Semiclassical Radiation Theory Research Articles

Plasmonic quantum yield enhancement of a single molecule near a nanoegg

We investigate the impact of the dipole-active modes formed via the mode-mixing of the dipole mode with higher-order surface plasmon modes of a nanoegg on the radiative decay rate and quantum yield of an excited molecule near the nanoegg. The Purcell factor, rate of power dissipation by the emitter, and antenna efficiency of the nanoegg, as well as quantum yield enhancement of the emitter, were studied using the quasistatic approximation and the semiclassical theory of radiation, following the Gersten–Nitzan and Ford–Weber approaches. Compared to the concentric nanoshell, we show that the dielectric core–metallic shell nanoegg is a more efficient plasmonic nanoantenna for radiative decay rate enhancement of single emitters. The quantum yield of the emitter was found to be more enhanced near the nanoshell, while its emission rate was found to be more enhanced near the nanoegg.

Radiation fields for nanoscale systems

Abstractmagnified imageFor a group of charged particles obeying quantum mechanics (QM) and interacting with an electromagnetic field, the charge, and current density in a pure state of the system are expressed in terms of the many‐body wave function. Using these as sources, the microscopic Maxwell equations can be written down for any given pure state of a many‐body system. By employing semi‐classical radiation theory (SCRT) with these sources, the microscopic Maxwell equations can be used to compute the strong radiation fields produced by interacting charged quantal particles. For a charged particle, three radiation fields involve only the vector potential A. This is another example demonstrating the observability of the vector potential. Five radiation fields are perpendicular to the canonical momentum of a single charged particle. For a group of charged particles, a new type of radiation field is predicted. This kind of radiation does not exist for a single charged particle. The macroscopic Maxwell equations are derived from the corresponding microscopic equations for a pure state by the Russakoff–Robinson procedure which requires only a spatial coarse graining. Because the sources of fields are also the responses of a system to an external field, one also has to give up the temporal coarse graining of the current density which is often supposed to be critical to the kinetic approach of conductivity.

Coherent effects in the incoherent channel of resonant radiation scattering from excited atoms

Scattering of a resonance electromagnetic field from excited atoms cannot be described by the semiclassical theory of radiation operating with nonquantized electromagnetic fields. Field quantization effects are manifested in this case on the macroscopic level and lead to evolution of statistical properties of radiation in the course of scattering. It is found that a combined process coupling elastic scattering from an atom and induced emission from the same atom, which cannot be studied by the methods of the standard perturbation theory, plays a significant role in this effect. The process of combined scattering in extended media exhibits coherent properties that cannot be described by the standard refractive index.

Quantum and semiclassical polarization correlations

We analyze the strength of polarization correlations between two light beams that can be achieved in the semiclassical regime using statistical mixtures of coherent states and binary on/off detectors. Under certain symmetry assumptions, the visibility of polarization correlations is shown to be bounded by 1 3 , which is in a striking contrast with perfect 100% correlations exhibited by photon pairs prepared in the singlet state. The semiclassical limit is demonstrated in a measurement performed on a pair of laser beams undergoing correlated depolarization. This result illustrates the dramatic difference between predictions of quantum mechanics and the semiclassical theory of electromagnetic radiation for the polarization degree of freedom.

Spin light identification in the presence of power synchrotron radiation

The relativistic radiation theory of the intrinsic magnetic moment of an electron (which is known as spin light) from the point of view of the correspondence principle of classical, semi-classical and quantum theory of radiation is discussed. It is shown that after separation of terms unbound with a spin in the power of the total radiation of electrons (with the example of the synchrotron radiation of an electron) the correspondence principle holds accurate within a second approximation by Plank’s constant. The formulas for the angular distribution, linear polarization and spectral structure of radiation obtainable here with an allowance for spin can find application for non-trivial problems of experimental identification of spin light.

Semiclassical theory of charged pion radiation by nucleons in a strong homogeneous magnetic field

Charged pions produced in very high energy hadronic interactions might be the dominant source of cosmic neutrinos in the GeV–TeV range. The spectral energy power of π+ radiation by high-energy protons moving in strong magnetic fields typical for magnetars is determined with a semiclassical treatment of the effective pion–nucleon model. The main characteristics emerging from a saddle-point approximation to the summation over the allowed range of Landau levels is a sharp lower cut: Eπ ⩾ 0.25Ep. The magnitude of the spectral power agrees in this region with the synchrotron radiation spectra of neutral pions.

