Quantization Of Electromagnetic Field Research Articles

Quantum optics of a quantum dot: Local-field effects

The role of local fields in quantum electrodynamics of isolated quantum dot (QD) has been analyzed. The system is modeled as a strongly confined in space two-level quantum oscillator illuminated by quantum light. Relation between local and acting fields in QD has been derived in the dipole approximation from the integral Maxwell equations for electromagnetic field operators. A formalism of the electromagnetic field quantization in electrically small scatterers has been developed. As a result, Hamiltonian of the system has been formulated in terms of the acting field with a separate term responsible for the effect of depolarization. Schroedinger equation with that Hamiltonian has been solved in linear approximation. Interaction of QD with different quantum states of light, such as Fock states, coherent states, Fock qubits, entangled states, has been analyzed. It has been shown that the local-fields induce a fine structure of the QD absorption (emission) spectrum: instead of a single line with the frequency corresponding to the exciton transition, a doublet appears with one component shifted to the blue (red). The value of the shift depends only on the geometrical and electronic properties of QD while the intensities of components are completely determined by the quantum light statistics. Itmore » has been demonstrated that in the limiting cases of classical light and single-photon state the doublet is reduced to a singlet shifted in the former case and unshifted in the latter one. A physical interpretation of the predicted effect has been proposed. Possible ways of experimental observation of the effect has been discussed together with the potentiality of its utilization in the quantum information processing.« less

Quantum theory of electromagnetic field for a dielectric–dielectric interface in three dimensions

The three dimensional scheme of the Green function approach of the electromagnetic field quantization is extended to the background medium made up of two adjacent semi-infinite dielectrics which show both loss and dispersion. It is shown that this system separates into a singlet system providing the normal polarization state of the electric field and a doublet system giving both the parallel state of polarization and the longitudinal part of the field. The longitudinal field expression is also derived by using the usual approach of vector decomposition. The overall results enable us to present the form of the field operators for each state of polarization as well as the longitudinal field contribution. The equal-time canonical commutation relations between the vector potential operator and its conjugate generalized momentum are verified in each case.

Electronic Wave Packet in a Quantized Electromagnetic Field

We study a non-stationary electronic wave packet in a quantizedelectromagnetic field. Generally, the electron and field becomeentangled as the electronic wave packet evolves. Here we find that,when the initial photon state is a coherent one, the wavefunction ofthe system can be factorized if we neglect the transferred photonnumber. In this case, the quantized-field calculation is equivalent tothe semi-classical calculation.

Quantum electromagnetic field in a three-dimensional oscillating cavity

We compute the photon creation inside a perfectly conducting, three-dimensional oscillating cavity, taking the polarization of the electromagnetic field into account. As the boundary conditions for this field are both of Dirichlet and (generalized) Neumann type, we analyze as a preliminary step the dynamical Casimir effect for a scalar field satisfying generalized Neumann boundary conditions. We show that particle production is enhanced with respect to the case of Dirichlet boundary conditions. Then we consider the transverse electric and transverse magnetic polarizations of the electromagnetic field. For resonant frequencies, the total number of photons grows exponentially in time for both polarizations, the rate being greater for transverse magnetic modes.

Nonclassical current fluctuation in a mesoscopic ring responded by a squeezed coherent state quantum field

We have investigated the quantum fluctuation of electron in a mesoscopic ring interacting with a quantum electromagnetic field (QEMF) in squeezed coherent state (SCS). The nonclassical AB, AC effects and dynamic current fluctuation are associated with the U(1)× SU(2) gauge quantum field. The dynamic current fluctuation is dependent on the quantum nature of external QEMF. The Zeeman split term takes effect in the dynamic current fluctuation, while it disappears as ω→0. This means that the scalar AC effect does not contribute to static current fluctuation. The time-dependent and temperature dependent situations are studied versus time and temperature, which reveal quite different behaviors for zero-temperature and finite-temperature systems.

