arXiv subjects

Francesco Di Colandrea

Publications and source records attributed to Francesco Di Colandrea.

28 records · Page 2Linked to original sources

arXiv2024

A genetic algorithm for the response of twisted nematic liquid crystals to an applied field

When an external field is applied across a liquid-crystal cell, the twist and tilt distributions cannot be calculated analytically and must be extracted numerically. In the standard approach, the Euler-Lagrange equations are derived from the minimization of the free energy of the system and then solved via finite-difference methods, often implemented in commercial software. These tools iterate from initial solutions that are compatible with the boundary conditions, providing limited to no flexibility for customization. Here, we present a genetic algorithm that outputs fast and accurate solutions to the integral form of the equations. In our approach, the evolutionary routine is sequentially applied at each position within the bulk of the cell, thus overcoming the necessity of assuming trial solutions. The predictions of our routine strongly support the experimental observations on different instances of spatially varying twisted nematic liquid-crystal cells, patterned with different topologies on the two alignment layers.

physics.comp-ph↗

arXiv2024

Quantum process tomography of structured optical gates with convolutional neural networks

The characterization of a unitary gate is experimentally accomplished via Quantum Process Tomography, which combines the outcomes of different projective measurements to reconstruct the underlying operator. The process matrix is typically extracted from maximum-likelihood estimation. Recently, optimization strategies based on evolutionary and machine-learning techniques have been proposed. Here, we investigate a deep-learning approach that allows for fast and accurate reconstructions of space-dependent SU(2) operators, only processing a minimal set of measurements. We train a convolutional neural network based on a scalable U-Net architecture to process entire experimental images in parallel. Synthetic processes are reconstructed with average fidelity above 90%. The performance of our routine is experimentally validated on complex polarization transformations. Our approach further expands the toolbox of data-driven approaches to Quantum Process Tomography and shows promise in the real-time characterization of complex optical gates.

quant-ph↗

arXiv2024

Manifestation of the Berry connection in chiral lattice systems

The Aharonov-Bohm effect is a physical phenomenon where the vector potential induces a phase shift of electron wavepackets in regions with zero magnetic fields. It is often referred to as evidence for the physical reality of the vector potential. A similar effect can be observed in solid-state systems, where the Berry connection can influence electron dynamics. Here, we show that in chiral-symmetric processes the Berry connection determines an observable effect on the mean chiral displacement of delocalized wavefunctions. This finding is supported by a photonic experiment realizing a topological quantum walk, and demonstrates a new effect that can be attributed directly to the presence of a gauge field.

cond-mat.mes-hall↗

arXiv2023

Fourier Quantum Process Tomography

The characterization of a quantum device is a crucial step in the development of quantum experiments. This is accomplished via Quantum Process Tomography, which combines the outcomes of different projective measurements to deliver a possible reconstruction of the underlying process. The tomography is typically performed by processing an overcomplete set of measurements and extracting the process matrix from maximum-likelihood estimation. Here, we introduce a new technique, referred to as Fourier Quantum Process Tomography, which requires a reduced number of measurements, and benchmark its performance against the standard maximum-likelihood approach. Fourier Quantum Process Tomography is based on measuring probability distributions in two conjugate spaces for different state preparations and projections. Exploiting the concept of phase retrieval, our scheme achieves a complete and robust characterization of the setup by processing a near-minimal set of measurements. We experimentally test the technique on different space-dependent polarization transformations, reporting average fidelities higher than 90% and significant computational advantage.

quant-ph↗

arXiv2023

Spatially twisted liquid-crystal devices

Nematic liquid-crystal devices are a powerful tool to structure light in different degrees of freedom, both in classical and quantum regimes. Most of these devices exploit either the possibility of introducing a position-dependent phase retardation with a homogeneous alignment of the optic axis -- e.g., liquid-crystal-based spatial light modulators -- or conversely, with a uniform but tunable retardation and patterned optic axis, e.g., $q$-plates. The pattern is the same in the latter case on the two alignment layers. Here, a more general case is considered, wherein the front and back alignment layers are patterned differently. This creates a non-symmetric device which can exhibit different behaviours depending on the direction of beam propagation and effective phase retardation. In particular, we fabricate multi-$q$-plates by setting different topological charges on the two alignment layers. The devices have been characterized by spatially resolved Stokes polarimetry, with and without applied electric voltage, demonstrating new functionalities.

physics.optics↗

arXiv2023

Retrieving space-dependent polarization transformations via near-optimal quantum process tomography