Manipulating the phase of a single-mode micromaser by polarized three-level atoms

We investigate the phase probability distribution (PPD) of a single-mode micromaser pumped by atoms injected in the most general case, i.e. in the superposition of the upper, intermediate and lower states by the Monte Carlo wave function approach. The phase properties of the cavity mode are greatly influenced by the relative phases and the amplitudes of the polarized atoms, and the detunings between the atom and cavity. The cavity field has a single preferred phase if the cavity is pumped by the atoms in the superposition of the upper and intermediate states or of the intermediate and lower states. However, a double-peak feature appears in the PPD of the cavity field when the cavity is pumped by the atoms in the superposition of the upper and lower states. With appropriate detunings, the double peaks become narrower and more remarkable, which shows the better defined phase of the cavity field, as compared to the resonant case. The PPD displays complicated characteristics when the cavity is pumped by the atoms in the superposition of the upper, intermediate and lower states. The phase distribution changes from a single peak to double peaks and to another single peak when we modulate the phase of the intermediate state, which has been explained in the semi-classical radiation theory.

Observation of Sub-Poisson Fluctuations in the Intensity of the Seventh Coherent Spontaneous Harmonic Emitted by a rf Linac Free-Electron Laser

We report the observation of sub-Poisson intensity fluctuations in the coherent spontaneous harmonic radiation generated by an infrared free-electron laser in a photon counting experiment using a well-defined ensemble of electron pulses. These observations constitute the first observation of a nonclassical state of the radiation field generated by a beam of free electrons. The fluctuations observed in the experiment are smaller than those expected from semiclassical radiation theory, and larger than those expected from electron shot noise.

Semiclassical theory of Compton and photoelectric effects

Scattering of a plane electromagnetic wave by free and bound wave packets is analyzed by semiclassical radiation theory. It is shown that the theory gives the correct answer to the question of radiation intensity in the photoelectric effect and to the correlation problem in Compton scattering. The expression for the intensity of the scattered radiation differs from the cross section which is derived from the model based on the particle nature of the electromagnetic field. The meaning of this difference is discussed. Low frequency spectrum of the scattered radiation on a bound charge is obtained.

Synchrotron radiation and spin light

Spin light, or μ-radiation, is a new phenomenon of nature, which observation has become possible due to development of technology of the elementary particles acceleration. In this work the description of the Novosibirsk experiment, where the spin dependence of synchrotron radiation was observed for the first time, is given. It is shown, that the spin light is decomposed to different on principle μL- and μTh-radiation types. μL-radiation is conditioned by Larmor precision of the intrinsic magnetic moment of the electron (and its anomalous part), while μTh-radiation is connected with Thomas precession of the electron spin and has pure kinematic origin. In the relativistic quantum theory of radiation based on the Dirac equation. μL-radiation and μTh-radiation do not differ one from another and from the other quantum effects of electron radiation. Separate consideration is possible only in Jackson's relativistic semiclassical radiation theory used in the given work.

Selective reflection of resonance radiation from excited media

According to quantum electrodynamics, the cross section for resonant scattering of radiation on an aggregate of excited atoms can be written as a sum of positive definite terms. This type of structure is not consistent with the Fresnel formulas for the reflection coefficient of radiation from thermally excited media. The difference shows up on a macroscopic level and indicates that semiclassical radiation theory cannot be used. A study of the correlation between elastic scattering and stimulated emission processes clarifies the reason for the discrepancies. The resulting singularities require summing of Feynman diagrams which appear beginning in the sixth order of perturbation theory. A lower bound estimate for the reflection coefficient from a plane layer is given, including processes which violate the statistics of radiation. The contribution of stimulated emission processes caused by the initially scattered photon are examined specifically. An experiment is proposed which would settle the choice of theories.

Semi-classical quantum theory for cyclotron radiation

A semi-classical quantum theory of the cyclotron radiation of the nonrelativistic thermal electrons in a very strong magnetic field is presented. The basic formulae of the absorption coefficient of cyclotron resonancekvand the absorption (scattering) cross-section of cyclotron resonance σv have been derived under the quadrupole approximation. σv is an important quantity in the study of the “magnetic inverse-Compton scattering”. It is shown that σv is greatly larger than the Thomson cross-sectron σT, which is important in discussing the magnetic inverse-Compton scattering of the relativistic electrons in a very strong magnetic field.

Simplified formulae of quantum cyclotron radiation

Using a semi-classical quantum theory of the cyclotron radiation of a nonrelativistic thermal electron in a very strong magnetic field, we present the simplified formulae of the absorption coefficient of cyclotron resonance k v and the absorption and/or scattering cross section of cyclotron resonance σ v at base frequency ω B ≡ eB m 0c in the quadrupole approximation. The results can be conveniently used for studying the “magnetic inverse-Compton scattering”, an important radiation mechanism in gamma-ray astronomy.

Radiation Pressure in a Superdense Electron Plasma

An expression for the radiation pressure in high density plasma is derived on the basis of plasma waves and semiclassical theory of radiation. Comparison of our result with that of Planck, Sommerfeld and Landau and Lifshitz is briefly discussed. It is shown that the radiation pressure in a high density plasma is not just one third of the corresponding energy density because of the different dependence on the index of refraction n (ω). Possible applications to the thermal history of early universe and late stage stellar evolution are also stressed.