Drastic violation of the U-matrix boundary condition by quantum-field theoretical on-shell renormalization and a new consistent renormalization concept involving bound-state problems

By generalizing the Gell-Mann–Low formula and applying the self-consistent projection-operator method, developed a decade ago by the present author, a connecting equation between the fermion propagator (involving the interaction with the quantum electromagnetic field in the presence of an external field) and the U-matrix elements, being valid to any order of the fermion–photon interaction, is derived. After proving rigorously, the drastic violation of the U-matrix boundary condition ( U( t, t)=1) by the conventional on-shell renormalization of the fermion propagator (removal of free-fermion pole and residue corrections), the absolute necessity for the formulation of a new renormalization concept becomes self-evident. This latter is achieved in the present paper by elaborating a consistent renormalization procedure, based on the self-consistent projection-operator method (which, unlike the standard perturbation method, guarantees the consistency of the applied approximation to any order as to the strength of the interaction). The new complete renormalization, unlike the conventional one, removes completely the experimentally unobservable free-electron Dyson self-energy from the fermion propagator. By applying the new concept, for the first time, consistently renormalized contributions (up to the fourth order) to the bound-electron self-energy function with the corresponding Feynman diagrams are derived.

Photons in a semibounded dielectric and the surface effect on spontaneous emission in nanostructures

Quantization of electromagnetic field in isotropic dielectric medium occupying a half space is carried out. For a dielectric having a plane boundary with vacuum, we have constructed a complete orthonormal set of light waves propagating in a whole space. Using this set we calculated the rate of spontaneous emission of photons by electrons in quantum dots and quantum wells. We predict oscillations of photon emission rate as a function of the distance between a quantum nanostructure and the surface.

Quantifying Nonclassicality of One-Mode Gaussian States of the Radiation Field

We define the degree of nonclassicality of a one-mode Gaussian state of the quantum electromagnetic field in terms of the Bures distance between the state and the set of all classical one-mode Gaussian states. We find the closest classical Gaussian state and the degree of nonclassicality using a recently established expression for the Uhlmann fidelity of two single-mode Gaussian states. The decrease of nonclassicality under thermal mapping is carefully analyzed. Along the same lines, we finally present the evolution of nonclassicality during linear amplification.

Field quantization, photons and non-Hermitean modes

Field quantization in unstable optical systems is treated by expanding the vector potential in terms of non-Hermitean (Fox-Li) modes. We define non-Hermitean modes and their adjoints in both the cavity and external regions and make use of the important bi-orthogonality relationships that exist within each mode set. We employ a standard canonical quantization procedure involving the introduction of generalized coordinates and momenta for the electromagnetic (EM) field. Three-dimensional systems are treated, making use of the paraxial and monochromaticity approximations for the cavity non-Hermitean modes. We show that the quantum EM field is equivalent to a set of quantum harmonic oscillators (QHOs), associated with either the cavity or the external region non-Hermitean modes, and thus confirming the validity of the photon model in unstable optical systems. Unlike in the conventional (Hermitean mode) case, the annihilation and creation operators we define for each QHO are not Hermitean adjoints. It is shown that the quantum Hamiltonian for the EM field is the sum of non-commuting cavity and external region contributions, each of which can be expressed as a sum of independent QHO Hamiltonians for each non-Hermitean mode, except that the external field Hamiltonian also includes a coupling term responsible for external non-Hermitean mode photon exchange processes. The non-commutativity of certain cavity and external region annihilation and creation operators is associated with cavity energy gain and loss processes, and may be described in terms of surface integrals involving cavity and external region non-Hermitean mode functions on the cavity-external region boundary. Using the essential states approach and the rotating wave approximation, our results are applied to the spontaneous decay of a two-level atom inside an unstable cavity. We find that atomic transitions leading to cavity non-Hermitean mode photon absorption are associated with a different coupling constant to that for transitions leading to photon emission, a feature consequent on the use of non-Hermitean mode functions. We show that under certain conditions the spontaneous decay rate is enhanced by the Petermann factor.

