Search

FFLUX is a biomolecular force field under construction, based on Quantum Chemical Topology (QCT) and machine learning (kriging), with a minimalistic and physically motivated design. A detailed analysis of the forces within the kriging models as treated in FFLUX is presented, taking as a test example a liquid water model. The energies of topological atoms are modelled as 3Natoms-6 dimensional potential energy surfaces, using atomic local frames to represent the internal degrees of freedom. As a result, the forces within the kriging models in FFLUX are inherently N-body in nature where N refers to Natoms. This provides a fuller picture that is closer to a true quantum mechanical representation of interactions between atoms. The presented computational example quantitatively showcases the non-negligible (as much as 9 %) three-body nature of bonded forces and angular forces in a water molecule. We discuss the practical impact on the pressure calculation with N-body forces and periodic boundary conditions (PBC) in molecular dynamics, as opposed to classical force fields with two-body forces. The equivalence between the PBC-related correction terms in the general virial equation is shown mathematically.

Determining the fate of nitroaromatic compounds (NACs) in the environment requires the use of predictive models for compounds and conditions for which experimental data are insufficient. Previous studies have developed linear free energy relationships (LFERs) that relate the thermodynamic energy of NAC reduction to its corresponding rate constant. Here we present a comprehensive LFER that incorporates both the reduction and oxidation half reactions through Quantum Chemically (QC) calculated energies. This article is protected by copyright. All rights reserved.

Named after the two-faced Roman god of transitions, transition metal dichalcogenide (TMDs) Janus monolayers have two different chalcogen surfaces, inherently breaking the out of plane mirror symmetry.[ 4] The broken mirror symmetry and the resulting potential gradient lead to the emergence of quantum properties[ 7] such as the Rashba effect[ 8] and the formation of dipolar excitons.[ 11] Experimental access to these quantum properties, however, hinges on the ability to produce high-quality 2D Janus monolayers. Here, our results introduce a holistic 2D Janus synthesis technique that allows real-time monitoring of the growth process. Our prototype chamber integrates in-situ spectroscopy, offering fundamental insights into the structural evolution and growth kinetics, that allow us to evaluate and optimize the quality of Janus monolayers. We demonstrate the versatility of this method by synthesizing and monitoring the conversion of SWSe, SNbSe, and SMoSe Janus monolayers. Deterministic conversion and real-time data collection further aid us to convert exfoliated TMDs to Janus monolayers for the first time and reach unparalleled exciton linewidth values compared to the current best standard. The results offer an insight into the process kinetics and aid in the development of new Janus monolayers with high optical quality, which is much needed to access their exotic properties. This article is protected by copyright. All rights reserved.

Efficiency and performance of light triggered molecular motors are crucial features that need to be mechanistically understood to improve the performance and enable conscious property tailoring for specific applications. In this work, three different hemithioindigo‐based molecular motors are investigated and all four steps in their complete unidirectional rotation are unraveled fully quantitatively. Transient absorption spectroscopy across twelve orders of magnitude in time is used to probe the fs nuclear motions up to the ms thermal kinetics, covering the timeframe of the whole motor rotation. The newly known full mechanisms allow simulation of the motor systems to scrutinize their performance at realistic illumination conditions. This highlights the importance of photoisomerization quantum yields for the rotation speed. The substitution pattern in close proximity to the rotation axle influences the excited and ground state properties. Reduction of electron donation and concomitant increase of steric hindrance leads to faster photoisomerization reactions with quasi‐ballistic behavior, but also to a slight decrease in the quantum efficiency. The expected decelerating effects of increased sterics are primarily manifested in the ground state. A promising approach for next‐generation hemithioindigo motors is to elevate electron donation at the rotor fragment followed by an increase of steric hindrance., In a spin: The unidirectional rotation mechanisms of three hemithioindigo based molecular motors are compared fully quantitatively over a dynamic range of twelve orders of magnitude in time.

The structure and properties of ZnO quantum dots is a very popular and rapidly growing field of research for which accurate quantum calculations are challenging to perform. Since the dependence between system size and wall time scales nonlinearly, certain compromises have to be made. A particularly important limiting factor is the size of the basis used, this is especially the case if accurate large calculations are to be carried out. In our work, we discovered that an important O(2p)->Zn(4p) back donation, which greatly influences the strength of the ZnO bond, can be reproduced only if diffuse functions are added to the basis set. We further tested the basis dependence for the magic-sized wurtzite nanophase ZnO clusters which were previously shown to be able to accurately reproduce the magnetically doped II-IV Q-dots. In this work, we outline the minimal basis sets required to properly describe ZnO bonds in a nanocluster. It was demonstrated that the rock salt nanophase is incorrectly stabilized if a basis set does not contain sufficiently diffuse functions while the correct wurtzite phase is stabilized when diffuse functions are added. This tendency, similar to that in the ZnO dimer case, was shown to stem from the incorrect lack of Zn(4p) electron density in calculations when using the diffuse-free basis set.

