Quantum Imaging of Nonlocal Spatial Correlations Induced by Orbital Angular Momentum

Quantum key distribution (QKD) has long been a promising area for the application of quantum effects in solving real-world problems. However, two major obstacles have stood in the way of its widespread application: low secure key generation rates and short achievable operating distances. In this paper, a new physical mechanism for dealing with the first of these problems is proposed: the interplay between different degrees of freedom in a hyperentangled system (parametric down-conversion) is used to increase the Hilbert space dimension available for key generation while maintaining security. Polarization-based Bell tests provide security checking, while orbital angular momentum (OAM) and total angular momentum (TAM) provide a higher key generation rate. Whether to measure TAM or OAM is decided randomly in each trial. The concurrent noncommutativity of TAM with OAM and polarization provides the physical basis for quantum security. TAM measurements link polarization to OAM, so that if the legitimate participants measure OAM while the eavesdropper measures TAM (or vice-versa), then polarization entanglement is lost, revealing the eavesdropper. In contrast to other OAM-based QKD methods, complex active switching between OAM bases is not required; instead, passive switching by beam splitters combined with much simpler active switching between polarization bases makes implementation at high OAM more practical.

Experimental observation of the conservation of orbital angular momentum in spontaneous parametric down-conversion has been theoretically attributed to phase-matching, transfer of plane-wave spectrum from pump beam to down-converted beams. However, according to quantum mechanics, the conservation of angular momentum arises from rotational symmetry of the Hamiltonian describing the studied physical process. Recently, experimental evidence has been found which shows that non-conservation of orbital angular momentum can occur in spontaneous parametric down-conversion due to rotational asymmetry of the Hamiltonian. In this paper, we theoretically show that all reported experimental results of conservation of orbital angular momentum in spontaneous parametric down-conversion are determined only by the Hamiltonian symmetry, and not by phase matching, transfer of plane-wave spectrum.

Relating to magnified image formation systems, we consider two processes in this work: quantum and classical incoherent imaging. There are similarities and differences between them. A similarity is that the optical transfer functions (OTFs) of both systems are obtained by calculating a correlation function. Concerning the differences, only two were found. The first difference is that, unlike classical incoherent imaging, quantum imaging with photon pairs generated by spontaneous parametric down-conversion is sensitive to the phase in the function which describes the object. The second difference is that the OTF of the quantum imaging system is a cross-correlation function of the OTFs of the signal and idler arms, while the OTF of the classical incoherent imaging system is an autocorrelation of the only pupil function existing in this case. We explore experimentally the second difference. We report the observation of a highly resolved image produced by a quantum light source in a setup where an incoherent light source is unable to spatially resolve the image of the object. The spatial resolution of the image is studied in a situation where the size of the object is magnified at the image.

Twisted light, or light with orbital angular momentum (OAM), plays an emerging role in both classical and quantum science, with important applications in areas as diverse as biophotonics, micromachines, spintronics, or quantum information. It offers fascinating opportunities for exploring new fundamental ideas in physics, as well as for being used as a tool for practical applications. One important point is to determine how to generate single photons, and two-photon states, with an appropriate OAM content. Here we describe the paraxial orbital angular momentum of entangled photon pairs generated by spontaneous parametric down-conversion (SPDC) in different non-collinear geometries. These geometries introduce a variety of new features. In particular, we find the OAM of entangled pairs generated in purely transverse-emitting configurations, where the entangled photons counter-propagate perpendicularly to the direction of propagation of the pump beam. The spatial walk-off of all interacting waves in the parametric process also determines the OAM content of the down-converted photons, and here its influence is also revealed.

