Non-Hermitian skin effect and chiral damping in open quantum systems (1904.08432v2)

Abstract: One of the unique features of non-Hermitian Hamiltonians is the non-Hermitian skin effect, namely that the eigenstates are exponentially localized at the boundary of the system. For open quantum systems, a short-time evolution can often be well described by the effective non-Hermitian Hamiltonians, while long-time dynamics calls for the Lindblad master equations, in which the Liouvillian superoperators generate time evolution. In this Letter, we find that Liouvillian superoperators can exhibit the non-Hermitian skin effect, and uncover its unexpected physical consequences. It is shown that the non-Hermitian skin effect dramatically shapes the long-time dynamics, such that the damping in a class of open quantum systems is algebraic under periodic boundary condition but exponential under open boundary condition. Moreover, the non-Hermitian skin effect and non-Bloch bands cause a chiral damping with a sharp wavefront. These phenomena are beyond the effective non-Hermitian Hamiltonians; instead, they belong to the non-Hermitian physics of full-fledged open quantum dynamics.

• The paper shows that the non-Hermitian skin effect transitions damping from algebraic to exponential behaviors in open quantum systems.
• The study introduces chiral damping, where damping propagates unidirectionally due to non-Bloch band effects.
• Analytical and numerical methods confirm that Liouvillian dynamics exhibit NHSE, offering new insights for experimental designs in non-Hermitian quantum systems.

Non-Hermitian Skin Effect and Chiral Damping in Open Quantum Systems: An Expert Overview

The exploration of non-Hermitian physics in quantum systems has unveiled distinct phenomena, such as the non-Hermitian skin effect (NHSE), which describes the exponential localization of eigenstates at system boundaries. The paper "Non-Hermitian skin effect and chiral damping in open quantum systems" extends this concept by examining open quantum systems governed by Lindblad master equations rather than non-Hermitian Hamiltonians alone. The authors, Song, Yao, and Wang, provide evidence that Liouvillian superoperators, responsible for the time evolution in open quantum systems, display the NHSE, leading to significant consequences for system dynamics.

Key Contributions and Findings

1. Interrelation Between NHSE and Long-Time Dynamics: The paper shows that the NHSE profoundly influences the long-term dynamics of open quantum systems. Particularly, it affects the damping behavior, characterized by a transition from algebraic under periodic boundary conditions to exponential under open boundary conditions.
2. Chiral Damping Phenomenon: A novel insight is the introduction of chiral damping, a unidirectional damping with a defined wavefront, driven by NHSE and non-Bloch bands. This chiral nature implies that damping propagates in a specific direction, offering a new perspective on how boundaries influence quantum dynamics beyond Hermitian systems.
3. Numerical and Analytical Validation: Through analytical methods and numerical simulations, the paper rigorously demonstrates the presence of NHSE in the Liouvillian formalism and its resulting chiral damping effect. Notably, periodic boundary systems exhibit different damping characteristics compared to open boundary systems due to NHSE.

Implications and Future Directions

The implications of these findings are multifaceted. Practically, this paper suggests that the open boundary conditions in experiments can lead to faster convergence to steady states than anticipated by traditional periodic boundary models. This realization can significantly impact experimental design and interpretation in systems involving non-Hermitian dynamics and open quantum systems, such as cold atoms or photonic systems.

Theoretically, the linkage between non-Hermitian physics and open quantum dynamics invites further exploration into related phenomena, including potential new classifications of topological matter and extensions of non-Hermitian topology. Additionally, the paper urges investigation into other aspects of non-Hermitian physics, such as PT symmetry breaking, within the framework of open systems.

Speculation on Future Developments

Looking forward, key areas for future research can include the extension of NHSE and chiral damping analysis to interacting systems, which could reveal richer dynamical behaviors. Integrating non-Hermitian topological invariants with the full-fledged Liouvillian dynamics also presents an exciting avenue. Understanding how these non-Hermitian features interact with dissipative quantum interactions could revolutionize our approach to quantum computation and simulation in open systems.

In conclusion, this paper provides a comprehensive insight into how NHSE affects open quantum dynamics, challenging and extending the conventional understanding of quantum system behavior. This work serves as a pivotal step in the burgeoning field of non-Hermitian quantum mechanics, bridging the gap between theoretical predictions and experimental realizations.