Topology of discrete feedback control: a new platform for exploring nonequilibrium phenomena
ORAL · Invited
Abstract
Functionality emerges as we move away from equilibrium. Furthermore, there are growing needs for ever-faster information processing devices, such as advanced semiconductor devices and quantum computers. For all of these, it is vital to create and stabilize nonequilibrium states. We report the summary of our latest effort toward this goal.
Topological phases are classified in terms of topology of relevant operators. At equilibrium, topology of Hamiltonians can be utilized to classify, e.g., topological insulators. For periodically driven Floquet systems, topological phases are characterized by the topology of unitary time evolution operators which can be used to produce topological pump. For non-Hermitian systems [1], topological phases are characterized by the topology of non-Hermitian Hamiltonians, which can be used to analyze topological lasers. In this talk, I will discuss yet another class of dynamical topological phases which can be realized by quantum feedback control and classified by the topology of quantum channels [2].
We present a general framework for analyzing topology of quantum channels of single-particle systems and use it to identify a class of genuinely dynamical topological phases that can be realized by means of discrete quantum feedback control. We provide a symmetry classification of quantum channels by identifying ten symmetry classes of discrete quantum feedback control with projective measurements. We construct various types of topological feedback control by using topological Maxwell’s demons that achieve robust feedback-controlled chiral or helical transport against external disturbances. Topological feedback control thus offers a versatile tool for creating and controlling nonequilibrium topological phases in open quantum systems that are distinct from non-Hermitian and Lindbladian systems and should provide a guiding principle for topology-based design of quantum feedback control.
[1] Y. Ashida, Z. Gong, and M. Ueda, Adv. Phys. 69, 249 (2021).
[2] M. Nakagawa and M. Ueda, arXiv: 2403.08406.
Topological phases are classified in terms of topology of relevant operators. At equilibrium, topology of Hamiltonians can be utilized to classify, e.g., topological insulators. For periodically driven Floquet systems, topological phases are characterized by the topology of unitary time evolution operators which can be used to produce topological pump. For non-Hermitian systems [1], topological phases are characterized by the topology of non-Hermitian Hamiltonians, which can be used to analyze topological lasers. In this talk, I will discuss yet another class of dynamical topological phases which can be realized by quantum feedback control and classified by the topology of quantum channels [2].
We present a general framework for analyzing topology of quantum channels of single-particle systems and use it to identify a class of genuinely dynamical topological phases that can be realized by means of discrete quantum feedback control. We provide a symmetry classification of quantum channels by identifying ten symmetry classes of discrete quantum feedback control with projective measurements. We construct various types of topological feedback control by using topological Maxwell’s demons that achieve robust feedback-controlled chiral or helical transport against external disturbances. Topological feedback control thus offers a versatile tool for creating and controlling nonequilibrium topological phases in open quantum systems that are distinct from non-Hermitian and Lindbladian systems and should provide a guiding principle for topology-based design of quantum feedback control.
[1] Y. Ashida, Z. Gong, and M. Ueda, Adv. Phys. 69, 249 (2021).
[2] M. Nakagawa and M. Ueda, arXiv: 2403.08406.
*This work was supported by KAKENHI Grant No. JP22H01152 from the Japan Society for the Promotion of Science and the CREST program "Quantum Frontiers" (Grant No. JPMJCR2311) by the Japan Science and Technology Agency.
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Publication: arXiv:2403.08406
Presenters
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Masahito Ueda
- Univ of Tokyo