Crystal structures and fluorescence spectroscopic properties were investigated for a series of all-(E) α,ω-di(4-pyridyl)polyenes (1-5) with different number of double bonds (n). Molecules 1 and 2 (n=1, 2) in crystals are arranged to form partially π-overlapped structures, whereas those of 3-5 (n=3-5) are stacked in a herringbone fashion. All these molecules, the shorter polyenes in particular, are almost nonfluorescent in solution. In the solid state, 1 and 2 are highly emissive as pure organic solids [fluorescence quantum yields (φf )=0.3-0.5], while 3 and 4 are only weakly fluorescent (φf

The impact of solvent flexibility and electron correlation on the simulation results of Cu2+ in liquid ammonia has been investigated via an ab initio quantum mechanical charge field molecular dynamics (QMCF MD) simulation approach. To achieve this, three different simulation systems were considered in this study, namely Cu2+ in rigid and flexible ammonia at Hartree-Fock (HF) level of theory, as well as resolution of identity second order Moller-Plesset (MP2) perturbation theory in the rigid body case. In all cases, a stable octahedral [Cu(NH3 )6 ]2+ complex subject to dynamic Jahn-Teller distortions without the occurrence of ligand exchange was observed. The Cu2+ - NH3 distance in the first shell agrees well with the experimental and other theoretical data. In all three cases, the structural data shows that the rigid-body ammonia model in conjunction with the HF level of theory provides accurate data for the first solvation shell, while at the same time, the computational demand and thus the achievable simulation time are much more beneficial. The vibrational analysis of the Cu2+ - NH3 interaction yields similar force constants in the three investigated systems indicating that there is no distinct difference on the dynamical properties of the first solvation shell. In addition to the QMCF MD simulations, a number of natural bond orbital (NBO) analyses were carried out, confirming the strong electrostatic character of the Cu2+ - NH3 interaction.

We define and construct a quantum Grothendieck ring for a certain monoidal subcategory of the category $\mathcal{O}$ of representations of the quantum loop algebra introduced by Hernandez-Jimbo. We use the cluster algebra structure of the Grothendieck ring of this category to define the quantum Grothendieck ring as a quantum cluster algebra. When the underlying simple Lie algebra is of type $A$, we prove that this quantum Grothendieck ring contains the quantum Grothendieck ring of the category of finite-dimensional representations of the associated quantum affine algebra. In type $A_1$, we identify remarkable relations in this quantum Grothendieck ring., Comment: 43 pages

Conjugated aromatic macrocycles are attractive due to their unique photophysical and optoelectronic properties. In particular, the cyclic radially oriented π-system of cycloparaphenylenes (CPPs) gives rise to photophysical properties unlike any other small molecule or carbon nanomaterial. CPPs have tunable emission, possess large extinction coefficients, wide effective Stokes shifts, and high quantum yields. However, accessing bright CPPs with emissions beyond 500 nm remains difficult. Herein, we present a novel and bright orange-emitting CPP-based fluorophore showing a dramatic 105 nm red-shift in emission and striking 237 nm effective Stokes shift while retaining a large quantum yield of 0.59. We postulate, and experimentally and theoretically support, that the quantum yield remains large due to the lack of intramolecular charge transfer.

Within the quantum topological energy partitioning method called Interacting Quantum Atoms (IQA) we transition from Møller-Plesset (MP4SDQ) to CCSD in calculating intra- and interatomic electron correlation energies for a set of hydrides, diatomics, a few simple molecules and non-covalently bonded complexes, using the uncontracted basis set 6-31++G(2d,2p). CCSD-IQA allows a more rigorous analysis of atomic electron correlation than that offered by Møller-Plesset, which returns IQA contributions that are identical to Hartree-Fock counterparts except for two-electron terms. The CCSD-IQA analysis returns bond and other interatomic correlation energies that are typically much larger in magnitude than the MP4SDQ values. Crisp patterns of energy transferability are detected in water clusters, both for intra-atomic and interatomic correlation energies. CCSD determines that the intra-atomic correlation energy of an oxygen drops by ~15 kJ mol-1 for donating a hydrogen and by ~25 kJ mol-1 for accepting a hydrogen.

