Exact solution to simultaneous intensity and phase encryption with a single phase-only hologram

Qudit-based variational quantum eigensolver using photonic orbital angular momentum states

Solving the electronic structure problem is a notorious challenge in quantum chemistry and material science. Variational quantum eigensolver (VQE) is a promising hybrid classical-quantum algorithm for finding the lowest-energy configuration of a molecular system. However, it typically requires many qubits and quantum gates with substantial quantum circuit depth to accurately represent the electronic wave function of complex structures. Here, we propose an alternative approach to solve the electronic structure problem using VQE with a single qudit. Our approach exploits a high-dimensional orbital angular momentum state of a heralded single photon and notably reduces the required quantum resources compared to conventional multi-qubit-based VQE. We experimentally demonstrate that our single-qudit-based VQE can efficiently estimate the ground state energy of hydrogen (H2) and lithium hydride (LiH) molecular systems corresponding to two- and four-qubit systems, respectively. We believe that our scheme opens a pathway to perform a large-scale quantum simulation for solving more complex problems in quantum chemistry and material science.

Polarization and Orbital Angular Momentum Encoded Quantum Toffoli Gate Enabled by Diffractive Neural Networks

Controlled quantum gates play a crucial role in enabling quantum universal operations by facilitating interactions between qubits. Direct implementation of three-qubit gates simplifies the design of quantum circuits, thereby being conducive to performing complex quantum algorithms. Here, we propose and present an experimental demonstration of a quantum Toffoli gate fully exploiting the polarization and orbital angular momentum of a single photon. The Toffoli gate is implemented using the polarized diffractive neural networks scheme, achieving a mean truth table visibility of 97.27±0.20%. We characterize the gate's performance through quantum state tomography on 216 different input states and quantum process tomography, which yields a process fidelity of 94.05±0.02%. Our method offers a novel approach for realizing the Toffoli gate without requiring exponential optical elements while maintaining extensibility to the implementation of other three-qubit gates.

Resolving ambiguities in phase correction term for optical field encoding

This article addresses ambiguities regarding the existence and definition of a phase correction term in phase and amplitude optical field encoding techniques. We present a generalized mixed Fourier-Taylor series expansion that is valid for any phase-wrapping interval. Our theoretical analysis, along with numerical and experimental validations, confirm that maintaining consistency within a given phase-wrapping convention ensures equivalent results and reconciles previously conflicting interpretations.

Optical vortex-antivortex crystallization in free space

Stable vortex lattices are basic dynamical patterns which have been demonstrated in physical systems including superconductor physics, Bose-Einstein condensates, hydrodynamics and optics. Vortex-antivortex (VAV) ensembles can be produced, self-organizing into the respective polar lattices. However, these structures are in general highly unstable due to the strong VAV attraction. Here, we demonstrate that multiple optical VAV clusters nested in the propagating coherent field can crystallize into patterns which preserve their lattice structures over distance up to several Rayleigh lengths. To explain this phenomenon, we present a model for effective interactions between the vortices and antivortices at different lattice sites. The observed VAV crystallization is a consequence of the globally balanced VAV couplings. As the crystallization does not require the presence of nonlinearities and appears in free space, it may find applications to high-capacity optical communications and multiparticle manipulations. Our findings suggest possibilities for constructing VAV complexes through the orbit-orbit couplings, which differs from the extensively studied spin-orbit couplings.

Coherent beam combining of optical vortices

We experimentally demonstrate the power scaling of optical vortices using the coherent beam combining technique, encompassing topological charges ranging from ℓ = 1 to ℓ = 5 realized on the basis of a Yb-doped fiber short-pulsed laser system. The combining efficiency varies from 83.2 to 96.9% depending on the topological charge and beam pattern quality generated by the spatial light modulators. This work is a proof of concept for using a coherent beam combining technique to surpass the physical power/energy limitation of any single source of optical vortices, regardless of the generation methods employed. These results open a pathway to power scaling of optical vortices with diverse applications in science and industry by utilizing advances in light-matter interactions.

Nanoradian-scale precision in light rotation measurement via indefinite quantum dynamics

The manipulation and metrology of light beams are pivotal for optical science and applications. In particular, achieving ultrahigh precision in the measurement of light beam rotations has been a long-standing challenge. Instead of using quantum probes like entangled photons, we address this challenge by incorporating a quantum strategy called "indefinite time direction" into the parameterizing process of quantum parameter estimation. Leveraging this quantum property of the parameterizing dynamics allows us to maximize the utilization of orbital angular momentum resources for measuring ultrasmall angular rotations of beam profile. Notably, a nanoradian-scale precision of light rotation measurement is lastly achieved in the experiment, which is the highest precision by far to our best knowledge. Furthermore, this scheme holds promise in various optical applications due to the diverse range of manipulable resources offered by photons.

