Spectroscopic Readout of Chiral Photonic Topology Reveals Chern Marker in Spin-Orbit-Coupled Bose-Einstein Condensate

Topological photonics promises robust and versatile control of light, but identifying topological phases typically requires complex measurements of light transmission or real-space imaging. Kashif Ammar Yasir and Gao Xianlong, from Zhejiang Normal University, now demonstrate a significantly simpler approach, directly linking the noise in light emitted from a specially prepared atomic gas to the underlying topological properties. Their work reveals how the power spectral density, essentially, a measure of the light’s ‘colour’, acts as a direct indicator of a photonic Chern marker, a key quantity defining the topological state. This breakthrough allows researchers to infer topological characteristics from spectral data alone, bypassing the need for extensive analysis of bulk band structures and opening new avenues for compact, tunable topological photonic devices across a range of materials and systems.

One-Dimensional Reduction Validates Cavity BEC Model

Scientists demonstrate that a simplified one-dimensional model accurately describes the behavior of a spin-orbit-coupled Bose-Einstein condensate within a cavity, despite the experiment involving a two-dimensional standing-wave potential. This simplification reduces computational complexity without sacrificing accuracy, allowing detailed exploration of how parameters like spin-orbit coupling, interspecies interactions, and atom-cavity coupling influence transmission characteristics, the Chern marker, and topological edge states. Detailed analysis supports the claims made in the main research paper. Analysis of the transmission power spectral density reveals it remains effectively one-dimensional because the Raman process primarily imparts momentum in one direction, and the cavity mode strongly overlaps with density modulations along that same direction.

Increasing spin-orbit coupling enhances spin-momentum locking, splitting the response into two hybridized branches and opening a gap, while increasing interspecies interactions renormalizes atomic dispersion and shifts the frequencies of observed ridges, providing control over the band geometry and spectral placement of topological edge states. Researchers also examined the influence of atom-cavity coupling and spin-orbit coupling on the power spectral density-derived Chern marker, finding that increasing atom-cavity coupling enhances hybridization and amplifies the contribution of edge states. Increasing spin-orbit coupling sharpens band separation and redistributes topological weight, providing control over the strength and activation of the topological edge response. This work validates the theoretical model and demonstrates control over topological states, with potential implications for quantum technologies and understanding non-Hermitian physics.

Chiral Photonic Topology via Cavity Spectroscopy

Scientists engineered a novel spectroscopic framework to probe chiral photonic topology within a driven cavity containing a spin-orbit-coupled Bose-Einstein condensate. The study pioneered a method where the cavity transmission power spectral density directly reveals a momentum- and frequency-resolved photonic Chern marker, bypassing the need for complex bulk-band tomography. Researchers established a system comprising approximately 180,000 atoms within a high-finesse Fabry-Pérot cavity, driven by a laser. The team applied a magnetic field perpendicular to the cavity axis, creating a Zeeman splitting and establishing a pseudo-spin degree of freedom.

By analyzing the cavity transmission power spectral density, scientists reconstructed the Berry curvature from the complex band structure, demonstrating its strong correlation with the distribution of the Chern marker. Experiments employed a near-dispersive regime, and in the loss-dominated regime, the power spectral density exhibits Dirac-like gapped hybrid modes, with the Chern marker concentrating in localized hotspots. Conversely, when atomic dissipation exceeds cavity decay, the system transitions into a parity-time symmetric regime, where eigenvalues coalesce and bifurcate into ring-shaped contours, reorganizing the Chern marker into annular structures. This approach establishes cavity transmission noise as a powerful tool for observing Chern markers, Berry curvature, and exceptional-point physics in hybrid atom-photon systems, offering a pathway toward topological sensing and information processing with quantum gases in cavities. This work demonstrates a new method for spectroscopically detecting chiral photonic topology without requiring complex band structure reconstructions or real-space imaging of edge modes.

Spectral Signatures Reveal Photonic Topology Directly

Scientists directly measure topological properties of light within a unique hybrid system combining a Bose-Einstein condensate and a high-quality optical cavity. This work establishes a new framework for spectroscopically detecting chiral photonic topology, bypassing the need for complex band structure reconstructions or real-space imaging of edge modes. The team demonstrates that the power spectral density of the cavity transmission serves as a direct and measurable proxy for a momentum- and frequency-resolved photonic Chern marker, effectively revealing topological characteristics from spectral data alone. Experiments reveal that in a loss-dominated regime, the power spectral density exhibits Dirac-like gapped hybrid modes with a vanishing Chern marker, indicating a trivial topological phase.

However, when the dissipation imbalance is reversed, a bright spectral ridge emerges, spanning the energy gap and co-localized with peaks in both the Chern marker and Berry curvature, signifying a transition to a non-trivial topological state. The researchers achieved this using a Bose-Einstein condensate containing approximately 180,000 atoms confined within a Fabry-Pérot cavity. Measurements confirm the presence of parity-time symmetric coalescences and gain-loss bifurcations within the complex spectrum, marking exceptional points and enabling chiral, gap-traversing transport of light. The team operates with a driving laser and applies a magnetic field, creating a Zeeman splitting. By linking noise spectroscopy to geometric and non-Hermitian topology within this minimal cavity-QED architecture, this work provides a pathway to compact, tunable topological photonics across a broad range of light-matter platforms.

Topological Phase Detection via Spectral Signatures

This research demonstrates a new method for identifying and characterizing topological photonic phases within a driven spin-orbit-coupled Bose-Einstein condensate. Scientists successfully linked the power spectral density of cavity transmission to a measurable momentum- and frequency-resolved photonic Chern marker, effectively transforming a standard optical measurement into a tool for probing topological characteristics without requiring complex band reconstruction techniques. The findings reveal that the presence of topological edge modes correlates directly with a gap-spanning spectral ridge and a concentrated Chern marker, appearing when atomic dissipation exceeds cavity decay. Importantly, the team established a clear distinction between topological and trivial phases, with a vanishing Chern marker in the loss-dominated regime confirming the absence of edge states.

Further analysis using Berry curvature maps provided geometric insight, while the identification of exceptional points linked to parity-time symmetry reveals the conditions governing chiral, gap-spanning transport. This advancement offers a pathway to engineer, read out, and tune topological phases using standard optical methods, representing a significant step towards more compact and accessible topological photonic devices. This work establishes a new method for identifying and characterizing topological photonic phases within a driven spin-orbit-coupled Bose-Einstein condensate.