An optical waveplate rotating light polarization can be modeled as a single-qubit unitary operator, whose action can be experimentally determined via quantum process tomography. Standard approaches to tomographic problems rely on the maximum-likelihood estimation, providing the most likely transformation to yield the same outcomes as a set of experimental projective measurements. The performances of this method strongly depend on the number of input measurements and the numerical minimization routine that is adopted. Here we investigate the application of genetic and machine learning approaches to this problem, finding that both allow for accurate reconstructions and fast operations when processing a set of projective measurements very close to the minimal one. We apply these techniques to the case of space-dependent polarization transformations, providing an experimental characterization of the optical action of spin-orbit metasurfaces having patterned birefringence. Our efforts thus expand the toolbox of methodologies for optical process tomography. In particular, we find that the neural network-based scheme provides a significant speed-up, that may be critical in applications requiring a characterization in real-time. We expect these results to lay the groundwork for the optimization of tomographic approaches in more general quantum processes, including non-unitary gates and operations in higher-dimensional Hilbert spaces.

quant-ph↗

arXiv2023

Ultra-long quantum walks via spin-orbit photonics

The possibility of fine-tuning the couplings between optical modes is a key requirement in photonic circuits for quantum simulations. In these architectures, emulating the long-time evolution of particles across large lattices requires sophisticated setups, that are often intrinsically lossy. Here we report ultra-long photonic quantum walks across several hundred optical modes, obtained by propagating a light beam through very few closely-stacked liquid-crystal metasurfaces. By exploiting spin-orbit effects, these implement space-dependent polarization transformations that mix circularly polarized optical modes carrying quantized transverse momentum. As each metasurface implements long-range couplings between distant modes, by using only a few of them we simulate quantum walks up to 320 discrete steps without any optical amplification, far beyond state-of-the-art experiments. To showcase the potential of this method, we experimentally demonstrate that in the long-time limit a quantum walk affected by dynamical disorder generates maximal entanglement between two system partitions. Our platform grants experimental access to large-scale unitary evolutions while keeping optical losses at a minimum, thereby paving the way to massive multi-photon multi-mode quantum simulations.

quant-ph↗

arXiv2022

Quantum walks of two correlated photons in a 2D synthetic lattice

Quantum walks represent paradigmatic quantum evolutions, enabling powerful applications in the context of topological physics and quantum computation. They have been implemented in diverse photonic architectures, but the realization of a two-particle dynamics on a multi-dimensional lattice has hitherto been limited to continuous-time evolutions. To fully exploit the computational capabilities of quantum interference it is crucial to develop platforms handling multiple photons that propagate across multi-dimensional lattices. Here, we report a discrete-time quantum walk of two correlated photons in a two-dimensional lattice, synthetically engineered by manipulating a set of optical modes carrying quantized amounts of transverse momentum. Mode-couplings are introduced via the polarization-controlled diffractive action of thin geometric-phase optical elements. The entire platform is compact, efficient, scalable, and represents a versatile tool to simulate quantum evolutions on complex lattices. We expect that it will have a strong impact on diverse fields such as quantum state engineering, topological quantum photonics, and Boson Sampling.

quant-ph↗

arXiv2022

Linking topological features of the Hofstadter model to optical diffraction figures

In two, three and even four spatial dimensions, the transverse responses experienced by a charged particle on a lattice in a uniform magnetic field are fully controlled by topological invariants called Chern numbers, which characterize the energy bands of the underlying Hofstadter Hamiltonian. These remarkable features, solely arising from the magnetic translational symmetry, are captured by Diophantine equations which relate the fraction of occupied states, the magnetic flux and the Chern numbers of the system bands. Here we investigate the close analogy between the topological properties of Hofstadter Hamiltonians and the diffraction figures resulting from optical gratings. In particular, we show that there is a one-to-one relation between the above mentioned Diophantine equation and the Bragg condition determining the far-field positions of the optical diffraction peaks. As an interesting consequence of this mapping, we discuss how the robustness of diffraction figures to structural disorder in the grating is a direct analogue of the robustness of transverse conductance in the Quantum Hall effect.

cond-mat.mes-hall↗

arXiv2020

Bulk detection of time-dependent topological transitions in quenched chiral models

The topology of one-dimensional chiral systems is captured by the winding number of the Hamiltonian eigenstates. Here we show that this invariant can be read-out by measuring the mean chiral displacement of a single-particle wavefunction that is connected to a fully localized one via a unitary and translational-invariant map. Remarkably, this implies that the mean chiral displacement can detect the winding number even when the underlying Hamiltonian is quenched between different topological phases. We confirm experimentally these results in a quantum walk of structured light.

cond-mat.mes-hall↗