Spatial resolution limit of single pixel imaging of complex light fields

Complex light fields with arbitrary amplitudes and phases can be measured by sampling them with an orthogonal basis (i.e., canonical, Hadamard) and performing single pixel interferometric measurements of the focused modes. In this work, we show that when the spatial resolution of the sampling basis is coarser than the spatial resolution of the phase in the complex field, the measured reconstructed amplitude exhibits cross talk with the phase, i.e., phase information appears in the amplitude. To demonstrate this phenomenon, we encode an arbitrary amplitude and a phase with a spatial light modulator and compare measurements with simulations.

Controllable orbital-angular-momentum Hall effect by engineering intrinsic orbit-orbit interaction

We report both theoretically and experimentally a process of optical intrinsic orbit-orbit interaction with a vortex-antivortex structure nested in a freely propagating light field. The orbit-orbit interaction is originating from the coupling between different vortices and antivortices. Based on this process, we reveal the resultant controllable orbital-angular-momentum Hall effect by considering a typical structure, which comprises a vortex-antivortex pair and another vortex (or antivortex) as a controllable knob. The intrinsic Hall effect can be spatially manipulated by appropriately engineering the orbit-orbit interaction, namely arranging the initial distribution of these elements. This work can find interesting potential applications. For example, it provides an effective technique for controllable paired photon generation.

Experimental recognition of vortex beams in oceanic turbulence combining the Gerchberg-Saxton algorithm and convolutional neural network

In underwater wireless optical communication (UWOC), vortex beams carrying orbital angular momentum (OAM) can improve channel capacity but are vulnerable to oceanic turbulence (OT), leading to recognition errors. To mitigate this issue, we propose what we believe to be a novel method that combines the Gerchberg-Saxton (GS) algorithm-based recovery with convolutional neural network (CNN)-based recognition (GS-CNN). Our experimental results demonstrate that superposed Laguerre-Gaussian (LG) beams with small topological charge are ideal information carriers, and the GS-CNN remains effective even when OT strength C n2 is high up to 10-11 K 2 m -2/3. Furthermore, we use 16 kinds of LG beams to transmit a 256-grayscale digital image, giving rise to an increase in recognition accuracy from 0.75 to 0.93 and a decrease in bit error ratio from 3.98×10-2 to 6.52×10-3 compared to using the CNN alone.

Tailoring nonuniform local orbital angular momentum density

As is well known, a light beam with a helical phase carries an optical orbital angular momentum (OAM), which can cause the orbital motion of trapped microparticles around the beam axis. Usually, the speed of the orbital motion is uniform along the azimuthal direction and depends on the amount of OAM and the light intensity. Here, we present the reverse customized method to tailor the nonuniform local OAM density along the azimuthal direction of the focal field, which has a hybrid polarization distribution and maintains a doughnut-shaped intensity profile. Theoretical analysis and experimental results about the orbital motion of the trapped polystyrene sphere show that the nonuniform local OAM density can be tailored by manipulating the polarization states of the focal field. Our results provide an ingenious way to control the local tangential optical force and the speed of the orbital motion of particles driven by the local OAM density and will promote exciting possibilities for exploring ways to control the mechanical dynamics of microparticles in optical trapping and microfluidics.

Tight focusing through scattering media via a Bessel-basis transmission matrix

The transmission matrix (TM) is a powerful tool for focusing light through scattering media. Here, we demonstrate a Bessel-basis TM that enables tight focusing through the scattering media and reduces the full width at half maximum of the focus by 23% on average, as compared to the normally used Hadamard-basis TM. To measure the Bessel-basis TM, we establish a common-path inter-mode interferometer (IMI), which can fully utilize the pixels of the spatial light modulator, leading to an enhancement in the peak-to-background intensity ratio (PBR) of the focus. Experimental results suggest that the Bessel-basis TM can achieve a tighter focus behind the scattering media, and the PBR of the focus obtained by the IMI is around 14.3% higher than that achieved using the normal peripheral reference interferometry.

Ultrahigh-fidelity spatial mode quantum gates in high-dimensional space by diffractive deep neural networks

While the spatial mode of photons is widely used in quantum cryptography, its potential for quantum computation remains largely unexplored. Here, we showcase the use of the multi-dimensional spatial mode of photons to construct a series of high-dimensional quantum gates, achieved through the use of diffractive deep neural networks (D2NNs). Notably, our gates demonstrate high fidelity of up to 99.6(2)%, as characterized by quantum process tomography. Our experimental implementation of these gates involves a programmable array of phase layers in a compact and scalable device, capable of performing complex operations or even quantum circuits. We also demonstrate the efficacy of the D2NN gates by successfully implementing the Deutsch algorithm and propose an intelligent deployment protocol that involves self-configuration and self-optimization. Moreover, we conduct a comparative analysis of the D2NN gate's performance to the wave-front matching approach. Overall, our work opens a door for designing specific quantum gates using deep learning, with the potential for reliable execution of quantum computation.