The two-photon state generated by spontaneous parametric down-conversion (SPDC) exhibit spatial entanglement embedded in the corresponding mode function. The control of the spatial characteristics of the generated two-photon state is an issue of paramount importance. For example, the spatial entanglement of the two down converted photons forms the basis of quantum imaging, and entanglement in orbital angular momentum has opened a new scenario for implementing multidimensional Hilbert spaces. We put forward several techniques to engineer the spatial structure of entangled two-photon states generated in SPDC. The first strategy we consider for spatial control of the quantum state makes use of the direct manipulation of the pump beam. This technique makes feasible to prepare arbitrary engineered entangled states in any d-dimensional Hilbert space. The second strategy is based on the proper preparation of the down-converting crystal itself, namely quantum state manipulation by quasi-phase-matching (QPM) engineering. We use properly designed transversely varying QPM gratings in nonlinear crystals.

The orbital angular momentum (OAM) of photons provides a pivotal resource for carrying out high-dimensional quantum Pauli-X operations due to its unique discrete infinite orthogonality, which opens enticing perspectives for high-capacity quantum communication and multi-parallel quantum computation. However, the state-of-the-art Pauli-X gates that require cyclic transformation of OAM modes are mostly limited to four modes, face scalability challenges owing to the system redundancy and fidelity degradation induced by increased processing modes. Here, we propose a general strategy to design scalable quantum Pauli-X gates in high-dimensional OAM space by taking full advantage of the order-correlated spatial divergence property of OAM modes. Leveraging the mechanism of balance mode filtering, partitioned phase is embedded between two structurally symmetric Q-plate elements that enable bidirectional mode shifting to filter out the highest-order OAM mode for spatially selective phase modulation. Derived from radial matching between modes and partitioned phase profiles, this design of parallel mode transformation underpins the extension to higher dimensions by merely adjusting filter parameters. We demonstrate the five-mode cyclic transformation with mode purity and diffraction efficiency higher than 92% and 92.7%, respectively. By incorporating polarization-entangled photon sources, we further realize five-dimensional quantum Pauli-X gates encoded on OAM space and experimentally verify the entanglement of output mode states. Low modulation loss and efficient quantum state tomography (QST) techniques endow the reconstructed density matrices with fidelities exceeding 92.3% ± 0.1%, indicating the well-performed entanglement preservation of output states. These results confirm that our approach achieves scalable quantum Pauli-X gate operations through a simple balanced architecture with high coherence, consolidating a theoretical and experimental foundation for large-scale quantum computation encoded on high-dimensional OAM space.

This paper presents a new algorithm for the non-local restoration of single-photon 3-Dimensional Lidar images acquired in the photon starved regime or with a reduced number of scanned spatial points (pixels). The algorithm alternates between two steps: evaluation of the spatial correlations between pixels using a graph, then restore the depth and reflectivity images by their spatial correlations. To reduce the computational cost associated with the graph, we adopt a non-uniform sampling approach, where bigger patches are assigned to homogeneous regions and smaller ones to heterogeneous regions. The restoration of 3D images is achieved by minimizing a cost function accounting for the data Poisson statistics and the non-local spatial correlations between patches. This minimization problem is efficiently solved using the alternating direction method of multipliers (ADMM) that presents fast convergence properties. Results on real Lidar data show the benefits of the proposed algorithm in improving the quality of the estimated depth images, especially in photon starved cases, which can contain a reduced number of photons.

Hardy's nonlocality proof is considered as "the best version of Bell's theorem". We report an experimental implementation of this by measuring the orbital angular momentum (OAM) of entangled twisted photon pairs. Two advantages arise from using twisted photons. First, the limited OAM spectrum generated by parametric down-conversion provides a natural set of OAM non-maximally entangled states with selective degrees of entanglement. Second, the measurement of any non-trivial superposition of OAM states can be conveniently done with spatial light modulators. We measure states that are defined on asymmetric OAM Bloch spheres and show results which are incompatible with local realism.