Purpose To capture the multiquantum coherence (MQC) 23 Na signal. Different phase-cycling options and sequences are compared in a unified theoretical layout, and a novel sequence is developed. Methods An open source simulation overview is provided with graphical explanations to facilitate MQC understanding and access to techniques. Biases such as B0 inhomogeneity and stimulated echo signal were simulated for 4 different phase-cycling options previously described. Considerations for efficiency and accuracy lead to the implementation of a 2D Cartesian single and triple quantum imaging of sodium (CRISTINA) sequence employing two 6-step cycles in combination with a multi-echo readout. CRISTINA was compared to simultaneous single-quantum and triple-quantum-filtered MRI of sodium (SISTINA) under strong static magnetic gradient. CRISTINA capabilities were assessed on 8 × 60 mL, 0% to 5% agarose phantom with 50 to 154 mM 23 Na concentration at 7 T. CRISTINA was demonstrated subsequently in vivo in the brain. Results Simulation of B0 inhomogeneity showed severe signal dropout, which can lead to erroneous MQC measurement. Stimulated echo signal was highest at the time of triple-quantum coherences signal maximum. However, stimulated echo signal is separated by Fourier Transform as an offset and did not interfere with MQC signals. The multi-echo readout enabled capturing both single-quantum coherences and triple-quantum coherences signal evolution at once. Signal combination of 2 phase-cycles with a corresponding B0 map was found to recover the signal optimally. Experimental results confirm and complement the simulations. Conclusion Considerations for efficient MQC measurements, most importantly avoiding B0 signal loss, led to the design of CRISTINA. CRISTINA captures triple-quantum coherences and single-quantum coherences signal evolution to provide complete sodium signal characterization including T 2 ∗ fast, T 2 ∗ slow, MQC amplitudes, and sodium concentration.

Monte Carlo integration approximates an integral of a black-box function by taking the average of many evaluations (i.e., samples) of the function (integrand). For $N$ queries of the integrand, Monte Carlo integration achieves the estimation error of $O(1/ \sqrt{N})$. Recently, Johnston introduced quantum supersampling (QSS) into rendering as a numerical integration method that can run on quantum computers. QSS breaks the fundamental limitation of the $O(1/ \sqrt{N})$ convergence rate of Monte Carlo integration and achieves the faster convergence rate. We introduce yet another quantum numerical integration algorithm, quantum coin (QCoin), and provide numerical experiments that are unprecedented in the fields of both quantum computing and rendering. We show that QCoin's convergence rate is equivalent to QSS's. We additionally show that QCoin is fundamentally more robust under the presence of noise in actual quantum computers due to its simpler quantum circuit and the use of fewer qubits. Considering various aspects of quantum computers, we discuss how QCoin can be a more practical alternative to QSS in quantum computers in the future., Comment: 14 pages, 13 figures

We describe an efficient implementation of the partition of the second-order Møller-Plesset (MP2) correlation energy within the interacting quantum atoms (IQA) energy decomposition. We simplify the IQA integration bottleneck by considering only the occupied to virtual elements of the second order reduced density matrix, a procedure that reduces substantially the size of the two-electron matrix, which has to be addressed. The algorithmic improvements described herein allow to perform the decomposition of the MP2 correlation energy for medium size molecular systems using moderate computational resources. We expect that the methods developed in this investigation will prove useful to understand electron correlation effects through a real space perspective.

Made available in DSpace on 2020-12-10T20:13:54Z (GMT). No. of bitstreams: 0 Previous issue date: 2020-05-06 Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq) Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) Ba3MgNb2O9 is a double perovskite niobate with a trigonal structure with space group D-3d(3). Such a niobium-based compound has a great potential for applications as microwave dielectrics in the telecommunication industry. In this work, we report the lattice dynamics calculation results using a Short-Range Force Field Model and Density Functional Theory to represent the optical phonon modes at Gamma-point of the Brillouin zone. The classical method uses the nearest neighbor interactions through the interatomic force constants to describe the local order for Raman and infrared spectra. At the same time, density functional theory methods took into account two functionals (PBE and B3LYP) in order to provide the optical modes through second derivatives of the total energy. In both methods, theoretical optical modes are in good agreement with reported experimental data. The combination of both classical and quantum theoretical methods provided basis for a systematic discussion on the origin of the optical modes including the prediction of the dielectric tensor. We believe that this work presents useful information about the structural and vibrational characterization of Ba3MgNb2O9 perovskite and possible targeting for its application as microwave dielectrics for the communication technology. Univ Fed Amazonas, Inst Ciencias Exatas, Programa Posgrad Quim, Manaus, Amazonas, Brazil Sao Paulo State Univ, Modeling & Mol Simulat, Bauru, SP, Brazil Univ Sao Paulo, Inst Fis Sao Carlos, Sao Carlos, Brazil CSIC, Inst Ciencia Mat Madrid, Madrid, Spain Sao Paulo State Univ, Modeling & Mol Simulat, Bauru, SP, Brazil CNPq: 432242/2018-0 CAPES: 88881.171031/2018-01 FAPESP: 2013/07296-2 FAPESP: 2019/08928-9

