Abstract We examine the quantum steering and coherence for two qubits that are immersed in an isotropic (I) and anisotropic (A) photonic band-gab (PBG) crystal. We show how the steerability and coherence of the qubits’ state depends on the essential parameters of the model and initial state setting of the qubits. We find that the prevention of the amount of quantum steering and coherence can be achieved in the presence of PBG materials by a considerable choice of the system parameters. Furthermore, we show that the quantum steering and coherence can resist the degradation during the dynamics in IPBG more than in APBG according to the same physical conditions. Finally, we illustrate the relationship between the quantum steering and coherence with respect to the system parameters under the decoherence effect. These obtained results reveal that quantum systems in PBG materials are very useful to implement diverse applications of quantum technology with optimal performance.
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.
The Page--Wootters construction gives time a Hilbert space, representing it as an internal degree of freedom whose readings the rest of the system evolves with respect to. We ask whether such a clock degree of freedom can carry a topological invariant, and we propose a photonic architecture in which it does and in which the invariant can be measured. Signal--idler pairs from spontaneous four-wave mixing in a coupled microring array supply the clock--system partition, with the idler occupying a Rice--Mele band whose staggered coupling and detuning are cycled adiabatically around a gap-closing point. One cycle acts on that band as a rigid translation by
C unit cells, times a geometric phase periodic in the crystal momentum, times a dynamical phase, an identity exact in the adiabatic limit and independent of the state on which it acts. The readout targets the winding of that geometric phase across the Brillouin zone. Reversing the traversal of the pump loop cancels the dynamical phase and isolates twice the geometric phase in a two-photon coincidence fringe, while energy anticorrelation lets a filter on the signal scan the clock momentum without touching the clock and supplies the phase reference relationally, in place of an external optical reference. The estimate is protected on two independent levels, by the gap against smooth deformation and by the digital character of the unwrapping against noise below a threshold. A parameter budget anchored to thin-film lithium niobate places the requirements within reach at a conservative operating point.