This paper presents a new algorithm for the learning of spatial correlation and non-local restoration of single-photon 3-Dimensional Lidar images acquired in the photon starved regime (fewer or less than one photon per pixel) or with a reduced number of scanned spatial points (pixels). The algorithm alternates between three steps: (i) extract multi-scale information, (ii) build a robust graph of non-local spatial correlations between pixels, and (iii) the restoration of depth and reflectivity images. A non-uniform sampling approach, which assigns larger patches to homogeneous regions and smaller ones to heterogeneous regions, is adopted to reduce the computational cost associated with the graph. The restoration of the 3D images is achieved by minimizing a cost function accounting for the multi-scale information and the non-local spatial correlation between patches. This minimization problem is efficiently solved using the alternating direction method of multipliers (ADMM) that presents fast convergence properties. Various results based on simulated and real Lidar data show the benefits of the proposed algorithm that improves the quality of the estimated depth and reflectivity images, especially in the photon-starved regime or when containing a reduced number of spatial points.

Optical vortex beams are profiled as helical wavefronts with a phase singularity carrying an orbital angular momentum (OAM) associated with their spatial distribution. The transverse intensity distribution of a conventional optical vortex has a strong dependence on the carried topological charge. However, perfect optical vortex (POV) beams have their transverse intensity distribution independent of their charge. Such “size-invariant” POV beams have found exciting applications in optical manipulation, imaging, and communication. In this paper, we investigate the use of POV modes in the efficient generation of high-dimensional quantum states of light. We generate heralded single photons carrying OAM using spontaneous parametric downconversion (SPDC) of POV beams. We show that the heralding efficiency of the SPDC single photons generated with a POV pump is greater than that with normal optical vortex beams. The dimensionality of the two-photon OAM states is increased with POV modes in the pump and projective measurements using Bessel–Gaussian vortex modes that give POV, instead of Laguerre–Gaussian modes.

Optical vortices are a new kind of laser beam and receiving more and more attention currently.The complex amplitudes of optical vortices comprise a helical term exp (il),with l being the topological charge and the azimuthal angle.Each photon in optical vortices carries the orbital angular momentum (OAM) with a value of lħ,where ħ is the Planck's constant divided by 2.The topological charge l is the eigenvalue of optical vortices,and determines the helical wavefront distribution,thus also known as OAM state.Moreover,such an OAM state can be an infinite integer state. And vortices with various OAM states are orthogonal to each other,making it possible to be employed in high capacity data-transmission system.In addition,the above unique features contribute to their widely applications in lots of areas such as optical tweezers and spanners,rotation detection,quantum entanglement,etc.In these applications,detecting OAM states is basic,and greatly significant.Recently researchers have developed lots of approaches to detecting the OAM states,including the methods of interference,diffraction gratings,metasurface,etc.Of such approaches,the scheme of diffraction gratings is the simplest and most widely used,where one or more diffraction gratings are employed. When optical vortices propagate through such gratings,the OAM states are acquired immediately through capturing and analyzing the distinct OAM-related diffraction patterns.In this review,we focus on the techniques of detecting OAM states through diffraction gratings,which have been demonstrated by our group and other researchers.Some of the main detection gratings,including double-slit,triangle aperture and slit,angular slit,cylindrical lens,graduallychanging-period grating,annular grating,are introduced.In addition,schemes like composite fork grating,Dammann vortex grating and integrated Dammann grating,are presented to detect the OAM state for coaxial multiplexed vortices. Besides diagnosing OAM state,measuring the intensity proportion of each OAM channel,known as OAM spectrum, in multiplexed vortices is also necessary in some cases.Therefore we also introduce the ways to measure the OAM spectrum,e.g.the OAM mode sorter,the gray-scale algorithm.

We discuss how to apply many-body methods to correlated nanoscopic systems, and provide general criteria of validity for a treatment at the dynamical mean field theory (DMFT) approximation level, in which local correlations are taken into account, while non-local ones are neglected. In this respect, we consider one of the most difficult cases for DMFT, namely for a quasi-one-dimensional molecule such as a benzene ring. The comparison against a numerically exact solution shows that non-local spatial correlations are relevant only in the limit of weak coupling between the molecule and the metallic leads and of low inter-atomic connectivity, otherwise DMFT provides a quantitative description of the system. As an application we investigate the role of correlations on electronic transport in quantum junctions, and we show that a local Mott-Hubbard crossover is a robust phenomenon in sharp nanoscopic contacts.