Results of approbation of a new quantum mechanical approach of lone pairs (LPs) visualization, its optimization and testing on a range of model molecules are presented. The main idea of proposed methodology is using 3 He atom as a probe for investigating electronic shells of species with LPs. As model objects, we consider "classical" examples of hydrogen cyanide, methanimine, ammonia, phosphine, formaldehyde, water, and hydrogen sulfide. It is shown that LPs can be visualized by means of 3D maps of Laplacian of 3 He chemical shift ∇2 δHe . NMR calculations could be performed using level of theory as low as B3LYP/6-31G, allowing for the reduction of computational time without significant loss of quality. Advantages of our approach are discussed in comparison with usual methods of lone pairs visualization (electron localization function, molecular electrostatic potential).

The [4+4] photocycloaddition of anthracene is one of most relevant photoreactions and is widely applied in materials science, as it allows to remote-control soft matter material properties by irradiation. However, highly energetic UV irradiation is commonly applied, which limits its application. Herein, the wavelength dependence of the photodimerization of anthracene is assessed for the first time, revealing that the reaction is induced just as effectively with mild visible light (410 nm). To fully establish [4+4] cycloadditions within defined chemical environments, a conceptual framework for the solution kinetics of the photo-dimerization up to long reaction times is established by developing a novel photoreaction rate law that is dependent on individual rate coefficients of the key reaction steps. These coefficients can be determined based on low conversion photochemical experiments. Both differential and integral quantum yields can subsequently be predicted that are strongly time-dependent, highlighting the need for a detailed reaction pathway analysis. The presented approach simplifies a complex photochemical scenario, making the photochemical anthracene dimerization, or potentially any other photochemical dimerization, amenable to a time-dependent understanding at the elementary reaction level.

This work presents a general approach for synthesis of substituted [5]-helical dispiroindeno[2,1-c]fluorenes based on Rh-catalyzed intramolecular cyclotrimerization of triynes. This approach was further extended for the first synthesis of configurationally stable [7]-helical dispiroindeno[2,1-c]fluorenes. A series of variously substituted derivatives was prepared and their photophysical and electrochemical properties were evaluated. Their fluorescence emission maxima were in the region of 351-428 nm and quantum yields up to 88 % are the highest measured among the full-carbon helical compounds.

We prove duality isomorphisms of certain representations of W-algebras which play an essential role in the quantum geometric Langlands Program and some related results., Comment: 30 pages, to appear in Compositio Mathematica

Charge-transfer emitters are attractive due to their color tunability and potentially high photoluminescence quantum yields (PLQYs). We herein present tetraaminospirenes as donor moieties, which, in combination with a variety of acceptors, furnished 12 charge-transfer emitters with a range of emission colors and PLQYs of up to 99 %. The spatial separation of their frontier molecular orbitals was obtained through careful structural design, and two DA structures were confirmed by X-ray crystallography. A range of photophysical measurements supported by DFT calculations shed light on the optoelectronic properties of this new family of spiro-NN-donor-acceptor dyes.

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link. Calculation of solution-state NMR parameters, including chemical shift values and scalar coupling constants, is often a crucial step for unambiguous structure assignment. Data-driven (sometimes called \textit{empirical}) methods leverage databases of known parameter values to estimate parameters for unknown or novel molecules. This is in contrast to popular \textit{ab initio} techniques which use detailed quantum computational chemistry calculations to arrive at parameter estimates. Data-driven methods have the potential to be considerably faster than ab inito techniques and have been the subject of renewed interest over the past decade with the rise of high-quality databases of NMR parameters and novel machine learning methods. Here we review these methods, their strengths and pitfalls, and the databases they are built on.

