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Advanced Photonics Nexus

High-precision detection of birefringence change using geometric phase transition

Xiliang Zhang, Qian Lin, Yanwen Hu, Haolin Lin, Zhen Li, Zhenqiang Chen, Shenhe Fu

Published Jan 13, 2026• 0 citations
Publisher

Abstract

We present both theoretical and experimental demonstrations of geometric phase (GP) transitions in a synthetic two-level photonic system. We demonstrate the use of this nontrivial phenomenon to achieve an unprecedented birefringence change detection, with a precision up to Δn∼10−11. This result represents a significant improvement of 3 orders of magnitude over conventional techniques (typically limited to the level of Δn∼10−8). In this system, two orthogonal polarizations of light constitute the effective two-level system, which is driven by a birefringence-sensitive synthetic magnetic field. A given photonic spin is able to precess around the “magnetic” field and exhibits a topological transition in its evolution trajectory in parameter space. We establish a direct relationship between the GP transition and birefringence change, which is the basis of our detection technique. This approach significantly improves detection sensitivity and stability as compared with previous detection techniques. Moreover, the presented results benefit many fundamental and applied research fields such as structured light shaping and photonic switching.

DOI
10.1117/1.apn.5.1.016015

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We present both theoretical and experimental demonstrations of geometric phase (GP) transitions in a synthetic two-level photonic system. We demonstrate the use of this nontrivial phenomenon to achieve an unprecedented birefringence change detection, with a precision up to Δn∼10−11. This result represents a significant improvement of 3 orders of magnitude over conventional techniques (typically limited to the level of Δn∼10−8). In this system, two orthogonal polarizations of light constitute the effective two-level system, which is driven by a birefringence-sensitive synthetic magnetic field. A given photonic spin is able to precess around the “magnetic” field and exhibits a topological transition in its evolution trajectory in parameter space. We establish a direct relationship between the GP transition and birefringence change, which is the basis of our detection technique. This approach significantly improves detection sensitivity and stability as compared with previous detection techniques. Moreover, the presented results benefit many fundamental and applied research fields such as structured light shaping and photonic switching.
High-precision birefringence detection is crucial in many fundamental and applied research fields such as chirality detection, optical clocks and quantum information. Although numerous techniques have been demonstrated to detect birefringence in optical materials, the current detection precision typically remains at 10−8. Here we introduce a different physical mechanism for birefringence detection in the classical regime, achieving an accuracy at the 10−11 level. Our technique uses an effective photonic two-level system, dynamically driven by a birefringence-sensitive synthetic magnetic field created by propagation-invariant spin-orbit-coupled structured light in the subwavelength regime. The magnetic field equivalent induces the Rabi oscillation of photonic state, manifested as a nontrivial periodic spin-orbital angular momentum conversion. The ultrahigh detection precision arises from high-birefringence-sensitive topological transition between different oscillatory modes with high Rabi frequencies. The detection precision is tunable by controlling envelope size of structured light at the subwavelength scale. Our technique benefits a broad range of applications involving optical birefringence. The authors demonstrate that high-precision birefringence detection at the 10−11 level can be achieved using spin-orbit-coupled Rabi oscillations in a photonic two-level system. The presented detection technique benefits a broad range of applications involving optical birefringence such as precise control of the entangled photonic states.
Although the geometric phase (GP) in two-level systems has been extensively studied, realizing tailored photonic-state evolution trajectories and experimentally resolving the corresponding phase responses within a controllable platform remain challenging. Here, we establish a synthetic two-level photonic system using rotated electro-optic crystals, in which two orthogonal polarization components serve as a pseudospin basis whose evolution is governed by a tunable synthetic magnetic field. Independent control of the field direction and magnitude enables tailored trajectories on the Poincaré sphere, while an explicit intensity-phase mapping provides a non-interferometric route to phase retrieval. We experimentally observe continuous GP evolution, abrupt π -phase jumps associated with antipodal crossings, and path-dependent GP accumulation along composite trajectories. These results provide a controllable electro-optic route to engineering and observing trajectory-dependent GP in synthetic photonic systems.
Photonic orbital angular momentum (OAM) offers a promising platform for high-dimensional quantum information processing. While geometric phase (GP) is the crucial tool in enabling intrinsically fault-tolerant quantum computation, the measurement of GP using linear optics remains relatively unexplored in the OAM state space. Here, we propose an experimental scheme to detect GP shifts resulting from the cyclic evolution of OAM qutrit states. Distinguished with the conventional evolution along cyclic path on the Poincaré sphere (PS), the nontrivial evolution in our theoretical scheme is along a cyclic path residing within the SU(3)/U(2) parameter space. By employing a combination of X-gates, dove prisms, and double cylindrical lenses, we achieve the cyclic evolution and analyse the resultant GP through our designed Sagnac interferometer. Our theoretical study may find potential in high-dimensional quantum computation using twisted photons and in exploring the geometric structure of such optical systems.
A key challenge of magnetometry lies in the simultaneous optimization of magnetic field sensitivity and maximum field range. In interferometry-based magnetometry, a quantum two-level system acquires a dynamic phase in response to an applied magnetic field. However, due to the 2π periodicity of the phase, increasing the coherent interrogation time to improve sensitivity reduces field range. Here we introduce a route towards both large magnetic field range and high sensitivity via measurements of the geometric phase acquired by a quantum two-level system. We experimentally demonstrate geometric-phase magnetometry using the electronic spin associated with the nitrogen vacancy (NV) color center in diamond. Our approach enables unwrapping of the 2π phase ambiguity, enhancing field range by 400 times. We also find additional sensitivity improvement in the nonadiabatic regime, and study how geometric-phase decoherence depends on adiabaticity. Our results show that the geometric phase can be a versatile tool for quantum sensing applications.
We investigate a class of cyclic evolutions for %the cyclic evolution of driven two-level quantum systems (effective spin-1/2) with a particular focus on the geometric characteristics of the driving and their specific imprints on the quantum dynamics. By introducing the concept of geometric field curvature for any field trajectory in the parameter space we are able to unveil underlying patterns in the overall quantum behavior: the knowledge of the field curvature provides a non-standard and fresh access to the interrelation between field and spin trajectories, and the corresponding quantum phases acquired in non-adiabatic cyclic evolutions. In this context, we single out setups in which the driving field curvature can be employed to demonstrate a pure geometric control of the quantum phases. Furthermore, the driving field curvature can be naturally exploited to introduce the geometrical torque and derive a general expression for the total quantum phase acquired in a cycle. Remarkably, such relation allows to access the mechanisms controlling the changeover of the quantum phase across a topological transition and to disentangle the role of the spin and field topological windings. As for implementations, we discuss a series of physical systems and platforms to demonstrate how the geometric control of the quantum phases can be realized for pendular field drivings. This includes setups based on superconducting islands coupled to a Josephson junction and inversion asymmetric nanochannels with suitably tailored geometric shapes.
Quantum entanglement offers a powerful tool for understanding and predicting complex geometric phase transitions, a challenge largely addressed through traditional analytical methods. This paper proposes a novel algorithm leveraging quantum entanglement to rapidly assess phase transition points within dynamically evolving geometric systems. We demonstrate the effectiveness of this approach through a rigorous theoretical analysis and initial experimental validation, showcasing a significant improvement over existing correlation-based techniques. The core mechanism involves a quantum-enhanced evolution algorithm that dynamically modifies the geometric structure, enabling the detection of subtle phase transition signatures. This research moves beyond simple correlation analysis, offering a fundamentally different perspective on the dynamics of complex systems.