Methods Of Quantum Electrodynamics Research Articles

Understanding Polaritonic Chemistry from Ab Initio Quantum Electrodynamics.

In this review, we present the theoretical foundations and first-principles frameworks to describe quantum matter within quantum electrodynamics (QED) in the low-energy regime, with a focus on polaritonic chemistry. By starting from fundamental physical and mathematical principles, we first review in great detail ab initio nonrelativistic QED. The resulting Pauli-Fierz quantum field theory serves as a cornerstone for the development of (in principle exact but in practice) approximate computational methods such as quantum-electrodynamical density functional theory, QED coupled cluster, or cavity Born-Oppenheimer molecular dynamics. These methods treat light and matter on equal footing and, at the same time, have the same level of accuracy and reliability as established methods of computational chemistry and electronic structure theory. After an overview of the key ideas behind those ab initio QED methods, we highlight their benefits for understanding photon-induced changes of chemical properties and reactions. Based on results obtained by ab initio QED methods, we identify open theoretical questions and how a so far missing detailed understanding of polaritonic chemistry can be established. We finally give an outlook on future directions within polaritonic chemistry and first-principles QED.

Strong coupling in the entanglement dynamics of two qubits interacting with a graphene nanodisk

We investigate the entanglement dynamics of two qubits interacting with a graphene nanodisk using the macroscopic quantum electrodynamics method. By modifying the free-space decay rate of each qubit, we study the coupling strength between the nanoparticle and the qubits. We find that as the free-space decay rate increases, the decaying Rabi oscillations featured in the qubit population dynamics change to complex non-Markovian dynamical population evolution. This is also reflected on the concurrence, which at weak or moderate light–matter coupling conditions, attains values up to 0.5, while as the coupling conditions become stronger, larger values are also transiently observed. Our findings indicate that graphene nanostructures can provide a platform for the realization of high degree of entanglement in the strong coupling regime at the nanoscale, essential for quantum technology applications.

Cavity-Modulated Proton Transfer Reactions.

Proton transfer is ubiquitous in many fundamental chemical and biological processes, and the ability to modulate and control the proton transfer rate would have a major impact on numerous quantum technological advances. One possibility to modulate the reaction rate of proton transfer processes is given by exploiting the strong light-matter coupling of chemical systems inside optical or nanoplasmonic cavities. In this work, we investigate the proton transfer reactions in the prototype malonaldehyde and Z-3-amino-propenal (aminopropenal) molecules using different quantum electrodynamics methods, in particular, quantum electrodynamics coupled cluster theory and quantum electrodynamical density functional theory. Depending on the cavity mode polarization direction, we show that the optical cavity can increase the reaction energy barrier by 10-20% or decrease the reaction barrier by ∼5%. By using first-principles methods, this work establishes strong light-matter coupling as a viable and practical route to alter and catalyze proton transfer reactions.

МОДЕЛИРОВАНИЕ ИЗЛУЧЕНИЯ В МИКРОСИСТЕМАХ С ПОМОЩЬЮ ЦЕПЕЙ МАРКОВА

To solve important problems related to radiation in microsystems, the methods of quantum electrodynamics are successfully used. At the same time, a number of problems remain (vacuum energy, divergence in local interaction, the physical meaning of the fine structure constant) that cannot be resolved within the framework of this theory. Therefore, an urgent task is to develop alternative mathematical models that can be additionally used to study the radiation process in microsystems. In this work, to model the radiation process in microsystems, Markov processes with continuous time and discrete states are used. The mathematical model is based on Heisenberg's uncertainty principles and conservation laws. The main mathematical tools are Kolmogorov graphs and their corresponding systems of equations. The key idea is that the phase space of a particle is discrete. The model of the discrete phase space is distinguished by its comparative simplicity and efficiency, and allows applying the well-developed theory of Markov processes to the phenomena under study. The scale of the model and its discrete structure make it possible to avoid irremovable singularities. The article presents: an original physical interpretation of the fine structure constant, a stochastic analogue of the redshift law and the magnitude of the Schwarzschild gravitational radius, a stochastic interpretation of the fine structure constant of the gravitational field is proposed. A comparative analysis of the fine structure constants for the gravitational and electromagnetic fields has been carried out.

