Linear Optics Research Articles

Enhancing nonclassical properties of quantum states of light using linear optics.

In this Letter, we present a simple and versatile scheme for enhancing the nonclassical properties of light states using only linear optics and photodetectors. By combining a coherent state |α〉 and an arbitrary pure state of light |ϕ〉 (excluding coherent states) at two beam splitters, we show that the amplitude α of the coherent state can be tuned to filter out specific Fock components and generate states of light with increased nonclassical features. We provide two examples of input states and demonstrate the effectiveness of our scheme in enhancing the sub-Poissonian statistics or the quadrature squeezing of the output states.

Performance analysis of photonic crystal fiber structure based on different highly nonlinear materials

Generally, fiber with a large mode area is desired for fiber laser and beam delivery applications. But the use of these fiber types is restricted to linear optical applications due to the lower value of the nonlinear coefficient. This paper investigates a single material-based photonic crystal fiber (PCF) with improved optical characteristics, applicable for linear and nonlinear optics. The light propagation in the structure is explored by applying finite element solver-based COMSOL multiphysics software. Five nonlinear optical materials are utilized as background material to get the optimized material with high performance PCF. Using this PCF, the improved optical properties of PCF such as moderate effective mode area of 115.85 [Formula: see text], chromatic dispersion, confinement loss of 10[Formula: see text] dB/m, the nonlinear coefficient of 543W[Formula: see text]Km[Formula: see text], splicing loss of 2.013 dB, and numerical aperture are numerically analyzed. This single-mode PCF also shows the low bending loss for the bending radius of 7[Formula: see text]mm. The amended PCF structure is found to be suitable for high-power fiber laser, supercontinuum generation, wavelength conversion, and slow-light generation.

The projector algorithm: A simple parallel algorithm for computing Voronoi diagrams and Delaunay graphs

The Voronoi diagram is a certain geometric data structure which has found numerous applications in various scientific and technological fields. The theory of algorithms for computing 2D Euclidean Voronoi diagrams of point sites is rich and useful, with several different and important algorithms. However, this theory has been quite steady during the last few decades in the sense that no essentially new algorithms have entered the game. In addition, most of the known algorithms are serial in nature and hence cast inherent difficulties on the possibility to compute the diagram in parallel. In this paper we present the projector algorithm: a new and simple algorithm which enables the (combinatorial) computation of 2D Voronoi diagrams. The algorithm is significantly different from previous ones and some of the involved concepts in it are in the spirit of linear programming and optics. Parallel implementation is naturally supported since each Voronoi cell (actually, even just portions of one cell) can be computed independently of the other cells. A new combinatorial structure for representing the cells (and any convex polytope) is described along the way and the computation of the induced Delaunay graph is obtained almost automatically.

Parallelizable synthesis of arbitrary single-qubit gates with linear optics and time-frequency encoding

Parallelizable synthesis of arbitrary single-qubit gates with linear optics and time-frequency encoding

Mixed Alkali Metal and Alkaline Earth Metal Scandium Borate Birefringence Material with Layered Structure and Short Ultraviolet Cutoff Edge.

Birefringent crystals are essential in the domains of linear and nonlinear optics that need light wave polarization control. Rare earth borate has become a popular study material for ultraviolet (UV) birefringence crystals due to its short cutoff edge in the UV area. RbBaScB6O12, a two-dimensional layered structure compound with the B3O6 group, was effectively synthesized through spontaneous crystallization. The UV cutoff edge of RbBaScB6O12 is shorter than 200 nm, and the experimental birefringence is 0.139 @ 550 nm. Theoretical research indicates that the large birefringence originates from the synergistic impact of the B3O6 group and the ScO6 octahedron. RbBaScB6O12 is an outstanding candidate material for birefringence crystals in the UV and even deep UV regions due to its short UV cutoff edge and significant birefringence.

Design and analysis of 1:2 line optical decoder based on linear optics

In this paper, a simple design of all-optical photonic crystal (PhC) based 1:2 line decoder has been proposed and its operating principle is based on light beam interference. The designed structure has a hexagonal arrangement of air holes in Si substrate with a finite slab height. In our proposed structure, different path lengths have been made so that the light beams should interact out of phase. Effective refractive index method has been adopted to reduce the simulation time. The Finite Difference Time Domain (FDTD) and Plane Wave Expansion (PWE) methods have been applied to evaluate the proposed structures. The required footprint area for proposed device is reported as 215 µm2. Minimum contrast ratio between the logic states of “1” and “0” is obtained as 10 dB. This device is designed based on solely linear optical phenomena in a holes-in-slab PhC structure. Therefore, mechanically stabled, ultra-compact design and simple working mechanism of the proposed optical decoder can be a potential candidate for future generation Photonic Integrated Circuits (PICs).

