image: (a) ergodicity in classical systems, (b) ETH supporting the thermalization in non-integrable quantum systems, and (c) GETH supporting the generalized thermalization in integrable quantum systems. view more
Credit: by 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, and Guang-Can Guo
Thermalization in classical systems can be well-understood by ergodicity. While ergodicity is absent for quantum systems, it is generally believed that the non-integrable quantum systems should satisfy an eigenstate thermalization hypothesis (ETH) and can be thermalized. For the integrable quantum systems having a set of conserved quantities, the ETH is invalid and a generalized version of ETH (GETH) can be used to understand the relaxation of the integrable systems to the maximum entropy state, a process referred to as the generalized thermalization. However, experimentally verifying the GETH is still a great challenge until now because of the difficulties in the special system initialization.
In a new paper published in Light Science & Application, a team of scientists, led by Professor Guang-Can Guo from CAS Key Laboratory of Quantum Information, University of Science and Technology of China, and co-workers utilized a quantum-walk (QW) platform, as a typical integrable model with spin-orbit coupling, to experimentally explore the GETH and the generalized thermalization in this model. To achieve this, a QW is developed in a photonic system based on the time-multiplexing method. These scientists summarize the power of their experimental QW platform as:
“The system can be well-isolated and consequently can maintain a long-time coherent evolution to explore the pure state quantum statistical mechanics. More importantly, as the key techniques for investigating the GETH, both the ability to engineer the initial states and the full reconstruction of the spinor eigenvectors of a given Hamiltonian are accessible in their framework.”
Based on the GETH, any superposition state of the mutual eigenstates with similar conserved quantities can locally relax to the same reduced state, which is independent of the details of the initial state. “To verify the GETH, they employed the quantum state engineering technique in QW to initialize the system in the superposition states in a narrow window of conserved quantities, and then the spin subsystem relaxation in a long-time coherent dynamics was monitored. They experimentally demonstrated that, for any superposition of the mutual eigenstates within a small energy-momentum window, the ‘universality’ of the local steady state of the spin subsystem is recovered.”
“Moreover, based on the GETH, they proposed and experimentally demonstrated that, in an extended scene where the initial states are within two separated windows, the local steady state can also be predicted by the GETH and exhibits the generalized thermalization.”
Journal
Light Science & Applications