Quantization Of Electromagnetic Field Research Articles

Perturbative approach to dynamical Casimir effect in an interface of dielectric mediums

Electromagnetic field quantization in the presence of two semi-infinite dielectrics with moving interface is investigated in $1+1$-dimensional space-time. The moving interface is modeled for small displacements and the field equation is solved perturbatively. Input-output relations and spectral distribution of emitted photons are obtained and the effect of small transitions trough the interface discussed.

Radiative processes of two entangled atoms outside a Schwarzschild black hole

We consider radiative processes of a quantum system composed by two identical two-level atoms in a black-hole background. We assume that these identical two-level atoms are placed at fixed radial distances outside a Schwarzschild black hole and interacting with a quantum electromagnetic field prepared in one of the usual vacuum states, namely the Boulware, Unruh or the Hartle-Hawking vacuum states. We study the structure of the rate of variation of the atomic energy. The intention is to identify in a quantitative way the contributions of vacuum fluctuations and radiation reaction to the entanglement generation between the atoms as well as the degradation of entangled states in the presence of an event horizon. We find that for a finite observation time the atoms can become entangled for the case of the field in the Boulware vacuum state, even if they are initially prepared in a separable state. In addition, the rate of variation of atomic energy is not well behaved at the event horizon due to the behavior of the proper accelerations of the atoms. We show that the thermal nature of the Hartle-Hawking and Unruh vacuum state allows the atoms to get entangled even if they were initially prepared in the separable ground state.

Radiation and matter: Electrodynamics postulates and Lorenz gauge

In general terms, we have considered matter as the system of charged particles and quantized electromagnetic field. For consistent description of the thermodynamic properties of matter, especially in an extreme state, the problem of quantization of the longitudinal and scalar potentials should be solved. In this connection, we pay attention that the traditional postulates of electrodynamics, which claim that only electric and magnetic fields are observable, is resolved by denial of the statement about validity of the Maxwell equations for microscopic fields. The Maxwell equations, as the generalization of experimental data, are valid only for averaged values. We show that microscopic electrodynamics may be based on postulation of the d'Alembert equations for four-vector of the electromagnetic field potential. The Lorenz gauge is valid for the averages potentials (and provides the implementation of the Maxwell equations for averages). The suggested concept overcomes difficulties under the electromagnetic field quantization procedure being in accordance with the results of quantum electrodynamics. As a result, longitudinal and scalar photons become real rather than virtual and may be observed in principle. The longitudinal and scalar photons provide not only the Coulomb interaction of charged particles, but also allow the electrical Aharonov-Bohm effect.

Is the Fulling–Davies–Unruh effect valid for the case of an atom coupled to quantum electromagnetic field?

We study, from the viewpoint of a co-accelerated observer, the average rate of change of atomic energy for an atom in uniform acceleration and coupled to quantum electromagnetic field at a thermal state with an arbitrary temperature T. We show that only when the temperature of the thermal state in the co-accelerated frame is assumed to be the Fulling–Davies–Unruh (FDU) temperature, T = a/2[Formula: see text], can the average rate of change of atomic energy in a local inertial frame be recovered, which exemplifies the equivalence between the Minkowski vacuum and a thermal bath of Rindler particles. This conclusion is verified to be valid not only in a free spacetime, but also in a spacetime with a boundary.

