Remote engineering of particle-like topologies to visualise entanglement dynamics

Abstract

Skyrmions are a particle-like topology with a quantised skyrmion number, realised across condensed matter and photonic platforms alike. In quantum photonics, they constitute an emerging resource, promising robust quantum information encoding, so far realised as single photon and bi-photon entangled states. Here we report the first visualisation of tripartite entanglement dynamics through topological structure using spin-skyrmion entangled states, where the topology of a single photon is remotely controlled through the spin of its entangled partner. We visualise our tripartite state theoretically by introducing the notion of a topological Bloch sphere that completely captures the entanglement and topolological features of the state. By leveraging this state, we realise the first quantum multiskyrmions, comprising multiple localised skyrmions within a single structure, that emulate signatures of their magnetic counterparts. We verify this experimentally and show that traversing our topological sphere reveals entanglement-driven particle-like motion of the localised topological structures. These dynamics unveil a physical manifestation of tripartite entanglement correlations which we illustrate by example of GHZ-like states, enabling a visualisation of multiple Bell states encoded within our system. Our work opens exciting possibilities for quantum sensing by mapping complex quantum channel features onto topological observables of multipartite states and offers a promising avenue for harnessing quantum topologies for multi-level encoding quantum communication schemes.

Figures (9)

• Figure 1: Non-local topological control and creation of quantum multiskyrmions.a, Photons A and B form an entangled state, where the polarization of photon A is coupled to a skyrmion state state on photon B. A measurement made on the polarization of photon A will collapse the state of photon B into a certain skyrmion state with a topological skyrmion number that can be switched between $n_1$ and $n_2$. b, Varying the polarization measurement on photon A allows us to traverse the topological landscape of the spin–skyrmion entangled state, revealing a quantum multiskyrmion composed of quasiparticle-like distributions at the equator of the sphere, and a higher order skyrmion at the poles (represented in the polarization vector plots where $\psi=\frac{1}{2}\mathrm{tan}^{-1}(S_2/S_1)$). The emergence of the different topological structures gives rise to a topological switch, yielding a skyrmion number of $n_1$ at the poles of the sphere, and $n_2$ at the equator.
• Figure 2: Experimental generation of spin-skyrmion entangled states.a, Schematic diagram of the non-degenerate quantum experiment used to generate and detect spin-skyrmion entangled states. A non-linear crystal (NLC) is used to produce dual-wavelength SPDC at $\lambda_A$ = 1550 nm and $\lambda_B$ = 810 nm. A dichroic mirror (DM) separates the wavelengths into two arms, with a q-plate and polarization optics (quarter- and half-wave plates) in each path. Both paths are directed to SLMs and thereafter coupled into SMFs connected to single photon detectors. Coincidences are recorded by a coincidence counter (CC) within a 0.5 ns window. To confirm the non-local nature of the states we generate, we demonstrate a b, violation of the Bell inequality for an example state where $\ell_1 = 0, \ell_2 = -2$ and $\ell_3 = -4$. c, The measurement matrix for the QST performed on the example state, constructed by 6 polarization measurements on photon A, and 15 spatial measurements coupled with 6 polarization measurements on photon B, shown in the zoomed-in insets in d. e, Corresponding experimentally reconstructed density matrix extracted from the full QST with real and imaginary components. f, Stokes measurements retrieved directly from the tomography data.
• Figure 3: Experimental verification of non-locally controlled topology. A switch in the topological skyrmion number of photon B is realised through non-local polarization measurements on photon A. The spin textures are illustrated at different points on the sphere for a state with a,$\ell_1 = 0, \ell_2 = -2$ and $\ell_3 = -4$, yielding a switching of the skyrmion number from $n_1=-2$ at the poles to $n_2=-4$ at the equator and b,$\ell_1 = 0, \ell_2 = -3$ and $\ell_3 = -6$, switching between the two distinct skyrmion numbers, $n_1=-3$ and $n_2=-6$.
• Figure 4: Experimental quantum multiskyrmions. Spin textures of the different flavours of quantum multiskyrmions realised, with zoom-in insets revealing the embedded local polarization texture of the quasiparticles in the structure for a state with a,$\ell_1 = 0, \ell_2 = -2$ and $\ell_3 = -4$, and b,$\ell_1 = 0, \ell_2 = -3$ and $\ell_3 = -6$.
• Figure 5: Quasiparticle dynamics. Non-locally derived polarization textures where the localized quasiparticle skyrmion vector distributions shift in and out radially when varying $\theta$ for $\alpha$ fixed at 3.77 rad from left to right, or exhibit an orbital and spin motion when varying $\alpha$ for $\theta$ fixed at $1.26$ rad, for the state with a,$\ell_1 = 0, \ell_2 = -2$ and $\ell_3 = -4$, and for the state with b,$\ell_1 = 0, \ell_2 = -3$ and $\ell_3 = -6$. In a, the amplitude ($\theta$) varies from left to right as $\theta=[0, 0.31, 0.63, 0.94, 1.26, 1.57, 2.20, 2.5, 3.14]$ rad and the phase ($\alpha$) as $\alpha=[0, 0.62, 1.26, 1.88, 3.14, 3.77, 5.03, 6.28]$ rad and in b,$\theta=[0, 0.94, 1.57, 1.88, 2.20, 2.83, 3.14]$ rad and $\alpha=[0, 0.62, 1.26, 1.88, 2.51, 3.14, 3.77, 4.40, 6.28]$ rad.