Quantization Of Electromagnetic Field Research Articles

Quantum Filtering Equations for a System Driven by Nonclassical Fields

Using Gardiner and Collet’s input-output model and the concept of cascade system, we determine the filtering equation for a quantum system driven by light in some specific nonclassical states. The quantum system and electromagnetic field are described by making use of quantum stochastic unitary evolution. We consider two examples of the nonclassical states of field: a combination of vacuum and single photon states and a mixture of two coherent states. The stochastic evolution conditioned on the results of the photon counting and quadrature measurements is described.

Resonance Dipole–Dipole Interaction between Two Accelerated Atoms in the Presence of a Reflecting Plane Boundary

We study the resonant dipole–dipole interaction energy between two non-inertial identical atoms, one excited and the other in the ground state, prepared in a correlated Bell-type state, and interacting with the scalar field or the electromagnetic field nearby a perfectly reflecting plate. We suppose the two atoms move with the same uniform acceleration, parallel to the plane boundary, and that their separation is constant during the motion. By separating the contributions of radiation reaction field and vacuum fluctuations to the resonance energy shift of the two-atom system, we show that Unruh thermal fluctuations do not affect the resonance interaction, which is exclusively related to the radiation reaction field. However, non-thermal effects of acceleration in the radiation-reaction contribution, beyond the Unruh acceleration–temperature equivalence, affect the resonance interaction energy. By considering specific geometric configurations of the two-atom system relative to the plate, we show that the presence of the mirror significantly modifies the resonance interaction energy between the two accelerated atoms. In particular, we find that new and different features appear with respect to the case of atoms in the free-space, related to the presence of the boundary and to the peculiar structure of the quantum electromagnetic field vacuum in the locally inertial frame. Our results suggest the possibility to exploit the resonance interaction between accelerated atoms as a probe for detecting the elusive effects of atomic acceleration on radiative processes.

Casimir forces on a bi-anisotropic absorbing magneto-dielectric slab between two parallel conducting plates

A fully canonical quantization of electromagnetic field in the presence of a bi-anisotropic absorbing magneto-dielectric slab is demonstrated. The electric and the magnetic polarization densities of the magneto-dielectric slab are defined in terms of the dynamical variables modeling the slab and the coupling tensors that couple the electromagnetic field to the slab. The four susceptibility tensors of the bi-anisotropic magneto-dielectric slab are expressed in terms of the coupling tensors that couple an electromagnetic field to the slab. It is shown that the four susceptibility tensors of the bi-anisotropic magneto-dielectric slab satisfy Kramers–Kronig relations. The Maxwell’s equations are exactly solved in the presence of the bi-anisotropic magneto-dielectric slab. The tangential and the normal components of the Casimir forces exerted on the bi-anisotropic magnet-dielectric slab exactly are calculated in the vacuum state and thermal state of the total system. It is shown that the tangential components of the Casimir forces vanish when the bi-anisotropic slab is converted to an isotropic slab.

Huygens-Fresnel principle: Analyzing consistency at the photon level

Typically the use of the Rayleigh-Sommerfeld diffraction formula as a photon propagator is widely accepted due to the abundant experimental evidence that suggests that it works. However, a direct link between the propagation of the electromagnetic field in classical optics and the propagation of photons where the square of the probability amplitude describes the transverse probability of the photon detection is still an issue to be clarified. We develop a mathematical formulation for the photon propagation using the formalism of electromagnetic field quantization and the path-integral method, whose main feature is its similarity with a fractional Fourier transform (FrFT). Here we show that, because of the close relation existing between the FrFT and the Fresnel diffraction integral, this propagator can be written as a Fresnel diffraction, which brings forward a discussion of the fundamental character of it at the photon level compared to the Huygens-Fresnel principle. Finally, we carry out an experiment of photon counting by a rectangular slit supporting the result that the diffraction phenomenon in the Fresnel approximation behaves as the actual classical limit.

Phase-sensitive atomic dynamics in quantum light

Interaction between a quantum electromagnetic field and a model Ry atom with possible transitions to the continuum and to the low-lying resonant state is investigated. Strong sensitivity of atomic dynamics to the phase of applied coherent and squeezed vacuum light is found. Methods to extract the quantum field phase performing the measurements on the atomic system are proposed. In the case of the few-photon coherent state high accuracy of the phase determination is demonstrated, which appears to be much higher in comparison to the usually used quantum-optical methods such as homodyne detection.

