Explorations in Non-Hermitian Physics: From Fundamentals to Quantum Information Science Applications

For a quantum system that evolves in isolation, conservation of the total energy demands that the generator of the dynamics, the Hamiltonian, obeys the mathematical constraint of “Hermiticity” – which ensures that observable quantities evolve reversibly in time. Still, non-Hermitian dynamics emerge naturally in open quantum systems whenever the interaction with the environment cannot be ignored, and dissipative, irreversible evolution ensues.

For quantum systems comprising many indistinguishable, “bosonic” degrees of freedom (such as photons, phonons, or even more exotic particles like “magnons”), non-Hermitian effects can arise in the dynamics as a sole consequence of quantum statistics, despite the physical Hamiltonian being Hermitian at the many-body level. The exploration of non-Hermitian dynamics has witnessed an impressive acceleration recently, due to both the merger with fundamental aspects from topological physics and the identification of novel dynamical phenomena.

Exciting applications have been uncovered, ranging from enhanced parameter sensing to new modalities for quantum-limited amplification and routing of quantum information. The broad aim of this project is to advance the knowledge frontiers of non-Hermitian physics, by both using concepts and tools from quantum information science (notably, “entanglement”) to characterize aspects of non-Hermitian dynamics in bosonic systems, and by fully embracing an open-system paradigm where non-Hermitian attributes and dissipation are integral to the operation and control of quantum devices.

In parallel, this program will incorporate a strong educational and training component at the graduate and postdoctoral level, on subjects at the boundary between open quantum systems and quantum statistical mechanics, dynamical system theory, and quantum information processing.

This project will synergistically incorporate theory and experiment throughout its duration. It builds on a body of theoretical results that the principal investigator has established for bosonic systems described by quadratic (“Lindblad”) master equations and on the joint experimental realization of a tunable non-Hermitian nonlinear microwave-cavity dimer, while pushing the investigation in several new directions.

Specific research objectives include: (i) to obtain a complete theoretical understanding of non-Hermitian dynamics in quadratic bosonic systems, by seeking a characterization of dynamical stability phase transitions through the lenses of entanglement theory, and by allowing for explicit time-dependence, with a focus on Floquet non-Hermitian dynamics; (ii) to experimentally demonstrate a quantum analog of the tunable nonlinear dimer we have currently realized at room temperature, and leverage it towards achieving enhanced quantum state transfer in quantum networks; (iii) to make headway toward implementing and exploring many-body non-Hermitian nonlinear dynamics in a six-site bosonic system. Besides being responsive to a timely motivation, we expect the proposed program to contribute fundamental insight into the interplay between non-Hermiticity and many-body quantum physics.

From a practical standpoint, these investigations may point to enhanced protocols for dissipative quantum information processing directly applicable in circuit quantum-electrodynamic settings.

This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.