Exploring the impact of longitudinal modulation on the twisting angle in Pancharatnam-Berry phase-based waveguides.

A circularly polarized (CP) beam propagating in a rotated anisotropic material acquires an additional phase delay proportional to the local rotation angle. This phase delay is a particular kind of geometric phase, the Pancharatnam-Berry phase (PBP), stemming from the path of the beam polarization on the Poincaré sphere. A transverse gradient in the geometric phase can thus be imparted by inhomogeneous rotation of the material, with no transverse gradient in the dynamic phase. A waveguide based upon this principle can be induced when the gradient accumulates in propagation, the latter requiring a longitudinal rotation in the optic axis synchronized with the natural rotation of the light polarization. Here, we evaluate numerically and theoretically the robustness of PBP-based waveguides, in the presence of a mismatch between the birefringence length and the external modulation. We find that the mismatch affects mainly the polarization of the quasi-mode, while the confinement is only slightly perturbed.

Ultra-sensitive measurement of transverse displacements with linear photonic gears.

Accurately measuring mechanical displacements is essential for a vast portion of current technologies. Several optical techniques accomplish this task, allowing for non-contact sensing even below the diffraction limit. Here we introduce an optical encoding technique, dubbed "linear photonic gears", that enables ultra-sensitive measurements of a transverse displacement by mapping it into the polarization rotation of a laser beam. In ordinary ambient conditions, we measure the relative shift between two objects with a resolution of 400 pm. We argue that a resolution of 50 pm should be achievable with existing state-of-the-art technologies. Our single-optical-path scheme is intrinsically stable and it could be implemented as a compact sensor, using cost effective integrated optics. We anticipate it may have a strong impact on both research and industry.

A versatile quantum walk resonator with bright classical light.

In a Quantum Walk (QW) the "walker" follows all possible paths at once through the principle of quantum superposition, differentiating itself from classical random walks where one random path is taken at a time. This facilitates the searching of problem solution spaces faster than with classical random walks, and holds promise for advances in dynamical quantum simulation, biological process modelling and quantum computation. Here we employ a versatile and scalable resonator configuration to realise quantum walks with bright classical light. We experimentally demonstrate the versatility of our approach by implementing a variety of QWs, all with the same experimental platform, while the use of a resonator allows for an arbitrary number of steps without scaling the number of optics. This paves the way for future QW implementations with spatial modes of light in free-space that are both versatile and scalable.

Tunable Two-Photon Quantum Interference of Structured Light.

Structured photons are nowadays an important resource in classical and quantum optics due to the richness of properties they show under propagation, focusing, and in their interaction with matter. Vectorial modes of light in particular, a class of modes where the polarization varies across the beam profile, have already been used in several areas ranging from microscopy to quantum information. One of the key ingredients needed to exploit the full potential of complex light in the quantum domain is the control of quantum interference, a crucial resource in fields like quantum communication, sensing, and metrology. Here we report a tunable Hong-Ou-Mandel interference between vectorial modes of light. We demonstrate how a properly designed spin-orbit device can be used to control quantum interference between vectorial modes of light by simply adjusting the device parameters and no need of interferometric setups. We believe our result can find applications in fundamental research and quantum technologies based on structured light by providing a new tool to control quantum interference in a compact, efficient, and robust way.

Experimental Engineering of Arbitrary Qudit States with Discrete-Time Quantum Walks.

The capability to generate and manipulate quantum states in high-dimensional Hilbert spaces is a crucial step for the development of quantum technologies, from quantum communication to quantum computation. One-dimensional quantum walk dynamics represents a valid tool in the task of engineering arbitrary quantum states. Here we affirm such potential in a linear-optics platform that realizes discrete-time quantum walks in the orbital angular momentum degree of freedom of photons. Different classes of relevant qudit states in a six-dimensional space are prepared and measured, confirming the feasibility of the protocol. Our results represent a further investigation of quantum walk dynamics in photonics platforms, paving the way for the use of such a quantum state-engineering toolbox for a large range of applications.

Symmetry Protection of Photonic Entanglement in the Interaction with a Single Nanoaperture.