Topological transitions of the generalized Pancharatnam-Berry phase

Distinct from the dynamical phase, in a cyclic evolution, a system's state may acquire an additional component, a.k.a. geometric phase. Recently, it has been demonstrated that geometric phases can be induced by a sequence of generalized measurements implemented on a single qubit. Furthermore, it has been predicted that these geometric phases may exhibit a topological transition as a function of the measurement strength. We demonstrate and study this transition experimentally by using an optical platform where the qubit is represented by the polarization of light and the weak measurement is performed by means of coupling with the spatial degree of freedom. Our protocol can be interpreted in terms of environment-induced geometric phases, whose values are topologically determined by the environment-system coupling strength. Our results show that the two limits of geometric phase induced by sequences of either weak or projective measurements are topologically distinct.

Shadows of structured beams in lenslike media

The self-healing phenomenon of structured light beams has been comprehensively investigated for its important role in various applications including optical tweezing, superresolution imaging, and optical communication. However, for different structured beams, there are different explanations for the self-healing effect, and a unified theory has not yet been formed. Here we report both theoretically and experimentally a study of the self-healing effect of structured beams in lenslike media, this is, inhomogeneous lenslike media with a quadratic gradient index. By observing the appearance of a number of shadows of obstructed structured wave fields it has been demonstrated that their self-healing in inhomogeneous media are the result of superposition of fundamental traveling waves. We have found that self-healing of structured beams occurs in this medium and, interestingly enough, that the shadows created in the process present sinusoidal propagating characteristics as determined by the geometrical ray theory in lenslike media. This work provides what we believe to be a new inhomogenous environment to explain the self-healing effect and is expected to deepen understanding of the physical mechanism.

Interferometric measurement of arbitrary propagating vector beams that are tightly focused

In this work, we demonstrate a simple setup to generate and measure arbitrary vector beams that are tightly focused. The vector beams are created with a spatial light modulator and focused with a microscope objective with an effective numerical aperture of 1.2. The transverse polarization components (E_x, E_y) of the tightly focused vector beams are measured with three-step interferometry. The axial component E_z is reconstructed using the transverse fields with Gauss's law. We measure beams with the following polarization states: circular, radial, azimuthal, spiral, flower, and spider web.

Simple algorithm for the design of accelerating Bessel-like beams with adjustable features along their propagation

We present an extremely simple method for designing self-accelerating non-diffracting beams having arbitrary trajectories while their intensity, width and orbital angular momentum are modulated in a prescribed way along their propagation. Different beams constructed with this method are demonstrated experimentally in the paraxial regime and numerically in the non-paraxial regime.

Experimental Test of High-Dimensional Quantum Contextuality Based on Contextuality Concentration

Contextuality is a distinctive feature of quantum theory and a fundamental resource for quantum computation. However, existing examples of contextuality in high-dimensional systems lack the necessary robustness required in experiments. Here, we address this problem by identifying a family of noncontextuality inequalities whose maximum quantum violation grows with the dimension of the system. At first glance, this contextuality is the single-system version of multipartite Bell nonlocality taken to an extreme form. What is interesting is that the single-system version achieves the same degree of contextuality but uses a Hilbert space of lower dimension. That is, contextuality "concentrates" as the degree of contextuality per dimension increases. We show the practicality of this result by presenting an experimental test of contextuality in a seven-dimensional system. By simulating sequences of quantum ideal measurements with destructive measurements and repreparation in an all-optical setup, we report a violation of 68.7 standard deviations of the simplest case of the noncontextuality inequalities identified. Our results advance the investigation of high-dimensional contextuality, its connection to the Clifford algebra, and its role in quantum computation.

Zero-order free holographic optical tweezers

Holographic optical tweezers (HOTs) use spatial light modulators (SLM) to modulate light beams, thereby enabling the dynamic control of optical trap arrays with complex intensity and phase distributions. This has provided exciting new opportunities for cell sorting, microstructure machining, and studying single molecules. However, the pixelated structure of the SLM will inevitably bring up the unmodulated zero-order diffraction possessing an unacceptably large fraction of the incident light beam power. This is harmful to optical trapping because of the bright, highly localized nature of the errant beam. In this paper and to address this issue, we construct a cost-effective, zero-order free HOTs apparatus, thanks to a homemade asymmetric triangle reflector and a digital lens. As there is no zero-order diffraction, the instrument performs excellently in generating complex light fields and manipulating particles.

Optical Encoding Model Based on Orbital Angular Momentum Powered by Machine Learning

Based on orbital angular momentum (OAM) properties of Laguerre-Gaussian beams LG(p,ℓ), a robust optical encoding model for efficient data transmission applications is designed. This paper presents an optical encoding model based on an intensity profile generated by a coherent superposition of two OAM-carrying Laguerre-Gaussian modes and a machine learning detection method. In the encoding process, the intensity profile for data encoding is generated based on the selection of p and ℓ indices, while the decoding process is performed using a support vector machine (SVM) algorithm. Two different decoding models based on an SVM algorithm are tested to verify the robustness of the optical encoding model, finding a BER =10-9 for 10.2 dB of signal-to-noise ratio in one of the SVM models.

