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Photonic Statistical Topological Transition (PSTT)

Jincheng Zhang

Published Aug 17, 2026• 0 citations
Publisher

Abstract

The statistical properties of photons, quantified by the normalized correlation functions g^(n), have traditionally been treated as passive descriptors of quantum light. This paper introduces the concept of a Photonic Statistical Topological Transition (PSTT), whereby the photon correlation functions undergo discrete, topologically protected changes as system parameters are varied. We demonstrate that the second‑order correlation g^(2) can transition from a value of unity, characteristic of coherent light, to zero, indicative of perfect photon antibunching, in a manner that is accompanied by a non‑trivial winding of the phase of the two‑point correlation function across a parameter space. This behavior is shown to be governed by a topological invariant analogous to a winding number or Chern number in condensed‑matter systems. The theoretical framework is illustrated using a one‑dimensional array of coupled nonlinear cavities, modeled by the Bose‑Hubbard Hamiltonian with nearest‑neighbor hopping. The results suggest that PSTT constitutes a new class of quantum photonic phase transitions, with potential implications for the discovery of novel quantum light states and applications in quantum technologies.

DOI
10.5281/zenodo.21972995

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The statistical properties of photons, quantified by the normalized correlation functions g^(n), have traditionally been treated as passive descriptors of quantum light. This paper introduces the concept of a Photonic Statistical Topological Transition (PSTT), whereby the photon correlation functions undergo discrete, topologically protected changes as system parameters are varied. We demonstrate that the second‑order correlation g^(2) can transition from a value of unity, characteristic of coherent light, to zero, indicative of perfect photon antibunching, in a manner that is accompanied by a non‑trivial winding of the phase of the two‑point correlation function across a parameter space. This behavior is shown to be governed by a topological invariant analogous to a winding number or Chern number in condensed‑matter systems. The theoretical framework is illustrated using a one‑dimensional array of coupled nonlinear cavities, modeled by the Bose‑Hubbard Hamiltonian with nearest‑neighbor hopping. The results suggest that PSTT constitutes a new class of quantum photonic phase transitions, with potential implications for the discovery of novel quantum light states and applications in quantum technologies.
The concept of a photonic statistical topological transition (PSTT) introduces a novel framework in which the statistical properties of photons, quantified by higher‑order correlation functions g^(n), undergo topological changes that give rise to new quantum photonic phases. This paper presents a comprehensive theoretical analysis of PSTT, establishes the mathematical conditions under which topological invariants associated with photon statistics can change, and discusses the physical implications of such transitions. We demonstrate that the second‑order correlation function g^(2) can evolve from values characteristic of classical light (g^(2) > 1) to those of non‑classical light (g^(2) < 1) via a topologically protected transition, and we generalize the argument to higher‑order correlations. The potential for discovering new quantum light states, which may have applications in quantum information processing, precision measurement, and fundamental tests of quantum mechanics, is highlighted.
Emerged as the quantum counterpart of classical random walks, quantum walks are established precious resources in a variety of quantum sciences. Recent studies have shown that quantum walks may be characterized by topological invariants, in close analogy to condensed matter systems exhibiting topological order. Exploiting these features, quantum walks are currently used to simulate topological systems and to probe their exotic features. Here we present the implementation of a one-dimensional quantum walk protocol based on the orbital angular momentum of light, manifesting the topological phases that characterize time-periodic systems (Floquet topological insulators) showing chiral symmetry. By considering the orbital angular momentum spectrum of a light beam undergoing this quantum evolution, we show that the associated statistical moments have marked differences in distinct phases and contain information on the system topology. While varying a control parameter determining the value of the invariants, these moments in the large step-number limit exhibit a sharp variation at the phase changes. We show that these phenomena arise from the singular behavior of the dispersion relation at the transition points. The extension of our results to systems featuring different symmetries, or characterized by higher spatial dimensions, may unveil novel intriguing features associated with these complex systems.
We study topological properties of phase transition points of one-dimensional topological quantum phase transitions by assigning winding numbers defined on closed circles around the gap closing points in the parameter space of momentum and a transition driving parameter, which overcomes the problem of ill definition of winding numbers on the transition points. By applying our scheme to the extended Kitaev model and to the extended Su-Schrieffer-Heeger model, we demonstrate that the topological phase transition can be well characterized by winding numbers of transition points, which reflect the change of the winding number of topologically different phases across the phase transition points.
Dynamical quantum phase transitions (DQPTs) manifested in the nonanalyticities in the temporal evolution of a closed quantum system generated by the time-independent final Hamiltonian, following a quench (or ramping) of a parameter of the Hamiltonian, is an emerging frontier of nonequilibrium quantum dynamics. We, here, introduce the notion of a dynamical topological order parameter (DTOP) that characterizes these DQPTs occurring in quenched (or ramped) two-dimensional closed quantum systems; this is quite a nontrivial generalization of the notion of DTOP introduced in Budich and Heyl [Phys. Rev. B 93, 085416 (2016)] for one-dimensional situations. This DTOP is obtained from the ``gauge-invariant'' Pancharatnam phase extracted from the Loschmidt overlap, i.e., the modulus of the overlap between the initially prepared state and its time-evolved counterpart reached following a temporal evolution generated by the time-independent final Hamiltonian. This generic proposal is illustrated considering DQPTs occurring in the subsequent temporal evolution following a sudden quench of the staggered mass of the topological Haldane model on a hexagonal lattice where it stays fixed to zero or unity and makes a discontinuous jump between these two values at critical times at which DQPTs occur. What is remarkable is that while the topology of the equilibrium model is characterized by the Chern number, the emergent topology associated with the DQPTs is characterized by a generalized winding number.
Abstract The topological properties of a circuit‐QED lattice are studied and it is found that the system undergoes a topological phase transition accompanied by the changes of Chern numbers from 2 to −1. For different lattice sizes, the energy eigenvalue spectra and the probability distributions of edge states are shown. Moreover, it is revealed that, depending on the strictly adiabatic evolution of the time‐dependent Hamiltonian, several different topological quantum state transfers between the first two sites and the last two sites can be achieved by employing the topologically protected edge states as the transfer channels. Further, it is demonstrated that, by using resonator‐based input–output process, the photonic topological edge state can be detected by measuring the average photon number in the steady state. The scheme opens up a new prospect for investigating the potential application of topological matter in quantum information processing.
Quantum technologies, holding the promise of exponentially superior performance in comparison to their classical counterparts for certain tasks, have consistently encountered challenges, including instability in quantum light sources, quantum decoherence, and vulnerability to losses that topological photonics happens to adeptly address. Here, we theoretically put forth a quantum Su-Schrieffer-Heeger-type chain designed to greatly enhance single-photon blockade (single PB) effect with topological protection. By designing the deliberate coupling strengths, the quantum level lattices take the form of a one-dimensional array with a topological edge state in single-excitation space and a two-dimensional square breathing lattice with topological corner states in two-excitation space, resulting in enhanced single-photon excitation and the suppression of two-photon transitions. Therefore, the second-order correlation function is diminished by up to 2 orders of magnitude at the cavity resonance frequency, accompanied by stronger brightness. Furthermore, the PB effect is robust to local perturbations in cavity-qubit coupling and qubit frequency, benefitting from topological protection.