and Technology of China, Hefei, 230088, China. cfli@ustc.edu.cn.

^# Contributed equally.

Abstract

Identifying the general mechanics behind the equilibration of a complex isolated quantum system towards a state described by only a few parameters has been the focus of attention in non-equilibrium thermodynamics. And several experimentally unproven conjectures are proposed for the statistical description of quantum (non-)integrable models. The plausible eigenstate thermalization hypothesis (ETH), which suggests that each energy eigenstate itself is thermal, plays a crucial role in understanding the quantum thermalization in non-integrable systems; it is commonly believed that it does not exist in integrable systems. Nevertheless, integrable systems can still relax to the generalized Gibbs ensemble. From a microscopic perspective, understanding the origin of this generalized thermalization that occurs in an isolated integrable system is a fundamental open question lacking experimental investigations. Herein, we experimentally investigated the spin subsystem relaxation in an isolated spin-orbit coupling quantum system. By applying the quantum state engineering technique, we initialized the system with various distribution widths in the mutual eigenbasis of the conserved quantities. Then, we compared the steady state of the spin subsystem reached in a long-time coherent dynamics to the prediction of a generalized version of ETH and the underlying mechanism of the generalized thermalization is experimentally verified for the first time. Our results facilitate understanding the origin of quantum statistical mechanics.