In this work, we experimentally show that quantum entanglement can be symmetry protected in the interaction with a single subwavelength plasmonic nanoaperture, with a total volume of V∼0.2λ^{3}. In particular, we experimentally demonstrate that two-photon entanglement can be either completely preserved or completely lost after the interaction with the nanoaperture, solely depending on the relative phase between the quantum states. We achieve this effect by using specially engineered two-photon states to match the properties of the nanoaperture. In this way we can access a symmetry protected state, i.e., a state constrained by the geometry of the interaction to retain its entanglement. In spite of the small volume of interaction, we show that the symmetry protected entangled state retains its main properties. This connection between nanophotonics and quantum optics probes the fundamental limits of the phenomenon of quantum interference.

Surface structures with unconventional patterns and shapes generated by femtosecond structured light fields.

We present an investigation on ultrashort laser surface structuring with structured light fields generated by various q-plates. In particular, q-plates with topological charges q = 1, 3/2, 2, 5/2 are used to generate femtosecond (fs) vector vortex beams, and form complex periodic surface structures through multi-pulse ablation of a solid crystalline silicon target. We show how optical retardation tuning of the q-plate offers a feasible way to vary the fluence transverse distribution of the beam, thus allowing the production of structures with peculiar shapes, which depend on the value of q. The features of the generated surface structures are compared with the vector vortex beam characteristics at the focal plane, by rationalizing their relationship with the local state of the laser light. Our experimental findings demonstrate how irradiation with fs complex light beams can offer a valuable route to design unconventional surface structures.

12 mode, WDM, MIMO-free orbital angular momentum transmission.

Simultaneous MIMO-free transmission of 12 orbital angular momentum (OAM) modes over a 1.2 km air-core fiber is demonstrated. WDM compatibility of the system is shown by using 60, 25 GHz spaced WDM channels with 10 GBaud QPSK signals. System performance is evaluated by measuring bit error rates, which are found to be below the soft FEC limit, and limited by inter-modal crosstalk. The crosstalk in the system is analyzed, and it is concluded that it can be significantly reduced with an improved multiplexer and de-multiplexer.

First observation of the quantized exciton-polariton field and effect of interactions on a single polariton.

Polaritons are quasi-particles that originate from the coupling of light with matter and that demonstrate quantum phenomena at the many-particle mesoscopic level, such as Bose-Einstein condensation and superfluidity. A highly sought and long-time missing feature of polaritons is a genuine quantum manifestation of their dynamics at the single-particle level. Although they are conceptually perceived as entangled states and theoretical proposals abound for an explicit manifestation of their single-particle properties, so far their behavior has remained fully accounted for by classical and mean-field theories. We report the first experimental demonstration of a genuinely quantum state of the microcavity polariton field, by swapping a photon for a polariton in a two-photon entangled state generated by parametric downconversion. When bringing this single-polariton quantum state in contact with a polariton condensate, we observe a disentangling with the external photon. This manifestation of a polariton quantum state involving a single quantum unlocks new possibilities for quantum information processing with interacting bosons.

Monstar polarization singularities with elliptically-symmetric q-plates.

Space-variant polarization patterns present in the transverse mode of optical beams highlight disclination patterns of polarization about a singularity, often a C-point. These patterns are important for understanding rotational dislocations and for characterizing complex polarization patterns. Liquid-crystal devices known as q-plates have been used to produce two of the three types of disclination patterns in optical beams: lemons and stars. Here we report the production of the third type of disclination, which is asymmetric, known as the monstar. We do so with elliptically-symmetric q-plates. We present theory and measurements, and find excellent agreement between the two.

Detection of Zak phases and topological invariants in a chiral quantum walk of twisted photons.

Topological insulators are fascinating states of matter exhibiting protected edge states and robust quantized features in their bulk. Here we propose and validate experimentally a method to detect topological properties in the bulk of one-dimensional chiral systems. We first introduce the mean chiral displacement, an observable that rapidly approaches a value proportional to the Zak phase during the free evolution of the system. Then we measure the Zak phase in a photonic quantum walk of twisted photons, by observing the mean chiral displacement in its bulk. Next, we measure the Zak phase in an alternative, inequivalent timeframe and combine the two windings to characterize the full phase diagram of this Floquet system. Finally, we prove the robustness of the measure by introducing dynamical disorder in the system. This detection method is extremely general and readily applicable to all present one-dimensional platforms simulating static or Floquet chiral systems.