Casimir force between two dielectric slabs

We examine the Casimir effect between two dispersive dissipative slabs in three dimensions. The dielectric function of the slabs is assumed to be an arbitrary complex function of frequency satisfying Kramers-Kronig relations. The Maxwell stress tensor is used to evaluate the vacuum radiation pressure of the electromagnetic field on each slab in terms of the field correlation functions. These correlations are simply related to the imaginary part of the vector potential Green function by using the fluctuation dissipation theorem and Kubo's formula. The response function is obtained by employing the standard method for the present configuration. The formalism enables us to calculate the attractive Casimir force between a pair of dielectric slabs without resorting to the electromagnetic field quantization. Special attention is paid to the various limits of the general expression and the results are compared with previous work whenever possible. The Lorentz model of the dielectric function is also used to show the typical behavior of this force in terms of the slab thickness. We also consider the effect of finite temperature on the Casimir force between two dielectric slabs.

Microscopic calculation of noise current operators for electromagnetic field quantization in absorbing material systems

We present a microscopic quantization scheme for the electromagnetic field in dispersive and lossy dielectrics of arbitrary geometry. This method also describes anisotropic media and media driven by light field via a spatially nonlocal permittivity. The method removes the need for complicated diagonalization of material, reservoir and field variables and allows us to include the effect of all the material excitations. Dissipation inside the medium is described by considering the coupling of the polarization quanta of the system with the reservoir oscillators in the usual Langevin approach.

Canonical theory of electromagnetic field quantization in dielectrics

We introduce a fully canonical theory for QED in a lossy dispersive dielectric without recourse to the detailed properties of the material medium and its interaction with the radiation field. The formalism relies only on the causal behavior of the medium by assuming that its dielectric function necessarily satisfies the Kramers–Kronig relations. This scheme is based on the Lagrangian approach and it is shown that the field operators are those given by the Green function method of the electromagnetic field quantization. Special attention is paid to the form of the Hamiltonian with which the coupling process of the dressed annihilation and creation operators as well as the dispersion relations are clarified. We also impose appropriate limits to display the consistency check of the formulation for nondissipative media and free space.

Quantization of the electromagnetic field outside static black holes and its application to low-energy phenomena

We discuss the Gupta-Bleuler quantization of the free electromagnetic field outside static black holes in the Boulware vacuum. We use a gauge which reduces to the Feynman gauge in Minkowski spacetime. We also discuss its relation with gauges used previously. Then we apply the low-energy sector of this field theory to investigate some low-energy phenomena. First, we discuss the response rate of a static charge outside the Schwarzschild black hole in four dimensions. Next, motivated by string physics, we compute the absorption cross sections of low-energy plane waves for the Schwarzschild and extreme Reissner-Nordstrom black holes in arbitrary dimensions higher than three.

Quantum electromagnetic fields in the presence of adielectric microsphere

A general quantization scheme of the electromagnetic (EM) fields,including the near-field, of a dielectric material is presented.By expanding the classical EM fields in terms of orthonormalmodes, the Lagrangian is expressed as a sum of the Lagrangiansof the independent harmonic oscillators. For a dielectricsphere, as an example, two possible modes satisfying the boundaryconditions, as well as the orthonormality conditions, areexplicitly obtained: spherical modes and Mie modes. Using thesemodes, the EM fields are quantized and the transformationbetween two one-photon states having different modes is alsodiscussed. We apply our results to calculate the expectationvalue of the quantum momentum-density operator for a one-photonstate and show that it is equivalent to the classical Poyntingvector. Our rigorous results may be useful in the study of thequantum optical properties of the EM near-fields of adielectric microsphere of sub-wavelength size.

Decoherence of Schrödinger cat states in a Luttinger liquid

Schrodinger cat states built from quantum superpositions of left or right Luttinger fermions located at different positions in a spinless Luttinger liquid are considered. Their decoherence rates are computed within the bosonization approach using as environments the quantum electromagnetic field or two or three dimensionnal acoustic phonon baths. Emphasis is put on the differences between the electromagnetic and acoustic environments.