Precision physics of muonic ions of lithium, beryllium and boron

The problem of determining the main parameters of light nuclei from precision atomic spectroscopy is considered. Within the framework of the quasipotential method in quantum electrodynamics, the energy interval [Formula: see text] in muonic ions of lithium, beryllium and boron is calculated. Corrections of orders [Formula: see text], which are determined by relativistic effects, effects of vacuum polarization, nuclear structure and recoil, as well as combined corrections, including the above, are taken into account. Nuclear structure effects are expressed in terms of the nuclear charge radius in the case of one-photon interaction and the electromagnetic form factors of nuclei in the case of two-photon interaction. The obtained numerical values for the [Formula: see text] interval can be used for comparison with future experimental data and for a more accurate determination of the nucleus charge radii.

Determination of the proton charge radius from the study of the hydrogen S-energy levels

On the basis of quasipotential method in quantum electrodynamics, the energy interval (3S – 1S) in muonic hydrogen is calculated. The corrections of orders α 3, α 4, α 5, α 6 are taken into account, which are determined by relativistic effects, the effects of vacuum polarization, nuclear structure and recoil, as well as combined corrections. In the leading order proton structure effects are expressed in terms of the charge radius of the proton. In the case of two-photon exchange interaction proton structure corrections are determined by the proton electromagnetic form factors. The value of the energy interval (3S – 1S) can be used for comparison with future experimental data and determining the proton charge radius with greater accuracy.

Energy interval 2S-1S in muonic ions of lithium, beryllium and boron

Within the framework of the quasipotential method in quantum electrodynamics, the energy interval (2S – 1S) in muonic ions of lithium, beryllium and boron is calculated. Corrections of order α 3 – α 6, which are determined by relativistic effects, effects of vacuum polarization, nuclear structure and recoil, as well as combined corrections, including the above, are taken into account. Nuclear structure effects are expressed in terms of the nuclear charge radius in the case of one-photon interaction and the electromagnetic form factors of nuclei in the case of two-photon interaction. The obtained numerical values for the (2S – 1S) energy interval can be used for comparison with future experimental data and for a more accurate determination of the nuclear charge radii.

Nuclear Structure Correction to Hyperfine Splitting in Light Muonic Ions

Within the framework of the quasipotential method in quantum electrodynamics, the corrections for the structure of the nucleus are calculated from two-photon exchange diagrams in the hyperfine splitting of energy levels in muon ions of lithium, beryllium and boron. The particle interaction operator is constructed using the method of projection operators on particle states with certain values of the total atomic momentum F and muon j. Corrections to the structure of the nucleus are presented in integral form containing the electromagnetic form factors of the nuclei. After the decomposition of form factors at small momentum transfers, the studied contribution is expressed in terms of the nuclear charge radii. The corrections obtained must be taken into account in the precision calculation of the transition frequencies between the 2S and 2P levels.

Quantum electrodynamics in modern optics and photonics: tutorial

One of the key frameworks for developing the theory of light–matter interactions in modern optics and photonics is quantum electrodynamics (QED). Contrasting with semiclassical theory, which depicts electromagnetic radiation as a classical wave, QED representations of quantized light fully embrace the concept of the photon. This tutorial review is a broad guide to cutting-edge applications of QED, providing an outline of its underlying foundation and an examination of its role in photon science. Alongside the full quantum methods, it is shown how significant distinctions can be drawn when compared to semiclassical approaches. Clear advantages in outcome arise in the predictive capacity and physical insights afforded by QED methods, which favors its adoption over other formulations of radiation–matter interaction.

