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Non-Abelian evolution is a landmark in modern theoretical physics. But if non-commutative dynamics has a significant impact in the control of entanglement and transport in quantum systems is an open question. Here we propose to utilize non-Abelian Thouless pumping in one-dimensional discrete-time quantum walks in lattices with degenerate Bloch-bands. We show how the interplay of non-commutativity and topology enables geometrically protected quantum coin and shift operators. By composing different non-Abelian pumping cycles, different classes of tunable protected quantum walks arise. Surprisingly, the walks break parity symmetry and generate a dynamic process described by a Weyl-like equation. The amount of entanglement can be varied by acting on the initial conditions. The asymptotic statistical distribution and its features are determined by closed form analytical expression and confirmed numerically.

Non-Abelian Thouless pumping intertwines adiabatic quantum control and topological quantum transport and it holds potential for quantum metrology and computing. In this work, we introduce a ladder model featuring two doubly-degenerate bands and we show that adiabatic manipulation of the lattice parameters results in non-Abelian Thouless pumping, inducing both the displacement of an initially localized state and a geometric unitary transformation within the degenerate subspace. Additionally, we show that the structure and symmetry of the ladder model can be understood through its connection to a Yang monopole model. The proposed Hamiltonian can be realized using cold atoms in optical lattices, enabling the experimental demonstration of non-Abelian Thouless pumping in a genuinely quantum many-body system.

Terahertz imaging provides valuable insights into the composition and structure of objects or materials, with applications spanning security screening, medical imaging, materials science, and cultural heritage preservation. Despite its widespread utility, traditional terahertz imaging is limited in spatial resolution to approximately 1 mm according to Abbe's formula. In this paper, we propose a novel super-resolution method for terahertz time-domain spectroscopy systems. Our approach involves spatial filtering through scattering in the far-field of high spatial frequency components of the imaged sample. This method leverages evanescent wave filtering using a knife edge, akin to a standard structured illumination scheme. We demonstrate improved spatial resolution in slit diffraction, edge imaging, and reflection imaging of structures fabricated on a paper substrate using commonly encountered materials in works of art and documents. Furthermore, we present super-resolved images of an ancient document on parchment, showcasing the effectiveness of our proposed method., Comment: 21 pages, 11 figures, submitted to IEEE Transactions on Terahertz Science and Technology

The rate and security of quantum communications between users placed at arbitrary points of a quantum communication network depend on the structure of the network, on its extension and on the nature of the communication channels. In this work we propose a strategy for the optimization of trusted-relays based networks that intertwines classical network approaches and quantum information theory. Specifically, by suitably defining a quantum communication efficiency functional, we identify the optimal quantum communication connections through the network by balancing security and the quantum communication rate. The optimized network is then constructed as the network of the maximal quantum communication efficiency connections and its performance is evaluated by studying the scaling of average properties as functions of the number of nodes and of the network spatial extension., Comment: 12 pages, 6 figures

We propose a straightforward and effective approach to design, by strain-engineering, photonic topological insulators supporting high quality factors edge states. Chiral strain-engineering creates opposite synthetic gauge fields in two domains resulting in Landau levels with the same energy spacing but different topological numbers. The boundary of the two topological domains hosts robust time-reversal and spin-momentum-locked edge states, exhibiting high quality factors due to continuous strain modulation. By shaping the synthetic gauge field, we obtain a remarkable field confinement and tunability, with the strain strongly affecting the degree of localization of the edge states. Notably the two-domain design stabilizes the strain-induced topological edge state. The large potential bandwidth of the strain-engineering and the opportunity to induce the mechanical stress at the fabrication stage enables large scalability for many potential applications in photonics, such as tunable microcavities, new lasers and information processing devices, including the quantum regime., Comment: 31 pages, 10 figures

Non-abelian gauge fields emerge naturally in the description of adiabatically evolving quantum systems having degenerate levels. Here we show that they also play a role in Thouless pumping in the presence of degenerate bands. To this end we consider a photonic Lieb lattice having two degenerate non-dispersive modes and we show that, when the lattice parameters are slowly modulated, the propagation of the photons bear the fingerprints of the underlying non-abelian gauge structure. The non-dispersive character of the bands enables a high degree of control on photon propagation. Our work paves the way to the generation and detection of non-abelian gauge fields in photonic and optical lattices., Comment: 11 pages, 6 figures