Quantum anomalous Hall (QAH) effect generates quantized electric charge Hall conductance without external magnetic field. It requires both nontrivial band topology and time-reversal symmetry (TRS) breaking. In most cases, one could break the TRS of time-reversal invariant topological materials to yield QAH effect, which is essentially a topological phase transition. Conventional topological phase transition induced by external field/stimulus needs a route along which the bandgap closes and re-opens. Hence, the phase transition occurs only when the magnitude of field/stimulus is larger than a critical value. In this work we propose that using gapless surface states, the transition can happen at arbitrarily weak (but finite) external field strength. This can be regarded as an unconventional topological phase transition, where the bandgap closing is guaranteed by bulk-edge correspondence and symmetries, while the bandgap reopening is induced by external fields. We demonstrate this concept on the 2D surface states of 3D topological insulators like $\rm Bi_2Se_3$, which become 2D QAH insulators once a circularly polarized light is turned on, according to van Vleck's effective Hamiltonian in Floquet time crystal theory. The sign of quantized Chern number can be controlled via the chirality of the light. This provides a convenient and dynamical approach to trigger topological phase transitions and create QAH insulators., Comment: 13 pages, 4 figures

A vehicular ad hoc network possesses highly advanced functioning in the intelligent transportation system. This system helps moving nodes equipped with advanced smart devices, to establish...

We report extremely strong chirality transfer from a chiral nickel complex to solvent molecules detected as Raman optical activity (ROA). Electronic energies of the complex were in resonance with the excitation-laser light. The phenomenon was observed for a wide range of achiral and chiral solvents. For chiral 2-butanol, the induced ROA was even stronger than the natural one. The observations were related to so-called quantum (molecular) plasmons that enable a strong chiral Rayleigh scattering of the resonating complex. According to a model presented here, the maximal induced ROA intensity occurs at a certain distance from the solute, in a three-dimensional "ring of fire", even after rotational averaging. Most experimental ROA signs and relative intensities could be reproduced. The effect might significantly increase the potential of ROA spectroscopy in bioimaging and sensitive detection of chiral molecules.

As a new class of sustainable carbon material, "carbon dots" is an umbrella term covering many types of materials. Herein, a broad range of techniques was used to develop the understanding of hydrothermally synthesized carbon dots, and it is shown how fine-tuning the structural features by simple reduction/oxidation reactions can drastically affect their excited-state properties. Structural and spectroscopic studies found that photoluminescence originates from direct excitation of localized fluorophores involving oxygen functional groups, whereas excitation at graphene-like features leads to ultrafast phonon-assisted relaxation and largely quenches the fluorescent quantum yields. This is arguably the first study to identify the dynamics of photoluminescence including Stokes shift and allow the relaxation pathways in these carbon dots to be fully resolved. This comprehensive investigation sheds light on how understanding the excited-state relaxation processes in different carbon structures is crucial for tuning the optical properties for any potential commercial applications.

Three implicit solvation models, the conductor-like polarizable continuum model (C-PCM), the conductor-like screening model (COSMO), and universal implicit solvent model (SMD), combined with a hybrid two layer QM/QM approach (ONIOM), were utilized to calculate the pKa values, using a direct thermodynamic scheme, of a set of Group 10 transition metal (TM) hydrides in acetonitrile. To obtain the optimal combination of quantum methods for ONIOM calculations with implicit solvation models, the influence of factors, such as the choice of density functional and basis set, the atomic radii used to build a cavity in the solvent, and the size of the model system in an ONIOM scheme, was examined. Additionally, the impact of Grimme's empirical dispersion correction and exact exchange was also investigated. The results were calibrated by experimental data. This investigation provides insight about effective models for the prediction of thermodynamic properties of TM-containing complexes with bulky ligands. © 2019 Wiley Periodicals, Inc.

International audience; The single-molecule magnet (SMM) properties of a series of ferrocenium complexes, [Fe(h5-C5R5)2]+ (R=Me, Bn), are reported. In the presence of an applied dc field, the slow dynamics of the magnetization in [Fe(h5-C5Me5)2]BArF are revealed. Multireference quantum mechanical calculationsshow a large energy difference between the ground and first excited states, excluding the commonly invoked, thermally activated (Orbach-like) mechanism of relaxation. In contrast, a detailed analysis of the relaxation time highlights that both direct and Raman processes are responsible forthe SMM properties. Similarly, the bulky ferrocenium complexes, [Fe(h5-C5Bn5)2]BF4 and [Fe(h5-C5Bn5)2]PF6, also exhibit magnetization slow dynamics, however an additional relaxation process is clearly detected for these analogous systems.