The Nature of the Photon and Quantum Optics

In a concise, but accessible for the first acquaintance form the procedure for the quantization of linear oscillator is set out. By analogy with this procedure the procedure of quantization (second quantization) of classical Maxwell’s electrodynamics is set up. The physical sense of the wave functions arguments of transverse electromagnetic field and its Fourier transformation is set up. One pay attention as for quantum coherent (almost a classic) states of the electromagnetic field and for photonics Fock states. Attention is drawn to the fact of absence the power of the universal content of such concepts as field amplitude, phase and number of particles (photons), which are used by experimenter’s to describe the states of a quantized field. The semi quantitative description the interaction processes of a quantum electromagnetic field with substance is set up. Specified situations are shown in which the discrepancy between the predictions of classical and quantum electrodynamics is noticeable at the macroscopic level.

Resonance interaction energy between two entangled atoms in a photonic bandgap environment

We consider the resonance interaction energy between two identical entangled atoms, where one is in the excited state and the other in the ground state. They interact with the quantum electromagnetic field in the vacuum state and are placed in a photonic-bandgap environment with a dispersion relation quadratic near the gap edge and linear for low frequencies, while the atomic transition frequency is assumed to be inside the photonic gap and near its lower edge. This problem is strictly related to the coherent resonant energy transfer between atoms in external environments. The analysis involves both an isotropic three-dimensional model and the one-dimensional case. The resonance interaction asymptotically decays faster with distance compared to the free-space case, specifically as 1/r2 compared to the 1/r free-space dependence in the three-dimensional case, and as 1/r compared to the oscillatory dependence in free space for the one-dimensional case. Nonetheless, the interaction energy remains significant and much stronger than dispersion interactions between atoms. On the other hand, spontaneous emission is strongly suppressed by the environment and the correlated state is thus preserved by the spontaneous-decay decoherence effects. We conclude that our configuration is suitable for observing the elusive quantum resonance interaction between entangled atoms.

Signatures of Plexcitonic States in Molecular Electroluminescence

We develop a quantum master equation (QME) approach to investigate the electroluminesence (EL) of molecules confined between metallic electrodes and coupled to quantum plasmonic modes. Within our general state-based framework, we describe electronic tunneling, vibrational damping, environmental dephasing, and the quantum coherent dynamics of coupled quantum electromagnetic field modes. As an example, we calculate the STM-induced spontaneous emission of a tetraphenylporphyrin (TPP) molecule coupled to a nanocavity plasmon. In the weak molecular exciton-plasmon coupling regime we find excellent agreement with experiments, including above-threshold hot luminescence, an effect not described by previous semiclassical calculations. In the strong coupling regime, we analyze the spectral features indicative of the formation of plexcitonic states.

Characteristics and expressions of entangled microwave signals

Entangled microwave signal is the reflection of the quantum characteristics of electromagnetic field in a GHz frequency range. Its generation is mainly dependent on superconducting circuits. Owing to the fact that there is no canonical expression to describe the format of entangled microwave signals, two expressional methods are presented on the basis of analyzing the characteristics of entangled microwave signals. One is in quantum frame, and the other is in classical frame. In quantum frame, we express entangled microwave signals in two-mode squeezed vacuum state. According to input-output relationship and parametric amplifier property in the generating process of entangled microwave signals, we describe the characteristics by two-mode squeezing operator and quantum Langevin equation. In the representation of photon number and Wigner function, we analyze the photon number distribution and the quadrature components' distribution of two-mode squeezed vacuum state, which shows the entangled two-photon correlation and the non-localized positive (negative) correlation of quadrature components. These are consistent with the characteristics of entangled microwave signals. Therefore, the results demonstrate that the entangled microwave signals can be expressed by two-mode squeezed vacuum state. In classical frame, we express entangled microwave signals in correlated random signals approximately. According to the relationship between quadrature components and the quantization of electromagnetic field, we construct the relation among electric-field intensity, input angular frequency, and squeezed parameter. The random number with Gaussian distribution is used as an input state to implement the simulation analysis. We illustrate the waveforms of entangled microwave signals after measurement and the extracted quadrature component waveform varying with time. The simulation results are consistent with the measurement results. These results show that the classical expression can reflect the one-path randomicity and two-path correlativity, which are the intrinsic characteristics of entangled microwave signals. Therefore, it is rational to express entangled microwave signals in correlated random signals. These two expressions properly reflect the continuous variable entanglement characteristics of entangled microwave signals. The expression of two-mode squeezed vacuum state is complete. Plenty of parameters that represent quantum information can be calculated by two-mode squeezed vacuum state, such as entanglement degree or the power of noise fluctuation. The merit of the expression of correlated random signals is intuitive, which makes it easier to understand the nonclassical characteristics of entangled microwave signals.