Overcoming Fundamental Bounds on Quantum Conference Key Agreement

Twin-Field Quantum Key Distribution (TF-QKD) enables two distant parties to establish a shared secret key, by interfering weak coherent pulses (WCPs) in an intermediate measuring station. This allows TF-QKD to reach greater distances than traditional QKD schemes and makes it the only scheme capable of beating the repeaterless bound on the bipartite private capacity. Here, we generalize TF-QKD to the multipartite scenario. Specifically, we propose a practical conference key agreement (CKA) protocol that only uses WCPs and linear optics and prove its security with a multiparty decoy-state method. Our protocol allows an arbitrary number of parties to establish a secret conference key by single-photon interference, enabling it to overcome recent bounds on the rate at which conference keys can be established in quantum networks without a repeater.

Capturing ultra-broadband complex-fields of arbitrary duration using a real-time spectrogram

One of the most intuitive representations of a waveform is achieved through time-frequency analysis, which depicts how the frequency components of a wave evolve over time. Time-frequency representations, such as the spectrogram, are well-known for allowing full-field characterization of a signal in terms of amplitude and phase. However, present methods to capture the spectrogram of a waveform are only suited for either relatively slow (<GHz bandwidth) waveforms of arbitrary duration or fast (>THz bandwidth) waveforms of short duration. It remains very challenging to capture the time-frequency representation of broadband waves extending over long durations, as required for many important fields in science and technology. Here, we introduce a linear optics temporal imaging concept based on electro-optic time-lensing and dispersive propagation to map the 2D spectrogram as a 1D waveform along the temporal domain. This technique enables ultra-broadband spectrogram analysis without any gaps in the acquisition and with no inherent limitation on maximum signal duration. The spectrogram is captured at unmatched processing rates, up to 16 × 109 Fourier transforms per second (∼60 ps per spectral frame), using a single photodetector and in a fully self-referenced manner. Under certain conditions, we show how this method enables the single-shot full-field characterization of optical waveforms spanning multiple THz. The method is further showcased through accurate amplitude and phase recovery of high-speed complex-modulated optical telecommunication signals using direct intensity detection. This concept will enable the study of physical phenomena unreachable to date and disruptive advancements in high-speed communications, sensing, and information processing.

Linear optics and photodetection achieve near-optimal unambiguous coherent state discrimination

Coherent states of the quantum electromagnetic field, the quantum description of ideal laser light, are prime candidates as information carriers for optical communications. A large body of literature exists on their quantum-limited estimation and discrimination. However, very little is known about the practical realizations of receivers for unambiguous state discrimination (USD) of coherent states. Here we fill this gap and outline a theory of USD with receivers that are allowed to employ: passive multimode linear optics, phase-space displacements, auxiliary vacuum modes, and on-off photon detection. Our results indicate that, in some regimes, these currently-available optical components are typically sufficient to achieve near-optimal unambiguous discrimination of multiple, multimode coherent states.

Correction of storage ring optics with an improved closed-orbit modulation method

We improved a previously proposed method of using closed-orbit modulation for linear optics and coupling correction. Instead of fitting individual closed orbits, the improved method decomposes the orbit oscillation data into two orthogonal modes and fits the amplitudes of the modes at all beam position monitors. While the original method is limited to process around tens to a hundred orbits, the improved method can process thousands of orbits, which are easily available when alternating-current waveforms are applied to the two modulating correctors. The method has been experimentally demonstrated on the National Synchrotron Light Source (NSLS)-II storage ring.

Efficient high harmonic generation in nonlinear photonic moiré superlattice

Photonic moir\'e superlattice as an emerging platform of flatbands can tightly confine the light inside the cavity and has important applications not only in linear optics but also in nonlinear optics. In this paper, we numerically investigate the third- and fifth-order harmonic generation (THG and FHG) in photonic moir\'e superlattices fabricated by the nonlinear material silicon. The high conversion efficiency of THG and FHG is obtained at a relatively low intensity of fundamental light, e.g., the maximum conversion efficiency of THG and FHG arrives even up to be $10^{-2}$ and $10^{-9}$ at the fundamental intensity of 30 kW/m2, respectively, in the moir\'e superlattice of near flat band formed by the twist angle 6.01o. The results indicate the photonic moir\'e superlattice of a high-quality factor and flatbands is a promising platform for efficient nonlinear processes and advanced photonic devices.

