Dual-wavelength quantum skyrmions from liquid crystal topological defect

TL;DR

The work addresses creating and controlling quantum skyrmions at dual wavelengths by integrating a reconfigurable spin–orbit device based on a true liquid-crystal topological defect with a dual-wavelength SPDC source. By tuning voltage and applying projective measurements, the authors demonstrate switching between nonlocal two-photon entangled skyrmions and heralded single-photon skyrmions, with robust entanglement evidenced by high fidelity tomographies and CHSH violations. A key contribution is the projection-controlled generation of dual-wavelength and single-wavelength topologies and the theoretical prospect of GHZ-like entanglement across polarization, OAM, and wavelength. This approach expands the quantum skyrmion toolbox for topological quantum optics and paves the way for multipartite topological states with potential applications in bio-imaging, fiber quantum communications, and quantum information processing, all within a dual-wavelength, voltage-tunable platform where the Skyrme number remains $N\approx-2$ for the topological states.

Abstract

We propose a spin-orbit strategy for generating dual-wavelength quantum skyrmions, realized either as entangled photon pairs at dual wavelengths or as heralded single-photon states at a given wavelength -- regimes neither previously conceptualized nor demonstrated. By coupling a two-photon entangled state to an electrically tunable liquid crystal topological defect, we engineer both nonlocal and local skyrmionic topologies in a reconfigurable platform. We highlight with examples how this approach may open new directions for engineered topological quantum states that exploit the topological richness of liquid crystals.

Figures (7)

• Figure 1: (a) Illustration of the quantum topological switch. A dual-wavelength entangled photon pair described by Eq. \ref{['eq:initial_entangled_state']} passes through a tunable, wavelength-dependent spin-orbit coupling device. By adjusting the control parameter $p$ (in this work, an applied voltage) and applying projection schemes $\Pi_i^{\rm x}$ on each of the three degrees of freedom of photons $i={\rm A},{\rm B}$ with ${\rm x} = {\rm (OAM, polarization, wavelength)}$, various quantum states can be prepared, including entangled skyrmionic topology and heralded single photons with a skyrmionic topology, with full details in the main text. (b)(i) Sketch of the experimental setup (see Supplemental Material Sec. IV for details Supplement). (ii) Crossed linear polarizers image of the optical spin-orbit liquid crystal device at wavelength $\lambda_1$ and $V=4.7~{\rm V}$. (iii) Spin-to-orbital conversion efficiency vs applied voltage (all voltages are given in rms value).
• Figure 2: Experimental observation of dual-wavelength nonlocal and single-wavelength local quantum skyrmionic topologies associated to the three main typical states under investigation. (a) Spin-orbit quantum state tomography based on combined polarization and OAM projections. Thumbnails to the left of each row indicate the polarization basis; those above each column show the spatial phase profiles of the projected state. (b) Transverse spatial distribution of the reduced Stokes vector components. (c) Corresponding Stokes vector textures mapped onto the Poincaré sphere, revealing skyrmionic polarization patterns with Skyrme number $N \approx -2$ in all cases. Experimental parameters: $V = 3.9$ V for the entangled topology; $V = 6.3$ V and $5.4$ V for the heralded topologies at $\lambda_1$ and $\lambda_2$, respectively.
• Figure 3: (a) Skyrme number as a function of the voltage applied to the spin-orbit device, for different circular polarization projections. Depending on the projection, the measurement probes either dual-wavelength two-photon states (bicolor markers) or heralded single-photon states (monocolor markers: purple for $\lambda_1$, red for $\lambda_2$). Insets show typical Poincaré sphere coverage for representative cases at distinct voltages from that used in Fig. 2: dual-wavelength entangled Skyrmion ($V=4.2$ V), dual-wavelength trivial topology ($V=4.9$ V), and single-wavelength heralded skyrmion ($V=6.0$ V at $\lambda_1$ and $V=5.3$ V at $\lambda_2$). (b) The generated quantum Skyrmion states are transmitted through a fly wing mounted to a microscope slide (pictured here as illuminated by a plane wave at wavelength, $\lambda=633$ nm) with (c) the resulting Poincaré sphere coverage for both single and entangled photon topological states.
• Figure 4: Spin-orbit device. (a) Schematic diagram of the device in which nematic liquid crystals are sandwiched between electrodes, and a ring magnet placed at distance $d$ = 2 mm. (b) Real image of packaged device highlighting the optical $z$ axis. (c) Coincidence counts with and without the spin orbit device monitored over $\sim1.5$ hours and normalised to the peak for each data set to allow for direct comparison. The measurements were taken over a 10s integration time to account for fluctuations and the stability with the device was monitored at a voltage of $V = 3.9$ V (by way of example) and without any alignment adjustments.
• Figure 5: Demonstration of OAM quantum entanglement of the prepared two-photon state in the absence of spin-orbit coupling. (a) Evaluation of the CHSH-Bell parameter $S$ from joint probabilities $C(\theta_A, \theta_B)$, with $\bar{C} = \max_{\theta_A,\theta_B}(C)$, for $\theta_A = 0$ (blue), $\tfrac{\pi}{8}$ (brown), $\tfrac{\pi}{4}$ (orange), and $\tfrac{3\pi}{8}$ (purple). (b) Quantum state tomography, where the projected states of each photon are identified by thumbnails depicting the corresponding spatial phase profiles. (c) Computed real and imaginary components of the density matrix from the data shown in panel (b).