Canonical relativistic quantization of electromagnetic field in the presence of an anisotropic conductor magneto-dielectric medium

A canonical relativistic quantization of the electromagnetic field is introduced in the presence of an anisotropic conductor magneto-dielectric medium in a standard way in the Gupta–Bleuler framework. The medium is modeled by a continuum collection of the vector fields and a continuum collection of the antisymmetric tensor fields of the second rank in Minkowski space–time. The collection of vector fields describes the conductivity property of the medium and the collection of antisymmetric tensor fields describes the polarization and the magnetization properties of the medium. The conservation law of the total electric charges, induced in the anisotropic conductor magneto-dielectric medium, is deduced using the antisymmetry conditions imposed on the coupling tensors that couple the electromagnetic field to the medium. Two relativistic covariant constitutive relations for the anisotropic conductor magneto-dielectric medium are obtained. The constitutive relations relate the antisymmetric electric–magnetic polarization tensor field of the medium and the free electric current density four-vector, induced in the medium, to the strength tensor of the electromagnetic field, separately. It is shown that for a homogeneous anisotropic medium the susceptibility tensor of the medium satisfies the Kramers–Kronig relations. Also it is shown that for a homogeneous anisotropic medium the real and imaginary parts of the conductivity tensor of the medium satisfy the Kramers–Kronig relations and a relation other than the Kramers–Kronig relations.

What Is a Photon

The concept of the photon is introduced by discussion of the process of electromagnetic field quantization within a closed cavity or in an open optical system. The nature of a single-photon state is clarified by consideration of its behaviour at an optical beam splitter. The importance of linear superposition or entangled states in the distinctions between quantum-mechanical photon states and classical excitations of the electromagnetic field is emphasized. These concepts and the ideas of wave-particle duality are illustrated by discussions of the effects of single-photon inputs to Brown-Twiss and Mach-Zehnder interferometers. Both the theoretical predictions and the-confirming experimental observations are covered. The defining property of the single photon in terms of its ability to trigger one. and only one, photodetection event is discussed.

QUANTUM MODEL OF A CHARGED BLACK HOLE

A canonical approach for constructing of the classical and quantum description spherically-symmetric con guration gravitational and electromagnetic fields is considered. According to the sign of the square of the Kodama vector, space-time is divided into R-and T-regions. By virtue of the generalized Birkho theorem, one can choose coordinate systems such that the desired metric functions in the T-region depend on the time, and in the R-domain on the space coordinate. Then, the initial action for the configuration breaks up into terms describing the elds in the T- and R-regions with the time and space evolutionary variable, respectively. For these regions, Lagrangians of the configuration are constructed, which contain dynamic and non-dynamic degrees of freedom, leading to constrains. We concentrate our attention on dynamic T-regions. There are two additional conserved physical quantities: the charge and the total mass of the system. The Poisson bracket of the total mass with the Hamiltonian function vanishes in the weak sense. A classical solution of the eld equations in the con guration space (minisuperspace) is constructed without xing non-dynamic variable. In the framework of the canonical approach to the quantum mechanics of the system under consideration, physical states are found by solving the Hamiltonian constraint in the operator form (the DeWitt equation) for the system wave function Ψ. It also requires that Ψ is an eigenfunction of the operators of charge and total mass. For the symmetric of the mass operator the corresponding ordering of operators is carried out. Since the total mass operator commutes with the Hamiltonian in the weak sense, its eigenfunctions must be constructed in conjunction with the solution of the DeWitt equation. The consistency condition leads to the ansatz, with the help of which the solution of the DeWitt equation for the state Ψ em with a defined total mass and charge is constructed, taking into account the regularity condition on the horizon. The mass and charge spectra of the con guration in this approach turn out to be continuous. It is interesting that formal quantization in the R-region with a space evolutionary coordinate leads to a similar result.