Surface Structuring with Polarization-Singular Femtosecond Laser Beams Generated by a q-plate.

In the last few years femtosecond optical vortex beams with different spatial distributions of the state of polarization (e.g. azimuthal, radial, spiral, etc.) have been used to generate complex, regular surface patterns on different materials. Here we present an experimental investigation on direct femtosecond laser surface structuring based on a larger class of vector beams generated by means of a q-plate with topological charge q = +1/2. In fact, voltage tuning of q-plate optical retardation allows generating a family of ultrashort laser beams with a continuous spatial evolution of polarization and fluence distribution in the focal plane. These beams can be thought of as a controlled coherent superposition of a Gaussian beam with uniform polarization and a vortex beam with a radial or azimuthal state of polarization. The use of this family of ultrashort laser beams in surface structuring leads to a further extension of the achievable surface patterns. The comparison of theoretical predictions of the vector beam characteristics at the focal plane and the generated surface patterns is used to rationalize the dependence of the surface structures on the local state of the laser beam, thus offering an effective way to either design unconventional surface structures or diagnose complex ultrashort laser beams.

Topological features of vector vortex beams perturbed with uniformly polarized light.

Optical singularities manifesting at the center of vector vortex beams are unstable, since their topological charge is higher than the lowest value permitted by Maxwell's equations. Inspired by conceptually similar phenomena occurring in the polarization pattern characterizing the skylight, we show how perturbations that break the symmetry of radially symmetric vector beams lead to the formation of a pair of fundamental and stable singularities, i.e. points of circular polarization. We prepare a superposition of a radial (or azimuthal) vector beam and a uniformly linearly polarized Gaussian beam; by varying the amplitudes of the two fields, we control the formation of pairs of these singular points and their spatial separation. We complete this study by applying the same analysis to vector vortex beams with higher topological charges, and by investigating the features that arise when increasing the intensity of the Gaussian term. Our results can find application in the context of singularimetry, where weak fields are measured by considering them as perturbations of unstable optical beams.

Birth and evolution of an optical vortex.

When a phase singularity is suddenly imprinted on the axis of an ordinary Gaussian beam, an optical vortex appears and starts to grow radially, by effect of diffraction. This radial growth and the subsequent evolution of the optical vortex under focusing or imaging can be well described in general within the recently introduced theory of circular beams, which generalize the hypergeometric-Gaussian beams and which obey novel kinds of ABCD rules. Here, we investigate experimentally these vortex propagation phenomena and test the validity of circular-beam theory. Moreover, we analyze the difference in radial structure between the newly generated optical vortex and the vortex obtained in the image plane, where perfect imaging would lead to complete closure of the vortex core.

Statistical moments of quantum-walk dynamics reveal topological quantum transitions.

Many phenomena in solid-state physics can be understood in terms of their topological properties. Recently, controlled protocols of quantum walk (QW) are proving to be effective simulators of such phenomena. Here we report the realization of a photonic QW showing both the trivial and the non-trivial topologies associated with chiral symmetry in one-dimensional (1D) periodic systems. We find that the probability distribution moments of the walker position after many steps can be used as direct indicators of the topological quantum transition: while varying a control parameter that defines the system phase, these moments exhibit a slope discontinuity at the transition point. Numerical simulations strongly support the conjecture that these features are general of 1D topological systems. Extending this approach to higher dimensions, different topological classes, and other typologies of quantum phases may offer general instruments for investigating and experimentally detecting quantum transitions in such complex systems.

Electromagnetic Confinement via Spin-Orbit Interaction in Anisotropic Dielectrics.

We investigate electromagnetic propagation in uniaxial dielectrics with a transversely varying orientation of the optic axis, the latter staying orthogonal everywhere in the propagation direction. In such a geometry, the field experiences no refractive index gradients, yet it acquires a transversely modulated Pancharatnam-Berry phase, that is, a geometric phase originating from a spin-orbit interaction. We show that the periodic evolution of the geometric phase versus propagation gives rise to a longitudinally invariant effective potential. In certain configurations, this geometric phase can provide transverse confinement and waveguiding. The theoretical findings are tested and validated against numerical simulations of the complete Maxwell's equations. Our results introduce and illustrate the role of geometric phases on electromagnetic propagation over distances well exceeding the diffraction length, paving the way to a whole new family of guided waves and waveguides that do not rely on refractive index tailoring.

