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arXiv:2405.12080 · Advanced Quantum Technologies

Universal Quantum Fisher Information and Simultaneous Occurrence of Landau‐Class and Topological‐Class Transitions in Non‐Hermitian Jaynes‐Cummings Models

Zu‐Jian Ying

Published Aug 4, 2024• 11 citations
arXivHTMLPDF

Abstract

Abstract Light‐matter interactions provide an ideal testground for interplay of critical phenomena, topological transitions, quantum metrology, and non‐Hermitian physics with high controllability and tunability. The present work considers two fundamental non‐Hermitian Jaynes‐Cummings models in light‐matter interactions that possess real energy spectra in parity‐time (PT) symmetry and anti‐PT symmetry. The quantum Fisher information is shown to be critical around the transitions at the exceptional points and exhibit a super universality, with respect to different parameters, all energy levels, both models, symmetric phases, and symmetry‐broken phases, which guarantees a universally high measurement precision in quantum metrology. In particular, the transitions are found to be both symmetry‐breaking Landau‐class transitions (LCTs) and symmetry‐protected topological‐class transitions (TCTs), thus realizing a simultaneous occurrence of critical LCTs and TCTs that are conventionally incompatible due to contrary symmetry requirements. Besides establishing a paradigmatic case to break the incompatibility of the LCTs and the TCTs in non‐Hermitian systems, the both availabilities of the sensitive critical feature and the robust topological feature can also provide more potential for designing quantum devices or sensors.

DOI
10.1002/qute.202400288

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Abstract Light‐matter interactions provide an ideal testground for interplay of critical phenomena, topological transitions, quantum metrology, and non‐Hermitian physics with high controllability and tunability. The present work considers two fundamental non‐Hermitian Jaynes‐Cummings models in light‐matter interactions that possess real energy spectra in parity‐time (PT) symmetry and anti‐PT symmetry. The quantum Fisher information is shown to be critical around the transitions at the exceptional points and exhibit a super universality, with respect to different parameters, all energy levels, both models, symmetric phases, and symmetry‐broken phases, which guarantees a universally high measurement precision in quantum metrology. In particular, the transitions are found to be both symmetry‐breaking Landau‐class transitions (LCTs) and symmetry‐protected topological‐class transitions (TCTs), thus realizing a simultaneous occurrence of critical LCTs and TCTs that are conventionally incompatible due to contrary symmetry requirements. Besides establishing a paradigmatic case to break the incompatibility of the LCTs and the TCTs in non‐Hermitian systems, the both availabilities of the sensitive critical feature and the robust topological feature can also provide more potential for designing quantum devices or sensors.
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ABSTRACT Non‐Hermitian systems have attracted increasing attention in recent years, particularly those exhibiting Parity‐Time (PT) symmetry. Quantum metrology establishes the ultimate attainable bounds for parameter estimation in both Hermitian and non‐Hermitian systems. However, comparatively little is known about non‐Hermitian systems with anti‐Parity‐Time (APT) symmetry. In this work, we investigate the theoretical bounds on quantum parameter estimation precision for an APT‐symmetric system governed by the Bogoliubov–de Gennes (BdG) Hamiltonian. We explicitly derive the expression for the quantum Fisher information (QFI) and compare the attainable precision limits for both multiplicative and non‐multiplicative parameters in the BdG Hamiltonian. Our analysis of the effective QFI reveals that quantum parameter estimation precision can be significantly enhanced as the system approaches the exceptional point with unbroken APT symmetry, where Heisenberg scaling becomes achievable. We also examine how the effective QFI depends on the choice of initial states. Furthermore, we demonstrate that entanglement in multi‐particle initial state can provide an additional enhancement to the QFI. The ratio of limit of parameter estimation precision of the entangled state to the greatest one we have found over all the tensor product states is 1.22, which is greater than 1. Our analysis of two‐particle states confirms that entanglement in the initial state can further increase the QFI, highlighting it as a valuable quantum resource. These findings lay a theoretical foundation for future experimental explorations of parameter estimation in APT‐symmetric non‐Hermitian systems.
Abstract Universality is a common quality in different physical parameters that is rooted in the deep nature of physical systems. Scaling relation is a typical universality for critical phenomena around a quantum phase transition, while topological classification provides another type of universality essentially different from the critical universality. Both classes of universalities can be present in a single‐qubit system with light‐matter interactions, as exhibiting generally in the fundamental quantum Rabi model with anisotropy not only for linear coupling but also for nonlinear Stark coupling (NSC). In low frequencies different levels of scaling relations are extracted, holding for anisotropic or/and NSCs, locally or globally. At finite frequencies such a critical universality breaks down and diversity is dominant. However, common topological feature of the ground state can be extracted from the node number, which yields a topological class of universality amidst the critical diversity. Both conventional and unconventional topological transitions emerge, with their meeting, which never occurs in linear interaction, enabled by the nonlinear coupling to form topological quadruple points which are found to be spin‐invariant points. Sensitivity analysis indicates that the NSC can be another applicable approach to manipulate topological transitions in addition to coupling anisotropy.
ABSTRACT Harnessing parity–time symmetry with balanced gain and loss profiles has created a variety of opportunities in an electronic system from wireless energy transfer to telemetry sensing and topological defect engineering. However, it is difficult to capture the ‐symmetry phase transition in an electronic system due to the limitation of probing the virtual energy spectrum. Here, we proposed a scheme to probe the ‐symmetry phase transition in an Non‐Hermitian (NH) Su–Schrieffer–Heeger (SSH) electronic chain coupled to a cavity. We show that, when ‐symmetry is broken, the cavity ground state is a Squeezed Displaced Schrödinger cat (SDSc) state, which immediately disappears when the symmetry recovers. Thus, our proposal provides a platform for capturing ‐symmetry phase transition based on cavity ground state. Furthermore, we demonstrate that the generation of the SDSc state in our scheme is related to spontaneous symmetry breaking mechanism. Besides, we exploit the cavity ground state to estimate the phase in the optical interferometer, and show that the quantum Fisher information and nonclassicality will sharply decline when symmetry recovers. This suggests that the phase estimation is preferably performed in the broken PT‐symmetry phase near the exceptional‐points. Our proposal offers a scheme not only to manipulate but also to probe the properties of electronic materials based on quantum Floquet engineering, and improve the utilization of cavity ground states in quantum metrology.
Superradiant phase transitions are fundamental phenomena in light-matter coupled systems. Here, we uncover a novel class of superradiant criticality that is topologically distinct from previously known superradiant transitions. Using cavity-mediated cluster-Ising chains as an illustrative example, we numerically demonstrate that the critical line separating the superradiant phase from the cavity topological phase hosts robust symmetry-protected edge degeneracies, a feature absent in conventional superradiant transitions. Remarkably, although its local bulk critical properties are indistinguishable from those of the previously identified topologically trivial superradiant transition, the two criticalities cannot be smoothly connected without breaking the protecting symmetries or passing through a multicritical point. We further show that such topological superradiant criticality is generic, also occurring in cavity-mediated Zn\mathbb{Z}_{n}^{}Zn​ cluster-qudit chains, as supported by complementary lattice simulations.