Coupling of three-spin qubits to their electric environment

We investigate the behavior of qubits consisting of three electron spins in double and triple quantum dots subject to external electric fields. Our model includes two independent bias parameters, $\ensuremath{\varepsilon}$ and ${\ensuremath{\varepsilon}}_{M}$, which both couple to external electromagnetic fields and can be controlled by gate voltages applied to the quantum dot structures. By varying these parameters, one can switch the qubit type by shifting the energies in the single quantum dots, thus changing the electron occupancy in each dot. Starting from the asymmetric resonant exchange qubit with a (2,0,1) and (1,0,2) charge admixture, one can smoothly cross over to the resonant exchange qubit with a detuned (1,1,1) charge configuration, and to the exchange-only qubit with the same charge configuration but equal energy levels down to the hybrid qubits with (1,2,0) and (0,2,1) charge configurations. Here, $(l,m,n)$ describes a configuration with $l$ electrons in the left dot, $m$ electrons in the center dot, and $n$ electrons in the right dot. We first focus on random electromagnetic field fluctuations, i.e., ``charge noise,'' at each quantum dot resulting in dephasing of the qubit, and we provide a complete map of the resulting dephasing time as a function of the bias parameters. We pay special attention to the so-called sweet spots and double sweet spots of the system, which are least susceptible to noise. In the second part, we investigate the coupling of the qubit system to the coherent quantized electromagnetic field in a superconducting strip-line cavity, and we also provide a complete map of the coupling strength as a function of the bias parameters. We analyze the asymmetric qubit-cavity coupling via $\ensuremath{\varepsilon}$ and the symmetric coupling via ${\ensuremath{\varepsilon}}_{M}$.

Exact quantisation of the relativistic Hopfield model

We investigate the quantisation in the Heisenberg representation of a relativistically covariant version of the Hopfield model for dielectric media, which entails the interaction of the quantum electromagnetic field with the matter dipole fields, represented by a mesoscopic polarisation field. A full quantisation of the model is provided in a covariant gauge, with the aim of maintaining explicit relativistic covariance. Breaking of the Lorentz invariance due to the intrinsic presence in the model of a preferred reference frame is also taken into account. Relativistic covariance forces us to deal with the unphysical (scalar and longitudinal) components of the fields, furthermore it introduces, in a more tricky form, the well-known dipole ghost of standard QED in a covariant gauge. In order to correctly dispose of this contribution, we implement a generalised Lautrup trick. Furthermore, causality and the relation of the model with the Wightman axioms are also discussed.

Quantization of electromagnetic field and analysis of Purcell effect based on formalism of scattering matrix

We have developed a rigorous self-consistent approach for the quantization of electromagnetic field in inhomogeneous structures. The approach is based on utilization of the scattering matrix of the system. Instead of the use of standard periodic Born-Karman boundary conditions, we use the quantization condition implying equating eigenvalues of the scattering matrix (S-matrix) of the system to unity (S-quantization). In the trivial case of uniform medium boundary condition for S-quantization is nothing but periodic boundary condition. S-quantization allows calculating modification of the spontaneous emission rate for arbitrary inhomogeneous structure and direction of the emitted radiation. S-quantization solves the long-standing problem coupled to normalization of the quasi-stationary electromagnetic modes. Examples of application of S-quantization for the calculation of spontaneous emission rate for the cases of Bragg reflector and microcavity are demonstrated.

Entanglement between two qubits induced by thermal field

We have investigated the influence of dipole-dipole interaction and initial atomic coherence on atomic entanglement dynamics of two qubits. We have considered a model, in which only one atom couples to a quantum electromagnetic field in a cavity, since one of them can move around the cavity. We have shown that the entanglement arises for all pure atomic state even when both atoms are initially in the excited states. We have also derived that degree of entanglement is enhanced in the presence of the atomic coherence.

The Formalism for Energy Changing Rate of an Accelerated Atom Coupled with Electromagnetic Vacuum Fluctuations

The structure of the rate of variation of the atomic energy for an arbitrary stationary motion of the atom in interaction with a quantum electromagnetic field is investigated. Our main purpose is to rewrite the formalism in Ref. \cite{zz} and to deduce the general expressions of the Einstein A coefficients of an atom on an arbitrary stationary trajectory. The total rate of change of the energy and Einstein coefficients of the atom near a plate with finite temperature or acceleration are also investigated.

Canonical Quantization of Electromagnetic Field in the Presence of Nonlinear Anisotropic Magnetodielectric Medium with Spatial-Temporal Dispersion

Modeling a nonlinear anisotropic magnetodielectric medium with spatial-temporal dispersion by two continuum collections of three dimensional harmonic oscillators, a fully canonical quantization of the electromagnetic field is demonstrated in the presence of such a medium. Some coupling tensors of various ranks are introduced that couple the magnetodielectric medium with the electromagnetic field. The polarization and magnetization fields of the medium are defined in terms of the coupling tensors and the oscillators modeling the medium. The electric and magnetic susceptibility tensors of the medium are obtained in terms of the coupling tensors. It is shown that the electric field satisfy an integral equation in frequency domain. The integral equation is solved by an iteration method and the electric field is found up to an arbitrary accuracy.

