Preparing arbitrary pure states of spatial qudits with a single phase-only spatial light modulator

Direct construction of an optical linear transform and its application on optical complex data generation

Optical computing technique has emerged as a promising platform for highly parallel data processing. In most optical computing architectures, optical linear transform is the basic composition, which is commonly designed by the established deep learning-based methods or general-purpose optimizers. There still lacks in-depth study to construct a solver targeted at optical linear transform applications. In this work, we propose a new algorithm that solves the transformation matrix of a linear optical system consisting of cascaded phase masks directly and show that its efficiency is significantly higher than those common solvers. As a direct application of this method, we can create target array of optical beams even with a single layer of phase mask in the experiment. The amplitude and phase of each beam in the array can be controlled independently without affecting each other. The optical system requires only one light source and one programmable phase mask. This setup can be readily incorporated into most current optical computing configurations. Our method may find broad applications in classic and quantum optical information processing.

Ptychographic reconstruction of pure quantum states

The quantum analogue of ptychography, a powerful coherent diffractive imaging technique, is a simple method for reconstructing d-dimensional pure states. It relies on measuring partially overlapping parts of the input state in a single orthonormal basis and feeding the outcomes to an iterative phase retrieval algorithm for postprocessing. We provide a proof of concept demonstration of this method by determining pure states given by superpositions of d transverse spatial modes of an optical field. A set of n rank-r projectors, diagonal in the spatial mode basis, is used to generate n partially overlapping parts of the input, and each part is projectively measured in the Fourier transformed basis. For d up to 32, we successfully reconstructed hundreds of random states using n=5 and n=d rank-⌈d/2⌉ projectors. The extension of quantum ptychography for other types of photonic spatial modes is outlined.

High-dimensional states of light with full control of OAM and transverse linear momentum

We present a compact scheme for the generation of high-dimensional states of light encoded in the transverse linear momentum of photons that carry orbital angular momentum (OAM). We use a programmable spatial light modulator in phase configuration to create correlations between these two spatial degrees of freedom. With our setup, we are able to control, independently, the relative phases and amplitudes of the spatial superposition in addition to the topological charge of the OAM. Moreover, we engineer correlations that emulate bipartite quantum states of dimensions d×m. Experimental results from the characterization of different generated states of dimensions up to 9×5 are in excellent agreement with the numerical simulations. Fidelity with the target state is, for all cases, above 95%.

Set of 4d-3 observables to determine any pure qudit state

We present a tomographic method which requires only 4d-3 measurement outcomes to reconstruct any pure quantum state of arbitrary dimension d. Using the proposed scheme, we have experimentally reconstructed a large number of pure states of dimension d=7, obtaining a mean fidelity of 0.94. Moreover, we performed numerical simulations of the reconstruction process, verifying the feasibility of the method for higher dimensions. In addition, the a priori assumption of purity can be certified within the same set of measurements, which represents an improvement with respect to other similar methods and contributes to answering the question of how many observables are needed to uniquely determine any pure state.

Remote temporal wavepacket narrowing

Quantum communication protocols can be significantly enhanced by careful preparation of the wavepackets of the utilized photons. Following the theoretical proposal published recently by our group, we experimentally demonstrate the effect of remote temporal wavepacket narrowing of a heralded single photon produced via spontaneous parametric down-conversion. This is done by utilizing a time-resolved measurement on the heralding photon which is frequency-entangled with the heralded photon. We then investigate optimal photon pair source characteristics to minimize heralded wavepacket width.

Combining average molecular tilt and flicker for management of depolarized light in parallel-aligned liquid crystal devices for broadband and wide-angle illumination

We demonstrate a complete semiphysical and analytical model describing the angular and wavelength dependencies not only of retardance, but also its flicker, in parallel aligned liquid crystal (PA-LC) devices. It relies on the fitting of the molecules' equivalent tilt angle as a function of applied voltage. The wide range of calculations it offers without requiring extensive characterization makes the model unique. We focus on PA-LCoS application as a polarization state generator across the visible spectrum and for a wide range of incidence angles. This approach offers novel capabilities for managing arbitrary states of both full and partial polarization. To highlight the richness of situations with PA-LCoS devices, we provide results for two different digital addressing sequences producing different levels of flicker.