Radial-mode sensitive probe beam in the rotational Doppler effect

The rotational Doppler effect (RDE) attracts much attention in various research areas, from acoustics to optics. The observation of RDE mostly depends on the orbital angular momentum of the probe beam, while the impression of radial mode is ambiguous. To clarify the role of radial modes in RDE detection, we reveal the mechanism of interaction between probe beams and rotating objects based on complete Laguerre-Gaussian (LG) modes. It is theoretically and experimentally proved that radial LG modes play a crucial role in RDE observation because of topological spectroscopic orthogonality between probe beams and objects. We enhance the probe beam by employing multiple radial LG modes, which makes the RDE detection sensitive to objects containing complicated radial structures. In addition, a specific method to estimate the efficiency of various probe beams is proposed. This work has the potential to modify RDE detection method and take the related applications to a new platform.

Direct generation of spatially entangled qudits using quantum nonlinear optical holography

Nonlinear holography shapes the amplitude and phase of generated new harmonics using nonlinear processes. Classical nonlinear holography influenced many fields in optics, from information storage, demultiplexing of spatial information, and all-optical control of accelerating beams. Here, we extend the concept of nonlinear holography to the quantum regime. We directly shape the spatial quantum correlations of entangled photon pairs in two-dimensional patterned nonlinear photonic crystals using spontaneous parametric down conversion, without any pump shaping. The generated signal-idler pair obeys a parity conservation law that is governed by the nonlinear crystal. Furthermore, the quantum states exhibit quantum correlations and violate the Clauser-Horne-Shimony-Holt inequality, thus enabling entanglement-based quantum key distribution. Our demonstration paves the way for controllable on-chip quantum optics schemes using the high-dimensional spatial degree of freedom.

Generation of arbitrary complex fields with high efficiency and high fidelity by cascaded phase-only modulation method

Independent or joint control over the amplitude and phase of the complex field by phase-only modulation element is crucial in numerous applications. Existing modulation methods can realize high levels of accuracy but are accompanied by noticeable losses in light-usage efficiency. Here a cascaded modulation method is proposed for the generation of arbitrary complex fields with high efficiency and high fidelity. This approach is based on a gradient descent optimization algorithm that minimizes a customized cost function. The major advantage of our approach over existing modulation methods is that the efficiency is significantly enhanced while ensuring high modulation accuracy. For the generation of Laguerre-Gaussian mode (LG₀₁), with similar high accuracy, the efficiency by our approach can reach 79.5%, which is enhanced by 192% compared with the theoretical maximum efficiency of 41.5% [Opt. Express25, 11692 (2017)10.1364/OE.25.011692]. Furthermore, the efficiency of existing modulation methods deteriorates rapidly as the target field turns more intricate, whereas in our approach it maintains at a relatively high level. The field generation fidelity and energy efficiency of the proposed cascaded modulation method are compared with that of several different single-pass modulation methods in generating a series of typical Hermite-Gaussian and Laguerre-Gaussian modes and an amplitude-only "OSA" pattern. Our proposed method features both high efficiency and high accuracy in the simulation and experiment, which may be of growing interest to applications such as optical manipulation or quantum communication.

Radially and Azimuthally Pure Vortex Beams from Phase-Amplitude Metasurfaces

To exploit the full potential of the transverse spatial structure of light using the Laguerre-Gaussian basis, it is necessary to control the azimuthal and radial components of the photons. Vortex phase elements are commonly used to generate these modes of light, offering precise control over the azimuthal index but neglecting the radially dependent amplitude term, which defines their associated corresponding transverse profile. Here, we experimentally demonstrate the generation of high-purity Laguerre-Gaussian beams with a single-step on-axis transformation implemented with a dielectric phase-amplitude metasurface. By vectorially structuring the input beam and projecting it onto an orthogonal polarization basis, we can sculpt any vortex beam in phase and amplitude. We characterize the azimuthal and radial purities of the generated vortex beams, reaching a purity of 98% for a vortex beam with l =50 and p = 0. Furthermore, we comparatively show that the purity of the generated vortex beams outperforms those generated with other well-established phase-only metasurface approaches. In addition, we highlight the formation of "ghost" orbital angular momentum orders from azimuthal gratings (analogous to ghost orders in ruled gratings), which have not been widely studied to date. Our work brings higher-order vortex beams and their unlimited potential within reach of wide adoption.

High purity orbital angular momentum of light

We present a novel technique for generating beams of light carrying orbital angular momentum (OAM) that increases mode purity and decreases singularity splitting by orders of magnitude. This technique also works to control and mitigate beam divergence within propagation distances less than the Rayleigh length. Additionally, we analyze a tunable parameter of this technique that can change the ratio of beam purity to power to fit desired specifications. Beam generation via this technique is achievable using only phase-modulating optical elements, which reduces experimental complexity and beam energy loss.