Direct Femtosecond Laser Surface Structuring with Optical Vortex Beams Generated by a q-plate.

Creation of patterns and structures on surfaces at the micro- and nano-scale is a field of growing interest. Direct femtosecond laser surface structuring with a Gaussian-like beam intensity profile has already distinguished itself as a versatile method to fabricate surface structures on metals and semiconductors. Here we present an approach for direct femtosecond laser surface structuring based on optical vortex beams with different spatial distributions of the state of polarization, which are easily generated by means of a q-plate. The different states of an optical vortex beam carrying an orbital angular momentum ℓ = ±1 are used to demonstrate the fabrication of various regular surface patterns on silicon. The spatial features of the regular rippled and grooved surface structures are correlated with the state of polarization of the optical vortex beam. Moreover, scattered surface wave theory approach is used to rationalize the dependence of the surface structures on the local state of the laser beam characteristics (polarization and fluence). The present approach can be further extended to fabricate even more complex and unconventional surface structures by exploiting the possibilities offered by femtosecond optical vector fields.

Vortex and half-vortex dynamics in a nonlinear spinor quantum fluid.

Vortices are archetypal objects that recur in the universe across the scale of complexity, from subatomic particles to galaxies and black holes. Their appearance is connected with spontaneous symmetry breaking and phase transitions. In Bose-Einstein condensates and superfluids, vortices are both point-like and quantized quasiparticles. We use a two-dimensional (2D) fluid of polaritons, bosonic particles constituted by hybrid photonic and electronic oscillations, to study quantum vortex dynamics. Polaritons benefit from easiness of wave function phase detection, a spinor nature sustaining half-integer vorticity, strong nonlinearity, and tuning of the background disorder. We can directly generate by resonant pulsed excitations a polariton condensate carrying either a full or half-integer vortex as initial condition and follow their coherent evolution using ultrafast imaging on the picosecond scale. The observations highlight a rich phenomenology, such as the spiraling of the half-vortex and the joint path of the twin charges of a full vortex, until the moment of their splitting. Furthermore, we observe the ordered branching into newly generated secondary couples, associated with the breaking of radial and azimuthal symmetries. This allows us to devise the interplay of nonlinearity and sample disorder in shaping the fluid and driving the vortex dynamics. In addition, our observations suggest that phase singularities may be seen as fundamental particles whose quantized events span from pair creation and recombination to 2D+t topological vortex strings.

Quantum walks and wavepacket dynamics on a lattice with twisted photons.

The "quantum walk" has emerged recently as a paradigmatic process for the dynamic simulation of complex quantum systems, entanglement production and quantum computation. Hitherto, photonic implementations of quantum walks have mainly been based on multipath interferometric schemes in real space. We report the experimental realization of a discrete quantum walk taking place in the orbital angular momentum space of light, both for a single photon and for two simultaneous photons. In contrast to previous implementations, the whole process develops in a single light beam, with no need of interferometers; it requires optical resources scaling linearly with the number of steps; and it allows flexible control of input and output superposition states. Exploiting the latter property, we explored the system band structure in momentum space and the associated spin-orbit topological features by simulating the quantum dynamics of Gaussian wavepackets. Our demonstration introduces a novel versatile photonic platform for quantum simulations.

Directly measuring mean and variance of infinite-spectrum observables such as the photon orbital angular momentum.

The standard method for experimentally determining the probability distribution of an observable in quantum mechanics is the measurement of the observable spectrum. However, for infinite-dimensional degrees of freedom, this approach would require ideally infinite or, more realistically, a very large number of measurements. Here we consider an alternative method which can yield the mean and variance of an observable of an infinite-dimensional system by measuring only a two-dimensional pointer weakly coupled with the system. In our demonstrative implementation, we determine both the mean and the variance of the orbital angular momentum of a light beam without acquiring the entire spectrum, but measuring the Stokes parameters of the optical polarization (acting as pointer), after the beam has suffered a suitable spin-orbit weak interaction. This example can provide a paradigm for a new class of useful weak quantum measurements.