Session A35: Non-Hermitian Physics in AMO and Condensed Matter Systems

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The fundamental premise of quantum theory is two-fold: unitary dynamics and nonunitary measurement. The former is generated by a hermitian operator, whereas the latter entails non-hermitian operation. Beyond-hermitian quantum physics has attracted much attention due to experimental and theoretical advances in AMO, condensed matter and nonequilibrium statistical physics [1]. These developments give us fresh insights into how to control strongly correlated dissipative systems with novel functionalities operating far from equilibrium. A full knowledge of types and occurrence times of quantum jumps allows a complete description of quantum trajectories. A subclass thereof without quantum jumps can be described by a non-hermitian Hamiltonian. Here many important properties such as symmetries, topological properties with many-body effects fundamentally altered. Transposition and complex comjugation, which are equivalent in hermitian physics, become inequivalent in the non-hermitian framework, leading to nontrivial topological phases [2] through unification and ramification of topological phases [3] and resulting in 38 symmetry classes instead of 10 in the Altland-Zirnbauer classification [4]. In random matrices, transposition symmetry leads to two new universality classes of level-spacing statistics other than the Ginibre ensemble. In many-body physics, non-hermiticity leads to the dynamical sign reversal of magnetic correlations in dissipative Hubbard models [6] and anomalous g-theorem-violating reversion of renormalization-group flows in the Kondo problem [7].
[1] Ashida, et al., arXiv:2006.01837. [2] Gong, et al., PRX 8, 031079. [3] Kawabata, et al., Nat. Commun. 10, 297 (2019). [4] Kawabata, et al., PRX 9, 041015 (2019). [5] Hamazaki, et al., Phys. Rev. Research 3, 023286 (2020). [6] Nakawaga, et al., PRL 124, 147203 (2020). [7] Nakawaga, et al., PRL 121, 203001 (2018).   

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The evolution of a quantum system is governed by its discrete energies. These energies are almost always assumed to be real, as is guaranteed by Hermiticity of the system Hamiltonian. Utilizing a dissipative submanifold of a superconducting circuit we realize effective non-Hermitian dynamics, revealing novel features arising from the topology of the Riemann manifolds that describe complex energies. The degeneracies that occur with these non-Hermitian Hamiltonians are known as exceptional points. We employ quasi-static dynamical tuning of Hamiltonian parameters to encircle the exceptional point degeneracies, leading to coherent evolution between quantum states. Our work demonstrates a wholly new method for control over quantum state vectors, highlighting new facets of quantum bath engineering enabled non-Hermitian control.   

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We report our recent experiments on dissipative quantum many-body system using cold atoms in an optical lattice. First, we describe the experiment on PT-symmetric quantum many-body system of bosons utilizing one-body atom loss as dissipation as well as a theoretical framework. We discuss the loss dynamics observed experimentally. Second, we describe the experiment on dynamical control of quantum magnetism utilizing two-body atom loss. We successfully demonstrate the formation of a ferromagnetic spin correlation of ultracold fermions by introducing the dissipation on the initially created antiferromagnetic spin correlation in an optical lattice. We will also discuss the prospects of our research.   

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TBD