Revisiting the Theory of Radiative and Nonradiative Transitions of a Polyatomic System

We have revisited the theory of radiative and nonradiative transitions using the crude adiabatic approximation and methods of quantum electrodynamics in order to calculate the transition rates for these processes. All the integrals involving vibrational wave functions have been calculated analytically using Laguerre functions. It has been argued that the radiative transitions will be mediated by the local vibrational modes, referred to as active modes. In the case of nonradiative transitions both local and nonlocal modes contribute to the transition rates. The multidimensional theory involving all the active normal coordinates has been applied to interpret the vibronic spectra of yttrium garnet doped with Pr3+(YAG:Pr3+) at low temperature. The Huang-Rhys parameters have been obtained for the normal frequencies observed for YAG. This approach provides a powerful technique to determine the Huang-Rhys parameters from the low temperature data, which can be used to predict the temperature dependence of luminescence from an optical ion in solid.

Energy Interval 1S–2S in Muonic Hydrogen and Helium

The interval of a large structure of energy spectrum (1S–2S) in muonic helium and hydrogen is calculated using a quasi-potential method in quantum electrodynamics. Corrections of the order α4, α5, and α6 determined by relativistic effects, vacuum polarization effects, nuclear structure and recoil, as well as by combined corrections including those listed above, are taken into account. The nuclear structure effects are expressed in terms of the charge radius of nuclei in the case of the one-photon interaction and electromagnetic form factors of nuclei in the case of the two-photon interaction. Numerical values obtained for the (1S–2S) interval can be used for comparison with future experimental data and for more accurate determination of the charge radii of nuclei.

Hyperfine structure of S-states in muonic ions of lithium, beryllium and boron

On the basis of quasipotential method in quantum electrodynamics we make precise calculation of hyperfine structure of S-states in muonic ions of lithium, beryllium and boron. Nuclear structure and recoil corrections of orders α1 and α6, vacuum polarization corrections in first and second orders of perturbation theory are taken into account. Total values of hyperfine splittings are obtained which can be used for a comparison with future experimental data.

Energy Levels of Mesomolecular Ions of Hydrogen in Variational Approach

Energies of the ground and excited states of mesomolecular ions tdμ, dpμ, and tpμ, are calculated based on the stochastic variational method of quantum electrodynamics. Basis wave functions are chosen in the Gaussian form. Hamiltonian matrix elements are calculated analytically. A computer code in the MATLAB environment is developed for numerical calculations. The values of energies of the ground and excited states are obtained.

Energy spectra of muonic atoms in quantum electrodynamics

Vacuum polarization, nuclear structure and recoil, radiative corrections to the hyperfine structure of S-states in muonic ions of lithium, beryllium and boron are calculated on the basis of quasipotential method in quantum electrodynamics. We consider contributions in first and second orders of perturbation theory which have the order α5 and α6 in the energy spectrum. Total values of hyperfine splittings are obtained which can be used for a comparison with future experimental data.

All-optical active control of photon correlations: Dressed-state-assisted quantum interference effects

We propose an all-optical scheme to control the photon statistics using the hybrid quantum plasmonic system. With the aid of dressed-state-assisted quantum interference effects, it is shown that the photon correlations of a signal field can be continuously modulated from bunching to antibunching under the control of a pump field. Apart from the exact multimode model, a single-mode model and an analytical treatment are also provided to help us identify the roles of multimode coupling and quantum interference between probability amplitudes. The proposed scheme, in contrast to the cavity quantum electrodynamics methods, works well even in the bad cavity limit. These findings suggest that this composite system provides a feasible nanophotonic platform for active modulation of photon statistics and for future quantum devices.

Corrections of two-photon interactions in the fine and hyperfine structure of the P-energy levels of muonic hydrogen

In the framework of the quasipotential method in quantum electrodynamics we calculate corrections to the nuclear structure proportional to $r_N^2$ from two-photon exchange amplitudes in the fine and hyperfine structure of P-states in muonic hydrogen, as well as the photon-photon interaction amplitudes, leading to the exchange of the axial vector meson. In constructing the quasipotential of the muon-nucleus interaction, we use the method of projection operators on states of two particles with a definite spin and total angular momentum. Analytical calculation of the matrix elements is performed and contributions to the fine and hyperfine structure of the $2P_{1/2}$ and $2P_{3/2}$ levels are obtained.