Photon Statistics of a Hybrid Quantum Dot-Metal Nanoparticle Cluster

A theoretical study of photon statistics of an optically driven quantum dot located near a metal nanoparticle cluster (composed of one or two nanoparticles) is presented. Considering the system in the weak Rabi frequency regime, an analytical formula for anti-bunching time is derived. Using a photon Green’s function method based on the exact quantization of electromagnetic field in a dissipative medium, the dependence of the anti-bunching time on the geometrical parameters (quantum dot radius and quantum dot distance from the metal nanoparticle) is studied. The results show that these geometrical parameters have pronounced impacts on the photon statistics. Furthermore, our findings reveal that the quantum dot dipole orientation possesses an important role in the quantum dot photon emission.

Quantum Electromagnetics: A New Look—Part I

In this work, quantization of electromagnetic fields in a general anisotropic inhomogeneous media is considered. First, the classical Hamiltonian is derived. Once the Hamiltonian is derived, with it the classical equations of motion follow. Next, the fields are elevated to become quantum operators, for which conjugate pairs are endowed with commutators. Since as previously shown, such commutators induce functional derivatives, the quantum equations of motion can be easily derived. Next, the mode decomposition of the fields is demonstrated. Upon substitution into the classical Hamiltonian, each mode then behaves like a simple harmonic oscillator. These oscillators can then be elevated to become quantum harmonic oscillators. Both the traveling wave modes and the standing wave modes are discussed. Furthermore, the longitudinal modes are described. Finally, the case of impressed sources are considered, with the corresponding Hamiltonian and field quantization. The Green's functions for the linear system are presented. Finally, the quantum Maxwell's equations are derived. A short discussion on field-atom interaction is given.

Quantum Electromagnetics: A New Look—Part II

In this work, quantization of electromagnetic fields in a general anisotropic inhomogeneous media is considered. First, the classical Hamiltonian is derived. Once the Hamiltonian is derived, with it the classical equations of motion follow. Next, the fields are elevated to become quantum operators, for which conjugate pairs are endowed with commutators. Since as previously shown, such commutators induce functional derivatives, the quantum equations of motion can be easily derived. Next, the mode decomposition of the fields is demonstrated. Upon substitution into the classical Hamiltonian, each mode then behaves like a simple harmonic oscillator. These oscillators can then be elevated to become quantum harmonic oscillators. Both the traveling wave modes and the standing wave modes are discussed. Furthermore, the longitudinal modes are described. Finally, the case of impressed sources are considered, with the corresponding Hamiltonian and field quantization. The Green's functions for the linear system are presented. Finally, the quantum Maxwell's equations are derived. A short discussion on field-atom interaction is given.

Vacuum fluctuations and radiation reaction in radiative processes of entangled states

We investigate radiative processes of inertial two-level atoms in an entangled state interacting with a quantum electromagnetic field. Our intention is to clarify and to analyze the contributions of vacuum fluctuations and radiation reaction to the decay rate of the entangled state. The possible relevance of the findings in the present work is discussed.

Theory of photon–electron interaction in single-layer graphene sheet

The purpose of this work is to elaborate the quantum theory of photon–electron interaction in a single-layer graphene sheet. Since the light source must be located outside the extremely thin graphene sheet, the problem must be formulated and solved in the three-dimensional physical space, in which the graphene sheet is a thin plane layer. It is convenient to use the orthogonal coordinate system in which the xOy coordinate plane is located in the middle of the plane graphene sheet and therefore the Oz axis is perpendicular to this plane. For the simplicity we assume that the quantum motions of electron in the directions parallel to the coordinate plane xOy and that along the direction of the Oz axis are independent. Then we have a relatively simple formula for the overall Hamiltonian of the electron gas in the graphene sheet. The explicit expressions of the wave functions of the charge carriers are easily derived. The electron–hole formalism is introduced, and the Hamiltonian of the interaction of some external quantum electromagnetic field with the charge carriers in the graphene sheet is established. From the expression of this interaction Hamiltonian it is straightforward to derive the matrix elements of photons with the Dirac fermion–Dirac hole pairs as well as with the electrons in the quantum well along the direction of the Oz axis.

