Framework for (non-)adiabatic chiral state conversion: from non-Hermitian Hamiltonians to Liouvillians

TL;DR

The paper tackles the problem of understanding chiral state conversion (CSC) in open quantum systems described by non-Hermitian dynamics. It develops a unified slow-driving framework that encompasses non-Hermitian Hamiltonians, Lindblad, and hybrid-Lindblad evolution, and shows that CSC can arise from first non-adiabatic corrections even far from ideal adiabaticity. Through two dissipative qubit models, Model A and Model B, the work derives analytical expressions for conversion fidelities and reveals how trajectory orientation (chirality) and dissipation-coupling balance control CSC; it also demonstrates CSC in a no-EP model under NHH, and discusses how EP encirclement is not a necessary condition. The framework connects to Floquet-Lindblad theory for periodic driving and highlights the potential of non-perturbative dynamics to enhance CSC, offering a practical toolkit for predicting CSC in complex open quantum systems.

Abstract

Adiabatic chiral state conversion (CSC) is one of the many counterintuitive effects associated with non-Hermitian physics. In quantum systems, numerous works have demonstrated this phenomenon under both non-Hermitian Hamiltonian and Lindblad evolution. However, despite considerable progress, the physical mechanism behind it has been a subject of debate. In this work, we present a unified framework that explains CSC in any non-Hermitian system, encompassing non-Hermitian Hamiltonian, Lindblad, and hybrid settings. Our framework relies on perturbative, non-adiabatic corrections to adiabatic evolution and consistently predicts CSC with only the lowest-order corrections. We demonstrate its efficacy with models of single and coupled dissipative qubits, obtaining analytical solutions for the conversion fidelity. Our analysis further reveals the role of non-perturbative dynamics, which can be present even in apparently slow trajectories. We show that this property can be utilised to considerably enhance state conversion. Finally, we demonstrate that CSC can be observed in a model without the presence of exceptional points.

Figures (10)

• Figure 1: A sketch of chiral state conversion. A non-Hermitian system is slowly driven from one eigenstate; depending on the orientation of the parameter trajectory, it either makes a non-adiabatic transition to another eigenstate or returns to the initial one. Even though the evolution may involve noisy or far-from-adiabatic behaviour along the trajectory due to its form or the inherent properties of the involved dynamics, the conversion is well described by slow-driving predictions.
• Figure 2: Conversion fidelity $F_-$ as a function of rescaled time $s= t/T$ for (a) CCW and (b) CW trajectories with the initial state $\rho(0)=\ketbra{+}{+}$, with $\gamma^+=0$ and $\gamma^-=\gamma(t)$. The slow-driving prediction corresponds to a two-step application of the slow-driving operator with $s^*=1/2$. Parameters: $\delta_0=1$, $\gamma'=0.1\delta_0$, $\gamma_0=0.1\delta_0$, $\kappa=0.12\delta_0$ and $\gamma' T =200$.
• Figure 3: (a) $F_-$ as a function of $s=t/T$ for $q=0.5$ with $\rho(0)=\ketbra{+}{+}$ for CCW (solid) and CW (dashed) trajectories. The slow-driving prediction is shown up to $s=0.99$. (b) $F_-(T)$ (with the full solution) and $F_-(0.99T)$ (with the slow-driving approximation) as a function of $q$ with the same initial state and CCW trajectory. Parameters: $\gamma^+=0$, $\gamma^-=\gamma(t)$, $\delta_0=1$, $\gamma'=0.1\delta_0$, $\gamma_0=0.05\delta_0$, $\kappa=0.15\delta_0$ and $\gamma' T =200$.
• Figure 4: CSC under Lindblad evolution with $\rho(0)=\ketbra{+}{+}$ with a CCW trajectory, calculated with the full solution (black), first-order approximation (red) and second-order approximation (green). We have taken $\gamma^+=0$ and $\gamma^-=\gamma(t)$. (a) $F_-$ as a function of $s=t/T$ with parameters taken from Fig. \ref{['Fig_1qub_Heff']}. (b) The same except with an increased $\kappa=0.25\delta_0$. (c) $F_-(T)$ as a function of $\kappa/\gamma'$ with fixed $\gamma'=0.1\delta_0$ (solid) and $\gamma'=0.06\delta_0$ (dashed), with $\delta_0=1$ and $T=2000$.
• Figure 5: $F_-$ as a function of $s=t/T$ with the global master equation for $q=0$ and CCW trajectory. Parameters: $\delta_0 =10$, $\gamma'=0.01\delta_0$, $\gamma_0=0.005\delta_0$, $g=0.02\delta_0$, $\gamma'T=200$, $s^*=1/2$.