Wave-front reconstruction via single-pixel homodyne imaging

We combine single-pixel imaging and homodyne detection to perform full object recovery (phase and amplitude). Our method does not require any prior information about the object or the illuminating fields. As a demonstration, we reconstruct the optical properties of several semi-transparent objects and find that the reconstructed complex transmission has a phase precision of 0.02 radians and a relative amplitude precision of 0.01.

Integrated orbital angular momentum mode sorters on vortex fibers

We design, fabricate, and characterize integrated mode sorters for multimode fibers that guide well-separated vortex modes. We use 3D direct laser printing to print a collimator and a Cartesian to a log-polar mode transformer on the tip of the fiber. This polarization insensitive device can send different modes into different exit angles and is therefore useful for space division multiplexed optical communication. Two types of fibers with two corresponding sorters are used, enabling the sorting of either four or eight different modes in a compact and robust manner. The integration of the vortex fiber and multiplexer opens the door for widespread exploitation of orbital angular momentum (OAM) for data multiplexing in fiber networks.

Generation of perfect optical vortex by Laguerre-Gauss beams with a high-order radial index

Perfect optical vortex (POV) beams have attracted extensive attention because they have the advantage of a radial profile that is independent of orbital angular momentum. To date, it is usually obtained by means of the Fourier transform performed by a lens on Bessel beams. We theoretically and experimentally demonstrate that POV can be generated by performing the Fourier transform on Laguerre-Gauss beams with a high-order radial index. Furthermore, we derive an analytical expression for the increase in vortex radius, which is beneficial to compensate for the influence of the radius change in actual experiments. Our results may shed new light for a variety of research utilizing POV.

Compact generation of robust Airy beam pattern with spatial coherence engineering

We present a class of partially coherent light sources having Airy-type amplitude and Airy-correlated spatial coherence. We show that the light beam generated by such sources can preserve the Airy beam pattern well during its propagation from source to far field. We demonstrate the robustness of the Airy beam pattern by introducing a hard aperture to largely block the beam source. We find that the coherence-induced Airy beam pattern can still be well reconstructed during propagation. We successfully synthesize such partially coherent source using the principle of complex random modes decomposition by using a single phase-only spatial light modulator. The proposed robust Airy beam pattern may find applications in information transmission through complex media.

High capacity topological coding based on nested vortex knots and links

Optical knots and links have attracted great attention because of their exotic topological characteristics. Recent investigations have shown that the information encoding based on optical knots could possess robust features against external perturbations. However, as a superior coding scheme, it is also necessary to achieve a high capacity, which is hard to be fulfilled by existing knot-carriers owing to the limit number of associated topological invariants. Thus, how to realize the knot-based information coding with a high capacity is a key problem to be solved. Here, we create a type of nested vortex knot, and show that it can be used to fulfill the robust information coding with a high capacity assisted by a large number of intrinsic topological invariants. In experiments, we design and fabricate metasurface holograms to generate light fields sustaining different kinds of nested vortex links. Furthermore, we verify the feasibility of the high-capacity coding scheme based on those topological optical knots. Our work opens another way to realize the robust and high-capacity optical coding, which may have useful impacts on the field of information transfer and storage.

Robust and high capacity optical coding will be at the base of future developments of information transfer and storage. Here the authors develop a topological all-optical coding scheme, which possesses good stability and a high capacity, using nested vortex knots and links.

Manipulating the radial components of LG pump beam for ultrahigh-dimensional maximally entangled orbital angular momentum states

High-dimensional maximally entangled orbital angular momentum (OAM) states are a promising resource for enhancing information capacity and robustness in quantum communication. However, it still lacks an effective method to increase the state dimensionality. Here, we theoretically propose an efficient scheme to generate maximally entangled OAM states of ultrahigh dimensionality by manipulating the radial components of a Laguerre-Gaussian (LG) pump beam. By optimizing the complex amplitudes of multiple radial modes of the LG pump light, one can feasibly achieve 101-dimensional OAM-based maximally entangled states. Our scheme has potential applications in high capacity quantum communication networks.

Demonstrating Shareability of Multipartite Einstein-Podolsky-Rosen Steering

Einstein-Podolsky-Rosen (EPR) steering, a category of quantum nonlocal correlations describing the ability of one observer to influence another party's state via local measurements, is different from both entanglement and Bell nonlocality by possessing an asymmetric property. For multipartite EPR steering, the monogamous situation, where two observers cannot simultaneously steer the state of the third party, has been investigated rigorously both in theory and experiment. In contrast to the monogamous situation, the shareability of EPR steering in reduced subsystems allows the state of one party to be steered by two or more observers and thus reveals more configurations of multipartite EPR steering. However, the experimental implementation of such a kind of shareability has still been absent until now. Here, in an optical experiment, we provide a proof-of-principle demonstration of the shareability of EPR steering without the constraint of monogamy in a three-qubit system. Moreover, based on the reduced bipartite EPR steering detection results, we verify the genuine three-qubit entanglement results. This work provides a complementary viewpoint for understanding multipartite EPR steering and has potential applications in many quantum information protocols, such as multipartite entanglement detection, quantum cryptography, and the construction of quantum networks.