Quantization of electromagnetic field in an inhomogeneous medium based on scattering matrix formalism (S-quantization)

We have developed a procedure for quantization of the electromagnetic field in a layered inhomogeneous media based on analysis of the eigenvalues of the scattering matrix (S-matrix). In contrast to the method involving quantization of the electromagnetic field, involving the use of periodic boundary conditions (Born–von Karman conditions), the proposed procedure (S-quantization) is based on equality of the amplitudes of waves incident on a quantization box and waves outgoing from the quantization box, which is equivalent to equating unity eigenvalues of the scattering matrix. We perform a comparison of the density of states and spatial structure of the field calculated with periodic boundary conditions and using the procedure of S-quantization.

Quantum marginal problems

The quantum marginal problem asks the question if elements of a given set of quantum states can be reduced states of some joint quantum state. In this paper we present various versions of the quantum marginal problem along with their solutions in the order in which they were published. The review begins with simple finite-dimensional composite systems and ends with results of the Gaussian quantum marginal problem that apply to systems of harmonic oscillators (e.g. modes of the quantum electromagnetic field).

The features of a quantum description of radiation in an optically dense medium

This paper is devoted to the theory of quantum electromagnetic field in an optically dense medium. Self-consistent equations describing interaction between a quantum field and a quantum dielectric medium are obtained from the first principles, i.e., outside a phenomenological description. Using these equations, we found a transformation (of the Bogoliubov transformation type) that converts the operators of the “vacuum” field into operators of collective perturbations of the field and an ensemble of atoms, that is, photons in the medium. Transformation parameter is the refractive index of the wave mode considered. It is shown that besides the energy of the collective electromagnetic field, the energy of photons in the medium includes the energy of the internal degrees of freedom of the substance and the energy of near-field dipole interaction between atoms in the polarized medium. The concept of negative energy photons is introduced on the basis of self-consistent equations.

QED representation for the net of causal loops

The present work tackles the existence of local gauge symmetries in the setting of Algebraic Quantum Field Theory (AQFT). The net of causal loops, previously introduced by the authors, is a model independent construction of a covariant net of local C*-algebras on any 4-dimensional globally hyperbolic space-time, aimed to capture structural properties of any reasonable quantum gauge theory. Representations of this net can be described by causal and covariant connection systems, and local gauge transformations arise as maps between equivalent connection systems. The present paper completes these abstract results, realizing QED as a representation of the net of causal loops in Minkowski space-time. More precisely, we map the quantum electromagnetic field Fμν, not free in general, into a representation of the net of causal loops and show that the corresponding connection system and the local gauge transformations find a counterpart in terms of Fμν.

A novel solution procedure for a three-level atom interacting with one-mode cavity field via modified homotopy analysis method

In this paper, the interaction of a three-level $ \Lambda$ -configration atom and a one-mode quantized electromagnetic cavity field has been studied. The detuning parameters, the Kerr nonlinearity and the arbitrary form of both the field and intensity-dependent atom-field coupling have been taken into account. The wave function when the atom and the field are initially prepared in the excited state and coherent state, respectively, by using the Schrodinger equation has been given. The analytical approximation solution of this model has been obtained by using the modified homotopy analysis method (MHAM). The homotopy analysis method is mentioned summarily. MHAM can be obtained from the homotopy analysis method (HAM) applied to Laplace, inverse Laplace transform and Pade approximate. MHAM is used to increase the accuracy and accelerate the convergence rate of truncated series solution obtained by the HAM. The time-dependent parameters of the anti-bunching of photons, the amplitude-squared squeezing and the coherent properties have been calculated. The influence of the detuning parameters, Kerr nonlinearity and photon number operator on the temporal behavior of these phenomena have been analyzed. We noticed that the considered system is sensitive to variations in the presence of these parameters.