Page curves and typical entanglement in linear optics

Bosonic Gaussian states are a special class of quantum states in an infinite dimensional Hilbert space that are relevant to universal continuous-variable quantum computation as well as to near-term quantum sampling tasks such as Gaussian Boson Sampling. In this work, we study entanglement within a set of squeezed modes that have been evolved by a random linear optical unitary. We first derive formulas that are asymptotically exact in the number of modes for the Rényi-2 Page curve (the average Rényi-2 entropy of a subsystem of a pure bosonic Gaussian state) and the corresponding Page correction (the average information of the subsystem) in certain squeezing regimes. We then prove various results on the typicality of entanglement as measured by the Rényi-2 entropy by studying its variance. Using the aforementioned results for the Rényi-2 entropy, we upper and lower bound the von Neumann entropy Page curve and prove certain regimes of entanglement typicality as measured by the von Neumann entropy. Our main proofs make use of a symmetry property obeyed by the average and the variance of the entropy that dramatically simplifies the averaging over unitaries. In this light, we propose future research directions where this symmetry might also be exploited. We conclude by discussing potential applications of our results and their generalizations to Gaussian Boson Sampling and to illuminating the relationship between entanglement and computational complexity.

Quantum Bit Commitment Without Quantum Memory

Abstract Commitment scheme is a fundamental cryptographic primitive that serve as building blocks for many other two-party protocols. In this paper, we propose a novel quantum bit commitment scheme, which is secure and does not require quantum memory. Our scheme processes the quantum information using coherent states and unambiguous state discrimination (USD) measurements, which can be experimentally realized by linear optics and photon detectors. We ensure the unconditionally hiding and binding property by preventing both Alice and Bob from obtaining complete information about the commitment in committing stage, and eliminate the requirement for quantum memory by performing USD measurements and phase shifts immediately after receiving the coherent states.

Photonic Floquet Landau-Zener tunneling and temporal beam splitters.

Landau-Zener tunneling (LZT), i.e., the nonadiabatic transition under strong parameter driving in multilevel systems, is ubiquitous in physics, providing a powerful tool for coherent wave control both in quantum and classical systems. While previous works mainly focus on LZT between two energy bands in time-invariant crystals, here, we construct synthetic time-periodic temporal lattices from two coupled fiber loops and demonstrate dc- and ac-driven LZTs between periodic Floquet bands. We show that dc- and ac-driven LZTs display distinctive tunneling and interference characteristics, which can be harnessed to realize fully reconfigurable LZT beam splitter arrangements. As a potential application to signal processing, we realize a 4-bit temporal beam encoder for classical light pulses using a reconfigurable LZT beam splitter network. Our work introduces and experimentally demonstrates a new class of reconfigurable linear optics circuits harnessing Floquet LZT, which may find versatile applications in temporal beam control, signal processing, quantum simulations, and information processing.

Near-deterministic hybrid generation of arbitrary photonic graph states using a single quantum emitter and linear optics

Since linear-optical two-photon gates are inherently probabilistic, measurement-based implementations are particularly well suited for photonic platforms: a large highly-entangled photonic resource state, called a graph state, is consumed through measurements to perform a computation. The challenge is thus to produce these graph states. Several generation procedures, which use either interacting quantum emitters or efficient spin-photon interface, have been proposed to create these photonic graph states deterministically. Yet, these solutions are still out of reach experimentally since the state-of-the-art is the generation of a linear graph state. Here, we introduce near-deterministic solutions for the generation of graph states using the current quantum emitter capabilities. We propose hybridizing quantum-emitter-based graph state generation with all-photonic fusion gates to produce graph states of complex topology near-deterministically. Our results should pave the way towards the practical implementation of resource-efficient quantum information processing, including measurement-based quantum communication and quantum computing.

Optical spin–orbit interaction in spontaneous parametric downconversion

Optical spin–orbit interaction (SOI), which can be used to simultaneously control the spin and orbital angular momentum of light, is important for both classical and quantum information applications. In linear and nonlinear optics, the SOI of light has been extensively explored in both artificial structures and conventional optical crystals. However, optical SOI in quantum nonlinear optical processes, such as spontaneous parametric downconversion (SPDC), has not been studied before. Here, we experimentally demonstrate that optical SOI in the SPDC process can be realized through a nonlinear crystal with threefold rotational symmetry. Two-photon quantum states with controlled angular momentum can be generated through the symmetry selection rules in nonlinear optics and the SOI of the pump wave. The proposed methodology may facilitate the generation and control of spin and orbital angular momentum of entangled photons.

