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arXiv:2605.10329 · Physical Review A

Partial Quantisation of Non-Hermitian Berry Phases in Time-Varying Media

Calvin Hooper

physics.opticsquant-phSubmitted May 11, 2026• Announced May 12, 2026• 0 citations
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Abstract

A fundamental symmetry of the non-Hermitian operators describing wave-propagation in time-varying media imbue such systems with non-trivial topology. This topology may be measured directly in a wide range of experimental settings as a quantised real part of the Berry phase, contrasting unconstrained geometric gain or loss. This topological index is provided explicitly for practical examples, including a non-Hermitian analogue of the Su-Schrieffer-Heeger model.

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A fundamental symmetry of the non-Hermitian operators describing wave-propagation in time-varying media imbue such systems with non-trivial topology. This topology may be measured directly in a wide range of experimental settings as a quantised real part of the Berry phase, contrasting unconstrained geometric gain or loss. This topological index is provided explicitly for practical examples, including a non-Hermitian analogue of the Su-Schrieffer-Heeger model.
Abstract We study the complex Berry phases in non-Hermitian systems with parity- and time-reversal   symmetry. We investigate a kind of two-level system with   symmetry. We find that the real part of the the complex Berry phases have two quantized values and they are equal to either 0 or π , which originates from the topology of the Hermitian eigenstates. We also find that if we change the relative parameters of the Hamiltonian from the unbroken-   -symmetry phase to the broken-   -symmetry phase, the imaginary part of the complex Berry phases are divergent at the exceptional points. We exhibit two concrete examples in this work, one is a two-level toys model, which has nontrivial Berry phases; the other is the generalized Su–Schrieffer–Heeger (SSH) model that has physical loss and gain in every sublattice. Our results explicitly demonstrate the relation between complex Berry phases, topology and   -symmetry breaking and enrich the field of the non-Hermitian physics.
We demonstrate that genuinely non-Hermitian topological phases and corresponding topological phase transitions can be naturally realized in monitored quantum circuits, exemplified by the paradigmatic non-Hermitian Su-Schrieffer-Heeger model.We emulate this model by a 1D chain of spinless electrons evolving under unitary dynamics and subject to periodic measurements that are stochastically invoked.The non-Hermitian topology is visible in topological invariants adapted to the context of monitored circuits.For instance, the topological phase diagram of the monitored realization of the non-Hermitian Su-Schrieffer-Heeger model is obtained from the biorthogonal polarization computed from an effective Hamiltonian of the monitored system.Importantly, our monitored circuit realization allows direct access to steady-state biorthogonal expectation values of generic observables, and hence, to measure physical properties of a genuine non-Hermitian model.We expect our results to be applicable more generally to a wide range of models that host non-Hermitian topological phases.
The geometrical Berry phase is key to understanding the behaviour of quantum states under cyclic adiabatic evolution. When generalised to non-Hermitian systems with gain and loss, the Berry phase can become complex, and should modify not only the phase but also the amplitude of the state. Here, we perform the first experimental measurements of the adiabatic non-Hermitian Berry phase, exploring a minimal two-site PT\mathcal{PT}PT-symmetric Hamiltonian that is inspired by the Hatano-Nelson model. We realise this non-Hermitian model experimentally by mapping its dynamics to that of a pair of classical oscillators coupled by real-time measurement-based feedback. As we verify experimentally, the adiabatic non-Hermitian Berry phase is a purely geometrical effect that leads to significant amplification and damping of the amplitude also for non-cyclical paths within the parameter space even when all eigenenergies are real. We further observe a non-Hermitian analog of the Aharonov--Bohm solenoid effect, observing amplification and attenuation when encircling a region of broken PT\mathcal{PT}PT symmetry that serves as a source of imaginary flux. This experiment demonstrates the importance of geometrical effects that are unique to non-Hermitian systems and paves the way towards the further studies of non-Hermitian and topological physics in synthetic metamaterials.
Composite topological phases with intriguing topology like M\"obius strips emerge in sublattice symmetric non-Hermitian systems due to spontaneous breaking of time-reversal symmetry at some parameter regime. While these phases have been characterized by nonadiabatic complex geometric phases of multiple participating complex bands, the physical properties of these phases remain largely unknown. We explore the dynamical response of these phases by studying Loschmidt echo from an initial state of the Hermitian Su-Schrieffer-Heeger (SSH) model, which is evolved by a non-Hermitian SSH Hamiltonian after a sudden quench in parameters. Topology-changing quenches display nonanalytical temporal behavior of return rates (logarithm of the Loschmidt echo) for the non-Hermitian SSH Hamiltonian in the trivial, M\"obius, and topological phase. Moreover, the dynamical topological order parameter appears only at one side of the Brillouin zone for the M\"obius phase case in contrast to both sides of the Brillouin zone for quench by the trivial and topological phase of the non-Hermitian SSH model. The last feature is a dynamical signature of different symmetry constraints on the real and imaginary parts of the complex bands in the M\"obius phase.
Abstract The dynamical and topological properties of non-Hermitian systems have attracted great attention in recent years. In this work, we establish an intrinsic connection between two classes of intriguing phenomena—topological phases and dynamical quantum phase transitions (DQPTs)—in non-Hermitian systems. Focusing on one-dimensional models with chiral symmetry, we find DQPTs following the quench from a trivial to a non-Hermitian topological phase. Moreover, the critical momenta and critical time of the DQPTs are found to be directly related to the topological invariants of the non-Hermitian system. We further demonstrate our theory in three prototypical non-Hermitian lattice models, the lossy Kitaev chain (LKC), the LKC with next-nearest-neighbor hoppings, and the nonreciprocal Su–Schrieffer–Heeger model. Finally, we suggest a proposal to experimentally verify the found connection by a nitrogen-vacancy center in diamond.
Concepts from non-Hermitian quantum mechanics have proven useful in understanding and manipulating a variety of classical systems, such as those encountered in optics, classical mechanics, and metamaterial design. Recently, the non-Hermitian analog of the Berry phase for adiabatic processes was experimentally measured. In non-Hermitian systems, the Berry phase can have an imaginary part, which contributes to the amplification or decay of the total wave intensity. When the imaginary part of the Berry curvature is zero, this geometric amplification factor is determined solely by the initial and final points of the adiabatic path in parameter space, and it does not depend on how these points are connected by the path. We list classes of non-Hermitian Hamiltonians where this path independence is guaranteed by suitable symmetries, and we find that, for some of these classes, the amplification factor can be written only in terms of the Petermann factors of the initial and final points. Our result can, in turn, be used to experimentally obtain the Petermann factor by observing how the norm of the wave function changes under adiabatic processes. We validate our theory using a couple of concrete examples of physical relevance.