Equivalence of the Duffin-Kemmer-Petiau and Klein-Gordon-Fock equations

A strict proof of equivalence between Duffin-Kemmer-Petiau (DKP) and Klein-Gordon (KG) theories is presented for physical S-matrix elements in the case of charged scalar particles interacting in minimal way with an external or quantized electromagnetic field. First, Hamiltonian canonical approach to DKP theory is developed in both component and matrix form. The theory is then quantized through the construction of the generating functional for Green functions (GF) and the physical matrix elements of S-matrix are proved to be relativistic invariants. The equivalence between both theories is then proved using the connection between GF and the elements of S-matrix, including the case of only many photons states, and for more general conditions - so called reduction formulas of Lehmann, Symanzik, Zimmermann.

Scattering of coherent light by a dielectric slab

We discuss a fully quantum mechanical theory of the scattering of coherent light by a dissipative dispersive slab. The Green function scheme of the electromagnetic field quantization is used as the base formalism to express the scattered field modes in terms of the incident modes. The theory applies to the transmission of light perpendicular to the slab interfaces. The single-mode as well as the continuum-mode propagation are considered in detail. Special attention is paid to the increase of the noise properties when the coherent light is scattered by a lossy dispersive slab. The power spectrum and the average normal order Poynting vector are both evaluated for the forward and backward scattered light pulses. The results are simplified analytically in the narrow band-width approximation.

On equivalence of Duffin-Kemmer-Petiau and Klein-Gordon equations

A strict proof of equivalence between Duffin-Kemmer-Petiau (DKP) and Klein-Gordon (KG) theories is presented for physical S-matrix elements in the case of charged scalar particles interacting in minimal way with an external or quantized electromagnetic field. First, Hamiltonian canonical approach to DKP theory is developed in matrix form. The theory is then quantized through the construction of the generating functional for Green functions (GF) and the physical matrix elements of S-matrix are proved to be relativistic invariants. The equivalence between both theories is then proved using the connection between GF and the elements of S-matrix in reduction formulas of Lehmann, Symanzik, Zimmermann.

Is There a Flaw in the Seminal Bohr‐Rosenfeld Paper on the Measurement Problem of the Free Quantum Electromagnetic Field?

In 1933, Bohr and Rosenfeld published a seminal paper in which they claimed to solve the measurement problem of the free quantum electromagnetic field. In 1951, however, Corinaldesi discovered, in the analysis of the above-mentioned authors, an error in the order of magnitude of a certain critical field. This paper shows, through a comparative analysis between the results of Bohr and Rosenfeld and Corinaldesi, that the error discovered by the latter does not affect the conclusions of the former. It is also possible to consider as a deficiency of their work the fact that Bohr and Rosenfeld never responded to the mistake found by Corinaldesi. It will be shown here that in fact Bohr and Rosenfeld studied a measurement situation, the problem of which was equal to the one that would be originated if the correction of Corinaldesi were taken into account.

Three-dimensional electromagnetic field quantization in absorbing and dispersive bounded dielectrics

We present a quantization scheme for the electromagnetic field in dispersive and lossy dielectrics with planar interfaces, incorporating propagation in all the spatial directions, and including both TE and TM polarized fields. Field quantization is carried out starting from a microscopic model for the polarization quanta interacting with the electromagnetic field. Dissipation is described by considering the coupling of the polarization quanta of the system with the reservoir oscillators in the usual Langevin approach. The method is applied to a semi-infinite medium and expressions for the electromagnetic field operators are obtained in the two different spatial regions, i.e., in the vacuum and in the dielectric. As a check of our quantization scheme, we have verified that the obtained vector potential operator and its conjugate momentum satisfy equal-time canonical commutation rules, giving rise to the prescribed transverse Dirac $\ensuremath{\delta}$ function.