In order to transport information with topological protection, we reveal and demonstrate experimentally the existence of a characteristic length $L_c$, coined as the transport length, in the bulk size for edge states in one-dimensional Su-Schrieffer-Heeger (SSH) chains. In spite of the corresponding wavefunction amplitude decays exponentially, characterized by the penetration depth $\xi$, the transport between two edge states remains possible even when the lattice size $L$ is much larger than the penetration depth, i.e., $\xi \ll L \le L_c$. Due to the non-zero coupling energy in a finite-size system, the supported SSH edge states are not completely isolated at the two ends, giving an abrupt change in the wave localization, manifested through the inverse participation ratio to the lattice size. To verify such a non-exponential scaling factor to the system size, we implement a chain of split-ring resonators and their complementary ones with controllable hopping strengths. By performing the measurements on the group velocity from the transmission spectroscopy of non-trivially topological edge states with pulse excitations, the transport velocity between two edge states is directly observed with the number of lattices up to $20$. Along the route to harness topology to protect optical information, our experimental demonstrations provide a crucial guideline for utilizing photonic topological devices., Comment: 6 pages, 5 figures

We study photonic crystal fibers and ring resonators with topological features induced by Aubry- Andre-Harper modulations of the cladding. We find non trivial gaps and edge states at the interface between regions with different Chern numbers. We calculate the field profile and eigenvalue dispersion by an exact recursive approach. Compared with conventional circular resonators and fibers, the proposed structure features topological protection and hence robustness against symmetry-preserving local perturbations that do not close the gap. These topological photonic crystal fibers sustain strong field localization and energy concentration at a given radial distance. As topological light guiding and trapping devices, they may bring about many opportunities for both fundamentals and applications unachievable with conventional optical devices., Comment: 9 pages, 5 figures

Topological concepts open many new horizons for photonic devices, from integrated optics to lasers. The complexity of large scale topological devices asks for an effective solution of the inverse problem: how best to engineer the topology for a specific application? We introduce a novel machine learning approach to the topological inverse problem. We train a neural network system with the band structure of the Aubry-Andre-Harper model and then adopt the network for solving the inverse problem. Our application is able to identify the parameters of a complex topological insulator in order to obtain protected edge states at target frequencies. One challenging aspect is handling the multivalued branches of the direct problem and discarding unphysical solutions. We overcome this problem by adopting a self-consistent method to only select physically relevant solutions. We demonstrate our technique in a realistic topological laser design and by resorting to the widely available open-source TensorFlow library. Our results are general and scalable to thousands of topological components. This new inverse design technique based on machine learning potentially extends the applications of topological photonics, for example, to frequency combs, quantum sources, neuromorphic computing and metrology.

The cascade of resonant topological structures with $\mathcal{PT}$-symmetry breaking is shown to emit laser light with a frequency-comb spectrum. We consider optically active topological Aubry-Andr\'e-Harper lattices supporting edge-modes at regularly spaced frequencies. When the amplified resonances in the $\mathcal{PT}$-broken regime match the edge modes of the topological gratings, we predict the emission of discrete laser lines. A proper design enables to engineer the spectral features for specific applications. The robustness of the topological protection makes the system very well suited for a novel generation of compact frequency comb emitters for spectroscopy, metrology, and quantum information., Comment: 6 pages, 6 figures

The use of virtually lossless topologically isolated edge states may lead to a novel class of thresholdless lasers operating without inversion. One needs however to understand if topological states may be coupled to external radiation and act as active cavities. We study a two-level topological insulator and show that self-induced transparency pulses can directly excite edge states. We simulate laser emission by a suitable designed topological cavity, and show that it can emit tunable radiation. For a configuration of sites following the off-diagonal Aubry-Andre-Harper model we solve the Maxwell-Bloch equations in the time domain and provide a first principle confirmation of topological lasers. Our results open the road to a new class of light emitters with topological protection for applications ranging from low-cost energetically-effective integrated lasers sources, also including silicon photonics, to strong coupling devices for studying ultrafast quantum processes with engineered vacuum.

The exciton-exciton effective scattering which rules the time evolution of two excitons is studied as a function of initial momentum difference, scattering angle and electron-to-hole mass ratio. We show that this effective scattering can collapse for energy-conserving configurations provided that the difference between the two initial exciton momenta is larger than a threshold value. Sizeable scatterings then exist in the forward direction only. We even find that, for an electron-to-hole mass ratio close to 1/2, the exciton-exciton effective scattering stays close to zero in all directions when the difference between the initial exciton momenta has a very specific value. This unexpected but quite remarkable collapse comes from tricky compensation between direct and exchange Coulomb processes which originates from the fundamental undistinguishability of the exciton fermionic components., Comment: Revised text version. Accepted for publication in Physical Review B