Considerable improvement of entanglement swapping by considering multiphoton transitions via cavity quantum electrodynamics method

Recently we studied the effect of photon addition in the initial coherent field on the entanglement swapping which causes some improvements in the process [Soltani et al., Int. J. Mod. Phys. B 31, 1750198 (2017)]. In this paper, we investigate the influence of multiphoton transitions in the atom–field interaction based on the cavity quantum electrodynamics on the entanglement swapping and show its considerable constructive effect on this process. The presented model consists of two two-level atoms namely A1and A2and two distinct cavity fields F1and F2. Initially, the atoms are prepared in a maximally entangled state and the fields in the cavities are prepared in hybrid entangled state of number and coherent states, separately. Making the atom A2to interact with the field F1(via the generalized Jaynes–Cummings model which allows m-photon transitions between atomic levels in the emission and absorption processes) followed by their detection allows us to arrive at the entanglement swapping from the two atoms A1, A2and the two fields F1, F2to the atom–field A1–F2system. Then, we pay our attention to the time evolution of success probability of detecting processes and fidelity. Also, to determine the amount of entanglement of the generated entangled state in the swapping process, the linear entropy is evaluated and the effect of parameter [Formula: see text] concerning the multiphoton transitions on these quantities is investigated, numerically. It is observed that, by increasing the number of photons in the transition process, one may obtain considerable improvement in the relevant quantities of the entanglement swapping. In detail, the satisfactorily acceptable values 1 and 0.5 corresponding to success probability and fidelity are obtained for most of the times during observing of the above-mentioned procedure. We concluded that the presented formalism in this paper is much more advantageous than our presentation model in our earlier work mentioned above.

Quadrupole Interaction Contribution to the Hyperfine Structure of P-States in Muonic Lithium, Beryllium, and Boron Ions

The contribution of the quadrupole interaction to the hyperfine structure of the spectrum of the energy of muonic lithium, beryllium, and boron ions is calculated within the quasipotential method in quantum electrodynamics. The numerical results obtained improve previous calculations due to the consideration of new corrections. They can be used for comparison with future experimental data.

Particles Actually Represent the Names of Types of Waves

It is accepted that quantum mechanics (QM) describes motion of waves and particles. Therefore, we must use wave-particle duality (WPD), which is usually considered as one of the foundations of QM; however, WPD is well known as a self-contradictory concept. These contradictions insensibly spoil our subconscious thinking about the micro-world (MW). This article shows that known trials to solve these contradictions are erroneous. Quantum jumps (QJs) are shown to be very lame arguments for the real existence of particles. I offer rejecting the concept of particles and using their names as labels for types of corresponding waves. Thus, we can discard contradictions created by WPD. This approach is validated in the article by careful analysis of real calculation methods of quantum electrodynamics (QED). For the first time, it is noticed that proper 4-coordinates of particles are not in use in real calculations in QED. This implies that particles do not take part in real calculations, which describe properties of atoms and molecules. It follows that particles do not exist as such. Therefore, we must acknowledge that we actually use the names of “particles” merely as names of types of given waves, but not as real, physical objects.

The contribution of pseudoscalar and axial-vector mesons to hyperfine structure of muonic hydrogen

In the framework of the quasipotential method in quantum electrodynamics we calculate the contribution of light pseudoscalar (PS) and axial-vector (AV) mesons to the interaction operator of a muon and a proton in muonic hydrogen atom. The coupling of mesons with the muon is via two-photon intermediate state. The parametrization of the transition form factor of two photons into PS and AV mesons, based on the experimental data on the transition form factors and QCD asymptotics, is used. Numerical estimates of the contributions to the hyperfine structure of the spectrum of the S and P levels are presented. It is shown that such contribution to the hyperfine splitting in muonic hydrogen is rather important for a comparison with precise experimental data.