Optimum quantum receiver for detecting weak signals in PAM communication systems

This paper deals with the modeling of an optimum quantum receiver for pulse amplitude modulator (PAM) communication systems. The information bearing sequence $$\{I_k\}_{k=0}^{N-1}$$ is estimated using the maximum likelihood (ML) method. The ML method is based on quantum mechanical measurements of an observable X in the Hilbert space of the quantum system at discrete times, when the Hamiltonian of the system is perturbed by an operator obtained by modulating a potential V with a PAM signal derived from the information bearing sequence $$\{I_k\}_{k=0}^{N-1}$$ . The measurement process at each time instant causes collapse of the system state to an observable eigenstate. All probabilities of getting different outcomes from an observable are calculated using the perturbed evolution operator combined with the collapse postulate. For given probability densities, calculation of the mean square error evaluates the performance of the receiver. Finally, we present an example involving estimating an information bearing sequence that modulates a quantum electromagnetic field incident on a quantum harmonic oscillator.

Quantization of the electromagnetic field at the presence of two dielectric slabs and application to the Casimir effect

The three dimensional formalism of the Green function method of the electro-magnetic field quantization is extended to quantize the electromagnetic field, at the presence of two dispersive and dissipative dielectric slabs. It is shown that the system decomposes into a singlet and a doublet parts. The singlet system corresponds to the normal polarization state of the electric field and the doublet system corresponds to the sum of parallel and longitudinal polarization states. Each part is quantized separately and vector potential operator of the each part is derived in terms of rightward and leftwards annihilation and creation operators. By using the assuming commutation properties of the noise current density, the equal time canonical commutation relations between the vector potential operator and its conjugate generalized momentum are verified for each part. Finally as an application, the explicit form of field operators are used to obtain an expression for the Casimir force between the two slabs via Maxwell stress tensor.

Quantum properties of the radiation emitted by a conductor in the Coulomb blockade regime

We present an input-output formalism describing a tunnel junction strongly coupled to its electromagnetic environment. We exploit it in order to investigate the dynamics of the radiation being emitted and scattered by the junction. We find that the non-linearity imprinted in the electronic transport by a properly designed environment generates strongly squeezed radiation. Our results show that the interaction between a quantum conductor and electromagnetic fields can be exploited as a resource to design simple sources of non-classical radiation.

Electromagnetic Duality Anomaly in Curved Spacetimes.

The source-free Maxwell action is invariant under electric-magnetic duality rotations in arbitrary spacetimes. This leads to a conserved classical Noether charge. We show that this conservation law is broken at the quantum level in the presence of a background classical gravitational field with a nontrivial Chern-Pontryagin invariant, in parallel with the chiral anomaly for massless Dirac fermions. Among the physical consequences, the net polarization of the quantum electromagnetic field is not conserved.

Investigation of charged particles radiation moving in a homogeneous dispersive medium

In this work, we use Drude-Lorents model description to study the radiation of a charged particles moving in a homogeneous dispersive medium. A suitable quantized electromagnetic field for such medium is utilized to obtain proper equations for energy loss of the particle per unit length. The energy loss is separately calculated for transverse and longitudinal components of the filed operators. The calculations show that the longitudinal component of the field operators contributes in electron radiation, when dielectric function is exceedingly dependent on the frequency. It is also shown that when the dispersion is not included, the obtained equations are in a good agreement with previous results. For negligible dispersion, the contribution of the field’s longitudinal component tends to zero and at the end the results are in agreement with Ginsberg’s calculations. This calculation can reveal a development for the fields’ quantization for permeable dielectric background medium.

The superluminal velocities as the consequence of non-classical states of electromagnetic field

It was shown within the framework of conventional quantum electrodynamics, and without using perturbation theory, the presence of superluminal signals, transferring the information, while investigating the scattering of quantum electromagnetic field by excited atom. The superluminal signals are impossible in the theory of free fields, but their existence is predicted by the theory of interacting fields.

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.