Optimization for maximum modulation of a double-pass twisted nematic liquid crystal display

Spatial light modulators are widely used to perform modulations of different properties of the electromagnetic field. In this work, a simple optimization method for general double-pass setups was developed. It takes into account the involved polarizing elements and displays, and a numerical simulation based on an exhaustive search routine finds the optimal optical axis orientations of the polarizing elements for the desired modulation. By simultaneously considering both impingements, we are able to take full advantage of the modulation capabilities of the chosen spatial light modulators. In particular, different polarization modulations and complex amplitude modulations were studied for twisted nematic liquid crystal displays and passive linear optical elements. Examples of different optimization criteria are shown and compared with experimental results, supporting the feasibility of this approach. This method offers the possibility of independent modulation of two properties of the input light state, outperforming the use of a single screen.

Photonic Angular Superresolution Using Twisted N00N States

The increased phase sensitivity of N00N states has been used in many experiments, often involving photon paths or polarization. Here we experimentally combine the phase sensitivity of N00N states with the orbital angular momentum (OAM) of photons up to 100  ℏ, to resolve rotations of a light field around its optical axis. The results show that both a higher photon number and larger OAM increase the resolution and achievable sensitivity. The presented method opens a viable path to unconditional angular supersensitivity and accessible generation of N00N states between any transverse light fields.

Superresolution Linear Optical Imaging in the Far Field

The resolution of optical imaging devices is ultimately limited by the diffraction of light. To circumvent this limit, modern superresolution microscopy techniques employ active interaction with the object by exploiting its optical nonlinearities, nonclassical properties of the illumination beam, or near field probing. Thus, they are not applicable whenever such interaction is not possible, for example, in astronomy or noninvasive biological imaging. Far field, linear optical superresolution techniques based on passive analysis of light coming from the object would cover these gaps. In this Letter, we present the first proof-of-principle demonstration of such a technique for 2D imaging. It works by accessing information about spatial correlations of the image optical field and, hence, about the object itself via measuring projections onto Hermite-Gaussian transverse spatial modes. With a basis of 21 spatial modes in both transverse dimensions, we perform two-dimensional imaging with twofold resolution enhancement beyond the diffraction limit.

Generation of Non-Rayleigh Nondiffracting Speckles

Optical speckle fields with both non-Rayleigh statistics and nondiffracting characteristics in propagation are an important light source for many applications. However, tailoring either non-Rayleigh statistical speckles or nondiffracting speckles are only investigated independently in previous studies. Here, we report the first observation of optical speckles that remain diffraction-free over a long axial distance while keeping non-Rayleigh statistics simultaneously. We further show the enhancement of Anderson localization of light with the non-Rayleigh nondiffracting speckles. The work presented here provides a versatile framework for customizing optical fields with desired speckle patterns for applications in the fields of solid-state physics, cold atoms, and optical imaging.

Demonstration of generating a 100 Gbit/s orbital-angular-momentum beam with a tunable mode order over a range of wavelengths using an integrated broadband pixel-array structure

We experimentally generate an orbital-angular-momentum (OAM) beam with a tunable mode order over a range of wavelengths utilizing an integrated broadband pixel-array OAM emitter. The emitter is composed of a 3-to-4 coupler, four phase controllers, and a mode convertor. An optical input is split into four waveguides by the coupler. Subsequently, the four waveguide fields are coherently combined and transformed into a free-space OAM beam by the mode convertor. By tuning the phase delay Δφ between the four waveguides using the integrated phase controllers, the OAM order of the generated beam could be changed. Our results show that (a) a single OAM beam with a tunable OAM order (ℓ=-1 or ℓ=+1) is generated with the intermodal power coupling of <-11dB, and (b) in a wavelength range of 6.4 nm, a free-space link of a single 50 Gbaud quadrature-phase-shift-keying (QPSK) channel carried by the tunable OAM beam is achieved with a bit error rate below the forward-error-correction threshold. As proof of concept, a 400 Gbit/s OAM-multiplexed and WDM QPSK link is demonstrated with a ∼1-dB OSNR penalty compared with a single-beam link.