Orbital angular momentum (OAM) entangled photon pairs with narrow bandwidths play a crucial role in the interaction of light and quantum states of matter. In this article, we demonstrate an approach for generating OAM entangled photon pairs with a narrow bandwidth by using a single driving beam in a 85Rb atomic vapor cell. This single driving beam is able to simultaneously couple two atomic transitions and directly generate OAM entangled biphotons by leveraging the OAM conservation law through the spontaneous four-wave mixing (SFWM) process. The photon pairs exhibit a maximum cross-correlation function value of 27.7 and a linewidth of 4 MHz. The OAM entanglement is confirmed through quantum state tomography, revealing a fidelity of 95.7% and a concurrence of 0.926 when compared to the maximally entangled state. Our scheme is notably simpler than previously proposed schemes and represents the first demonstration of generating subnatural-linewidth entangled photon pairs in hot atomic systems.

A single-photon state was generated by heralding cavity-enhanced spontaneous parametric downconversion in a PPKTP optical parametric oscillator. The Wigner distribution was reconstructed by quantum state tomography, using photon-number-resolving measurements with a system efficiency of 58±2%. © 2019 The Author(s)

Tidal effects have important imprints on gravitational waves (GWs) emitted during the final stage of the coalescence of binaries that involve neutron stars (NSs). Dynamical tides can be significant when NS oscillations become resonant with orbital motion; understanding this process is important for accurately modeling GW emission from these binaries and for extracting NS information from GW data. In this paper, we use semianalytic methods to carry out a systematic study on the tidal excitation of fundamental modes ($f$-modes) of spinning NSs in coalescencing binaries, focusing on the case when the NS spin is antialigned with the orbital angular momentum---where the tidal resonance is most likely to take place. We first expand NS oscillations into stellar eigenmodes, and then obtain a Hamiltonian that governs the tidally coupled orbit-mode evolution. (Our treatment is at Newtonian order, including a gravitational radiation reaction at quadrupole order.) We then find a new approximation that can lead to analytic expressions of tidal excitations to a high accuracy, and are valid in all regimes of the binary evolution: adiabatic, resonant, and postresonance. Using the method of osculating orbits, we obtain semianalytic approximations to the orbital evolution and GW emission; their agreements with numerical results give us confidence in our understanding of the system's dynamics. In particular, we recover both the averaged postresonance evolution, which differs from the preresonance point-particle orbit by shifts in orbital energy and angular momentum, as well as instantaneous perturbations driven by the tidal motion. Finally, we use the Fisher matrix technique to study the effect of dynamical tides on parameter estimation. We find that, for a system with component masses of $(1.4,1.4)\text{ }\text{ }{M}_{\ensuremath{\bigodot}}$ at 100 Mpc, the constraints on the effective Love number of the (2,2) mode at Newtonian order can be improved by a factor of $3\ensuremath{\sim}4$ if spin frequency is as high as 500 Hz. The relative errors are $0.7\ensuremath{\sim}0.8$ in the Cosmic Explorer, and they might be further improved by post-Newtonian effects. The constraints on the $f$-mode frequency and the spin frequency are improved by factors of $5\ensuremath{\sim}6$ and $19\ensuremath{\sim}27$, respectively. In the Cosmic Explorer case, the relative errors are $0.2\ensuremath{\sim}0.4$ and $0.7\ensuremath{\sim}1.0$, respectively. Hence, the dynamical tides may potentially provide an additional channel to study the physics of NSs. The method presented in this paper is generic and not restricted to $f$-mode; it can also be applied to other types of tides.