Liquid-Crystal-on-Silicon for Augmented Reality Displays

In this paper, we review liquid-crystal-on-silicon (LCoS) technology and focus on its new application in emerging augmented reality (AR) displays. In the first part, the LCoS working principles of three commonly adopted LC modes—vertical alignment and twist nematic for amplitude modulation, and homogeneous alignment for phase modulation—are introduced and their pros and cons evaluated. In the second part, the fringing field effect is analyzed, and a novel pretilt angle patterning method for suppressing the effect is presented. Moreover, we illustrate how to integrate the LCoS panel in an AR display system. Both currently available intensity modulators and under-developing holographic displays are covered, with special emphases on achieving high image quality, such as a fast response time and high-resolution. The rapidly increasing application of LCoS in AR head-mounted displays and head-up displays is foreseeable.

Photonic Discrete-time Quantum Walks and Applications

We present a review of photonic implementations of discrete-time quantum walks (DTQW) in the spatial and temporal domains, based on spatial- and time-multiplexing techniques, respectively. Additionally, we propose a detailed novel scheme for photonic DTQW, using transverse spatial modes of single photons and programmable spatial light modulators (SLM) to manipulate them. Unlike all previous mode-multiplexed implementations, this scheme enables simulation of an arbitrary step of the walker, only limited, in principle, by the SLM resolution. We discuss current applications of such photonic DTQW architectures in quantum simulation of topological effects and the use of non-local coin operations based on two-photon hybrid entanglement.

Experimental Minimum-Error Quantum-State Discrimination in High Dimensions

Quantum mechanics forbids perfect discrimination among nonorthogonal states through a single shot measurement. To optimize this task, many strategies were devised that later became fundamental tools for quantum information processing. Here, we address the pioneering minimum-error (ME) measurement and give the first experimental demonstration of its application for discriminating nonorthogonal states in high dimensions. Our scheme is designed to distinguish symmetric pure states encoded in the transverse spatial modes of an optical field; the optimal measurement is performed by a projection onto the Fourier transform basis of these modes. For dimensions ranging from D=2 to D=21 and nearly 14 000 states tested, the deviations of the experimental results from the theoretical values range from 0.3% to 3.6% (getting below 2% for the vast majority), thus showing the excellent performance of our scheme. This ME measurement is a building block for high-dimensional implementations of many quantum communication protocols, including probabilistic state discrimination, dense coding with nonmaximal entanglement, and cryptographic schemes.

Predictive capability of average Stokes polarimetry for simulation of phase multilevel elements onto LCoS devices

Parallel-aligned (PA) liquid-crystal on silicon (LCoS) microdisplays are especially appealing in a wide range of spatial light modulation applications since they enable phase-only operation. Recently we proposed a novel polarimetric method, based on Stokes polarimetry, enabling the characterization of their linear retardance and the magnitude of their associated phase fluctuations or flicker, exhibited by many LCoS devices. In this work we apply the calibrated values obtained with this technique to show their capability to predict the performance of spatially varying phase multilevel elements displayed onto the PA-LCoS device. Specifically we address a series of multilevel phase blazed gratings. We analyze both their average diffraction efficiency ("static" analysis) and its associated time fluctuation ("dynamic" analysis). Two different electrical configuration files with different degrees of flicker are applied in order to evaluate the actual influence of flicker on the expected performance of the diffractive optical elements addressed. We obtain a good agreement between simulation and experiment, thus demonstrating the predictive capability of the calibration provided by the average Stokes polarimetric technique. Additionally, it is obtained that for electrical configurations with less than 30° amplitude for the flicker retardance, they may not influence the performance of the blazed gratings. In general, we demonstrate that the influence of flicker greatly diminishes when the number of quantization levels in the optical element increases.

Applying the simplest Kochen-Specker set for quantum information processing

Kochen-Specker (KS) sets are key tools for proving some fundamental results in quantum theory and also have potential applications in quantum information processing. However, so far, their intrinsic complexity has prevented experimentalists from using them for any application. The KS set requiring the smallest number of contexts has been recently found. Relying on this simple KS set, here we report an input state-independent experimental technique to certify whether a set of measurements is actually accessing a preestablished quantum six-dimensional space encoded in the transverse momentum of single photons.

Averaged Stokes polarimetry applied to evaluate retardance and flicker in PA-LCoS devices

Recently we proposed a novel polarimetric method, based on Stokes polarimetry, enabling the characterization of the linear retardance and its flicker amplitude in electro-optic devices behaving as variable linear retarders. In this work we apply extensively the technique to parallel-aligned liquid crystal on silicon devices (PA-LCoS) under the most typical working conditions. As a previous step we provide some experimental analysis to delimitate the robustness of the technique dealing with its repeatability and its reproducibility. Then we analyze the dependencies of retardance and flicker for different digital sequence formats and for a wide variety of working geometries.