Phase gradient protection of stored spatially multimode perfect optical vortex beams in a diffused rubidium vapor

We experimentally investigate the optical storage of perfect optical vortex (POV) and spatially multimode perfect optical vortex (MPOV) beams via electromagnetically induced transparency (EIT) in a hot vapor cell. In particular, we study the role that phase gradients and phase singularities play in reducing the blurring of the retrieved images due to atomic diffusion. Three kinds of manifestations are enumerated to demonstrate such effect. Firstly, the suppression of the ring width broadening is more prominent for POVs with larger orbital angular momentum (OAM). Secondly, the retrieved double-ring MPOV beams' profiles present regular dark singularity distributions that are related to their vortex charge difference. Thirdly, the storage fidelities of the triple-ring MPOVs are substantially improved by designing line phase singularities between multi-ring MPOVs with the same OAM number but π offset phases between adjacent rings. Our experimental demonstration of MPOV storage opens new opportunities for increasing data capacity in quantum memories by spatial multiplexing, as well as the generation and manipulation of complex optical vortex arrays.

Uniform and efficient beam shaping for high-energy lasers

Phase-only beam shaping with liquid crystal on silicon spatial light modulators (SLM) allows modulating the wavefront dynamically and generating arbitrary intensity patterns with high efficiency. Since this method cannot take control of all degrees of freedom, a speckle pattern appears and drastically impairs the outcome. There are several methods to overcome this issue including algorithms which directly control phase and amplitude, but they suffer from low efficiency. Methods using two SLMs yield excellent results but they are usually limited in the applicable energy due to damage to the SLM's backplane. We present a method which makes use of two SLMs and simultaneously gives way for high-energy laser applications. The algorithm and setup are designed to keep the fluence on the SLMs low by distributing the light over a large area. This provides stability against misalignment and facilitates experimental feasibility while keeping high efficiency.

Full-mode characterization of correlated photon pairs generated in spontaneous downconversion

Spontaneous parametric downconversion is the primary source to generate entangled photon pairs in quantum photonics laboratories. Depending on the experimental design, the generated photon pairs can be correlated in the frequency spectrum, polarization, position-momentum, and spatial modes. Exploring the spatial modes' correlation has hitherto been limited to the polar coordinates' azimuthal angle, and a few attempts to study Walsh mode's radial states. Here, we study the full-mode correlation, on a Laguerre-Gauss basis, between photon pairs generated in a type-I crystal. Furthermore, we explore the effect of a structured pump beam possessing different spatial modes onto bi-photon spatial correlation. Finally, we use the capability to project over arbitrary spatial mode superpositions to perform the bi-photon state's full quantum tomography in a 16-dimensional subspace.

High-Dimensional Two-Photon Interference Effects in Spatial Modes

Two-photon interference is a fundamental quantum optics effect with numerous applications in quantum information science. Here, we study two-photon interference in multiple transverse-spatial modes along a single beam-path. Besides implementing the analog of the Hong-Ou-Mandel interference using a two-dimensional spatial-mode splitter, we extend the scheme to observe coalescence and anticoalescence in different three- and four-dimensional spatial-mode multiports. The operation within spatial modes, along a single beam path, lifts the requirement for interferometric stability and opens up new pathways of implementing linear optical networks for complex quantum information tasks.

Optical storage of Ince-Gaussian modes in warm atomic vapor

We report on the optical storage of Ince-Gaussian modes in a warm rubidium vapor cell based on electromagnetically induced transparency protocol, and we also qualitatively analyze how atomic diffusion affects the retrieved beams after storage. Ince-Gaussian modes possess very complex and abundant spatial structures and form a complete infinite-dimensional Hilbert space. Successfully storing such modes could open up possibilities for fundamental high-dimensional optical communication experiments.

Optical mode conversion in coupled Fabry-Perot resonators

Low-loss conversion among a complete and orthogonal set of optical modes is important for high-bandwidth quantum and classical communication. In this Letter, we explore tunable impedance mismatch between coupled Fabry-Perot resonators as a powerful tool for manipulation of the spatial and temporal properties of optical fields. In the single-mode regime, frequency-dependent impedance matching enables tunable finesse optical resonators. Introducing the spatial dependence of the impedance mismatch enables coherent spatial mode conversion of optical photons at near-unity efficiency. We experimentally demonstrate a NIR resonator whose finesse is tunable over a decade, and an optical mode converter with efficiency >75% for the first six Hermite-Gauss modes. We anticipate that this new perspective on coupled multimode resonators will have exciting applications in micro- and nano-photonics and computer-aided inverse design.

Reduced volume and reflection for bright optical tweezers with radial Laguerre-Gauss beams

Spatially structured light has opened a wide range of opportunities for enhanced imaging as well as optical manipulation and particle confinement. Here, we show that phase-coherent illumination with superpositions of radial Laguerre-Gauss (LG) beams provides improved localization for bright optical tweezer traps, with narrowed radial and axial intensity distributions. Further, the Gouy phase shifts for sums of tightly focused radial LG fields can be exploited for phase-contrast strategies at the wavelength scale. One example developed here is the suppression of interference fringes from reflection near nanodielectric surfaces, with the promise of improved cold-atom delivery and manipulation.