A significant consequence of the quantum nature of light in optical instruments is the presence of quantum noise in optical measurements. This noise limits the range of signals that can be used and signal‐to‐noise ratios that can be achieved. In addition, the performance of the system is different for very large signals, or modulations, and for small signals close to the quantum noise level. Some of the limitations introduced by quantum noise can be avoided by using non‐classical, or squeezed, states of light. Technology has now advanced to the point where fundamental quantum effects such as the fluctuations of the vacuum field and the discreteness of light can be demonstrated in undergraduate teaching laboratories, and there are a growing number of applications for quantum light, in particular in precision metrology and applications ranging from large‐scale gravitational‐wave detectors to imaging and precision clocks.

Quantum measurements has practical applications and four areas that stand out as the most likely applications: optical sensors, optical communication, spatial effects and imaging, and interferometric detectors for gravitational waves. This chapter discusses the standard quantum limits that apply to coherent states and ways to overcome them. It also discusses a different class of applications based on quantum information concepts. An optical sensor is a device that monitors a property and translates a change of this property into an optical signal. The chapter then discusses a more general approach that finds the ultimate precision limit for any detection strategy. Optical communication has been one of the motivations for the development of quantum optics technology. More applications will emerge from multiple squeezed modes and the generation of beams of entangled light. The simplest case is a pair of entangled beams from two squeezed beams, followed by beams with high‐dimensional quantum correlations and generalized version of entanglement.

This chapter discusses experiments aimed at testing three of these concepts: complementarity, or more particularly wave‐particle duality; indistinguishability; and non‐locality. Quantum systems can display both particle‐like and wave‐like properties. A few experiments have been carried out to probe wave‐particle duality in this intermediate domain, both with massive particles and in optics. The chapter expresses that the trajectories evolve from a particle‐like situation as they emerge from the fibres to a wave‐like interference pattern. Another fundamental difference between classical and quantum physics is the indistinguishability of quantum particles. In classical mechanics one can always label different particles in an ensemble by their position and momentum. A unique feature of quantum mechanics is its non‐local character. The effect of entanglement can be observed by measuring continuous quadrature variables of the entangled beams with homodyne detection. The detection of quantum correlation is carried out via the suitable combination of the photocurrents from both beams.

The laser is the key component in any quantum optics experiment. The performance of a laser can be described by the following parameters: optical power, spatial mode structure, output wavelength, frequency spectrum, and noise spectrum. The spatial properties of the laser beams are determined by the properties of the optical resonator. Lasers are available that produce output beams, which are very close to the theoretical limit. In order to determine the dynamics of the fluctuations of the laser system, a quantum model is required. Diode lasers use the band gap in doped semiconductor materials to produce optical gain directly from an electrical current. The chapter focuses on continuous‐wave lasers since they are very common in quantum optics experiments, in precision metrology. It considers the theoretical limits to amplification of quantum limited light and discusses the theory of the non‐linear interaction. The chapter discusses the measurement‐based quantum amplifiers based on electro‐optic feed forward and heralded devices based on photon counting.

In quantum optics experiments light is considered as laser beams or modes of radiation. This chapter describes the effect of the various components on a single spatial and temporal mode. It explains the concept of linear systems, beamsplitters, interferometers, and resonators that can be used to describe many devices. The chapter summarizes the many practical ways of building beamsplitters, interferometers, and resonators that have been developed to create devices that use the principles of quantum physics. One of the most common and simplest optical components is a mirror. A mirror has two output beams for every input beam, one transmitted and the other reflected. The chapter analyses the properties of a beamsplitter. The beamsplitter acts like a random selector for the photons. The chapter considers a quantum model of the interferometer. It also considers the intensity noise observed at the interferometer output when a bright beam is incident.

Many fascinating effects are due to the quantum nature of light; they are the foundation of quantum optics . This chapter introduces the concept of the photon as the smallest detectable quantity of light and develops some of the basics required for modelling quantum optics experiments. It shows two examples of images that are typical for the detection of individual photons in one laser beam at very low light intensity. The chapter focuses on the example of light emitted by a broadband thermal source. The classical description provides the tools for describing the statistical properties of light. The measurement of interference, made accessible through the use of instruments such as a Michelson interferometer, clearly demonstrates the wave nature and the coherence properties of light. The nature of the light depends on the type of experiment: a single beamsplitter can often be well described by the photon picture, and a complete interferometer requires the wave picture.