Loschmidt echo and fidelity decay near an exceptional point

Abstract

Non-Hermitian classical and open quantum systems near an exceptional point (EP) are known to undergo strong deviations in their dynamical behavior under small perturbations or slow cycling of parameters as compared to Hermitian systems. Such a strong sensitivity is at the heart of many interesting phenomena and applications, such as the asymmetric breakdown of the adiabatic theorem, enhanced sensing, non-Hermitian dynamical quantum phase transitions and photonic catastrophe. Like for Hermitian systems, the sensitivity to perturbations on the dynamical evolution can be captured by Loschmidt echo and fidelity after imperfect time reversal or quench dynamics. Here we disclose a rather counterintuitive phenomenon in certain non-Hermitian systems near an EP, namely the deceleration (rather than acceleration) of the fidelity decay and improved Loschmidt echo as compared to their Hermitian counterparts, despite large (non-perturbative) deformation of the energy spectrum introduced by the perturbations. This behavior is illustrated by considering the fidelity decay and Loschmidt echo for the single-particle hopping dynamics on a tight-binding lattice under an imaginary gauge field.

11 pages, 6 figures, to appear in Annalen der Physik

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• Exceptional Topology of Non-Hermitian Systems
• Non-Hermitian Topological Sensors
• Probing non-Hermitian Skin Effect and non-Bloch Phase Transitions
• Exact solution of non-Hermitian systems with generalized boundary conditions: size-dependent boundary effect and fragility of skin effect
• Non-Bloch band collapse and chiral Zener tunneling
• Deconstructing effective non-Hermitian dynamics in quadratic bosonic Hamiltonians
• Ultrafast and Anharmonic Rabi Oscillations between Non-Bloch-Bands
• Non-Hermitian skin effect as an impurity problem
• General properties of fidelity in non-Hermitian quantum systems with PT symmetry
• Sensitivity of non-Hermitian systems
• Non-adiabatic transitions through exceptional points in the band structure of a PT-symmetric lattice
• Probing non-Hermitian phase transitions in curved space via quench dynamics
• Anomalous dynamical response of non-Hermitian topological phases
• Quantum probing topological phase transitions by non-Markovianity
• Arnold's potentials and quantum catastrophes
• Non-Hermitian Multimode Interference
• Fidelity and quantum geometry approach to Dirac exceptional points in diamond nitrogen-vacancy centers
• Precision-Induced Irreversibility in non-Hermitian systems