Optical framed knots as information carriers

Modern beam shaping techniques have enabled the generation of optical fields displaying a wealth of structural features, which include three-dimensional topologies such as Möbius, ribbon strips and knots. However, unlike simpler types of structured light, the topological properties of these optical fields have hitherto remained more of a fundamental curiosity as opposed to a feature that can be applied in modern technologies. Due to their robustness against external perturbations, topological invariants in physical systems are increasingly being considered as a means to encode information. Hence, structured light with topological properties could potentially be used for such purposes. Here, we introduce the experimental realization of structures known as framed knots within optical polarization fields. We further develop a protocol in which the topological properties of framed knots are used in conjunction with prime factorization to encode information.

Fast generation and detection of spatial modes of light using an acousto-optic modulator

Spatial modes of light provide a high-dimensional space that can be used to encode both classical and quantum information. Current approaches for dynamically generating and measuring these modes are slow, due to the need to reconfigure a high-resolution phase mask such as a spatial light modulator or digital micromirror device. The process of updating the spatial mode of light can be greatly accelerated by multiplexing a set of static phase masks with a fast, image-preserving optical switch, such as an acousto-optic modulator (AOM). We experimentally realize this approach, using a double-pass AOM to generate one of five orbital angular momentum states with a switching rate of up to 500 kHz. We then apply this system to perform fast quantum state tomography of spatial modes of light in a 2-dimensional Hilbert space by projecting the unknown state onto six spatial modes comprising three mutually unbiased bases. We are able to reconstruct arbitrary states in under 1 ms with an average fidelity of 96.9%.

Light beams with volume superoscillations

Using a superposition of shifted Bessel beams with different longitudinal wave vectors and orbital angular momenta, we realize an optical beam having simultaneous axial, angular, and radial focusing narrower than the Fourier limit. Our findings can be useful for optical particle manipulation and high-resolution microscopy.

Hiding Ignorance Using High Dimensions

The absence of information-entirely or partly-is called ignorance. Naturally, one might ask if some ignorance of a whole system will imply some ignorance of its parts. Our classical intuition tells us yes, however quantum theory tells us no: it is possible to encode information in a quantum system so that despite some ignorance of the whole, it is impossible to identify the unknown part [T. Vidick and S. Wehner, Phys. Rev. Lett. 107, 030402 (2011).PRLTAO0031-900710.1103/PhysRevLett.107.030402]. Experimentally verifying this counterintuitive fact requires controlling and measuring quantum systems of high dimension (d>9). We provide this experimental evidence using the transverse spatial modes of light, a powerful resource for testing high-dimensional quantum phenomena.

Rapidly and accurately shaping the intensity and phase of light for optical nano-manipulation

Holographic optical tweezers can be applied to manipulate microscopic particles in various optical patterns, which classical optical tweezers cannot do. This ability relies on accurate computer-generated holography (CGH), yet most CGH techniques can only shape the intensity profiles while the phase distributions remain poor. Here, we introduce a new method for fast generation of holograms that allows for accurately shaping both the intensity and phase distributions of light. The method uses a discrete inverse Fourier transform formula to directly calculate a hologram in one step, in which a random phase factor is introduced into the formula to enable complete control of intensity and phase. Various optical patterns can be created, as demonstrated by the experimentally measured intensity and phase profiles projected from the holograms. The high-quality shaping of intensity and phase of light provides new opportunities for optical trapping and manipulation, such as controllable transportation of nanoparticles in optical trap networks with variable phase profiles.

Exact design of complex amplitude holograms for producing arbitrary scalar fields

Typical methods to holographically encode arbitrary wavefronts assume the hologram medium only applies either phase shifts or amplitude attenuation to the wavefront. In many cases, phase cannot be introduced to the wavefront without also affecting the amplitude. Here we show how to encode an arbitrary wavefront into an off-axis transmission hologram that returns the exact desired arbitrary wavefunction in a diffracted beam for phase-only, amplitude-only, or mixed phase and amplitude holograms with any periodic groove profile. We apply this to design thin holograms for electrons in a TEM, but our results are generally applicable to light and X-ray optics. We employ a phase reconstruction from a series of focal plane images to qualitatively show the accuracy of this method to impart the expected amplitude and phase to a specific diffraction order.

Talbot effect in waveforms containing subwavelength multilobe superoscillations

The self-imaging of periodic light patterns, also known as the Talbot effect, is usually limited to periods that are larger than the wavelength. Here we present, theoretically and experimentally, a method to overcome this limitation by using superoscillating light patterns. The input intensity distribution is a periodic band-limited function with relatively large periods, but it contains regions of multilobe periodic oscillations with periods that are smaller than half of the wavelength. We observe the revival of the input pattern, including the subwavelength superoscillating regions, at large distances of more than 40 times the optical wavelength. Moreover, at fractional Talbot distances, we observe even faster local oscillations, with periods of approximately one-third of the optical wavelength.