Large Baseline Optical Imaging Assisted by Single Photons and Linear Quantum Optics.

In this Letter, we show that by combining quantum metrology and networking tools, it is possible to extend the baseline of an interferometric optical telescope and thus improve diffraction-limited imaging of point source positions. The quantum interferometer is based on single-photon sources, linear optical circuits, and efficient photon number counters. Surprisingly, with thermal (stellar) sources of low photon number per mode and high transmission losses across the baseline, the detected photon probability distribution still retains a large amount of Fisher information about the source position, allowing for a significant improvement in the resolution of positioning point sources, on the order of 10 μas. Our proposal can be implemented with current technology. In particular, our proposal does not require experimental optical quantum memories.

Near-field terahertz nonlinear optics with blue light

The coupling of terahertz optical techniques to scattering-type scanning near-field microscopy (s-SNOM) has recently emerged as a valuable new paradigm for probing the properties of semiconductors and other materials on the nanoscale. Researchers have demonstrated a family of related techniques, including terahertz nanoscopy (elastic scattering, based on linear optics), time-resolved methods, and nanoscale terahertz emission spectroscopy. However, as with nearly all examples of s-SNOM since the technique’s inception in the mid-1990s, the wavelength of the optical source coupled to the near-field tip is long, usually at energies of 2.5 eV or less. Challenges in coupling of shorter wavelengths (i.e., blue light) to the nanotip has greatly inhibited the study of nanoscale phenomena in wide bandgap materials such as Si and GaN. Here, we describe the first experimental demonstration of s-SNOM using blue light. With femtosecond pulses at 410 nm, we generate terahertz pulses directly from bulk silicon, spatially resolved with nanoscale resolution, and show that these signals provide spectroscopic information that cannot be obtained using near-infrared excitation. We develop a new theoretical framework to account for this nonlinear interaction, which enables accurate extraction of material parameters. This work establishes a new realm of possibilities for the study of technologically relevant wide-bandgap materials using s-SNOM methods.

Determination of Linear, Nonlinear, and the Optical Limiting Properties of Sudan Brown RR in a Solid Film and Solution.

The casting technique is employed to prepare the film from a mixture of sudan brown RR (SBRR) dye and poly methyl methacrylate (PMMA). The surface profile of this film is identified using a scanning probe microscope and image J software. The linear optical (LO) properties of the solid film were studied. The nonlinear optical (NLO) properties of SBRR/PMMA film and sudan brown (RR) solution in dimethylformamide (DMF) as a solvent are evaluated using two methods including diffraction ring patterns and Z-scan. The optical limiting (OLg) property for the SBRR/PMMA film and SBRR solution was extensively investigated. The values of nonlinear refractive index (NRI) and threshold limiting (TH) of the solid film and dye solution were compared.

Monte-Carlo simulation of a thick lens IOL power calculation.

The purpose of this Monte-Carlo study is to investigate the effect of using a thick lens model instead of a thin lens model for the intraocular lens (IOL) on the resulting refraction at the spectacle plane and on the ocular magnification based on a large clinical data set. A pseudophakic model eye with a thin spectacle correction, a thick cornea (curvatures for both surfaces and central thickness) and a thick IOL (equivalent power PL derived from a thin lens IOL, Coddington factor CL (uniformly distributed from -1.0 to 1.0), either preset central thickness LT = 0.9 mm (A) or optic edge thickness ET = 0.2 mm, (B)) was set up. Calculations were performed on a clinical data set containing 21 108 biometric measurements of a cataractous population based on linear Gaussian optics to derive spectacle refraction and ocular magnification using the thin and thick lens IOL models. A prediction model (restricted to linear terms without interactions) was derived based on the relevant parameters identified with a stepwise linear regression approach to provide a simple method for estimating the change in spectacle refraction and ocular magnification where a thick lens IOL is used instead of a thin lens IOL. The change in spectacle refraction using a thick lens IOL with (A) or (B) instead of a thin lens IOL with identical power was within limits of around ±1.5 dpt when the thick lens IOL was placed with its haptic plane at the plane of the thin lens IOL. In contrast, the change in ocular magnification from considering the IOL as a thick lens instead of a thin lens was small and not clinically significant. This Monte-Carlo simulation shows the impact of using a thick lens model IOL with preset LT or ET on the resulting spherical equivalent refraction and ocular magnification. If IOL manufacturers would provide all relevant data on IOL design data and refractive index for all power steps, this would make it possible to perform direct calculations of refraction and ocular magnification.