Positivity of entropy in the semiclassical theory of black holes and radiation.

Quantum stress-energy tensors of fields renormalized on a Schwarzschild background violate the classical energy conditions near the black hole. Nevertheless, the associated equilibrium thermodynamical entropy $\Delta S$ by which such fields augment the usual black hole entropy is found to be positive. More precisely, the derivative of $\Delta S$ with respect to radius, at fixed black hole mass, is found to vanish at the horizon for {\it all} regular renormalized stress-energy quantum tensors. For the cases of conformal scalar fields and U(1) gauge fields, the corresponding second derivative is positive, indicating that $\Delta S$ has a local minimum there. Explicit calculation shows that indeed $\Delta S$ increases monotonically for increasing radius and is positive. (The same conclusions hold for a massless spin 1/2 field, but the accuracy of the stress-energy tensor we employ has not been confirmed, in contrast to the scalar and vector cases). None of these results would hold if the back-reaction of the radiation on the spacetime geometry were ignored; consequently, one must regard $\Delta S$ as arising from both the radiation fields and their effects on the gravitational field. The back-reaction, no matter how "small",

Positivity of entropy in the semiclassical theory of black holes and radiation

Positivity of entropy in the semiclassical theory of black holes and radiation

Operational approach to the phase of a quantum field.

We examine the problem of determining the phase difference between two optical fields, first for classical and later for quantum fields, by reference to two simple measurement schemes that yield the sine and/or cosine of the phase difference between classical fields. We show that certain difficulties exist even within the framework of semiclassical radiation theory when the field is very weak, and particularly when amplitude and phase fluctuations are correlated. We find that a clear distinction has to be made between the measured values of the sine or cosine and the values that can be inferred from a series of repeated measurements. A corresponding distinction can be made also for a quantum field, although the interpretation is not the same. The dynamical variables chosen to represent the cosine and sine that emerge from the discussion of the measurement schemes commute when the sine and cosine are obtained together, but not when the measurement yields one or the other. These sine and cosine operators have well-defined values only when there is a large dispersion of the photon number. We arrive at expressions for the moments of the measured and of the inferred sines and cosines that differ from most previous treatments. The expressions are applied to optical fields in several different quantum states. Only for the Fock state and for the so-called phase state, which was treated recently at some length by Pegg and Barnett [Phys. Rev. A 39, 1665 (1989)], do the measured and the inferred moments coincide. Our analysis of the problem of phase measurement leads to the conclusion that the appropriate dynamical variables for the measured sine and cosine depend on the measurement scheme, and that different schemes correspond to different operators.

Semi-classical approximation and the problem of boundary conditions in the theory of relativistic particle radiation

Abstract The process of relativistic particle radiation in an external field has been studied in the semi-classical approximation rather extensively. The main problem arising in the studies is to express the formula of the quantum theory of radiation in terms of classical quantities, for example of the classical trajectories. However, it still remains unclear how the particle trajectory is assigned, that is which particular initial or boundary conditions determine the trajectory in semi-classical approximation quantum theory of radiation. We shall try to solve this problem. Its importance comes from the fact that in some cases one and the same boundary conditions may give rise to two or more trajectories. We demonstrate that this fact must necessarily be taken into account on deriving the classical limit for the formulae of the quantum theory of radiation, since it leads to a specific interference effect in radiation. The method we used to deal with the problem is similar to the method employed by Fock to...

Self-fields in semiclassical radiation theory.

The interaction of an atomic system with an unquantized electromagnetic field is studied by means of the Heisenberg-operator equations of motion. The electromagnetic fields created by the atom are taken into account by assuming that the charge and probability current densities are the actual charge and current source terms in Maxwell's equation. When Ehrenfest's theorem is written to order (1/c${)}^{2}$, the equations of motion are found to have a constant of motion that can be interpreted as stating that the sum of the atomic energy, energy of interaction, and energy stored in the electromagnetic field is constant. This constant of integration can be expressed as an expectation of a new semiclassical Hamiltonian that now includes the effects of the atomic self-fields to order 1/${\mathit{c}}^{2}$. This Hamiltonian is related to the classical Darwin Lagrangian. Since the new approximate Hamiltonian is the sum of an atomic and a field Hamiltonian, it provides a formulation of semiclassical radiation theory that is formally close to the usual formulation of quantum electrodynamics. A Schr\"odinger equation can be derived by applying the variational principle to the expectation of the new Hamiltonian. The result is a nonlinear integro-differential equation, in \ensuremath{\Psi}, which is somewhat similar to Hartree's self-consistent equation for a multielectron atom.When the Heisenberg equations are written to include the next-higher-order terms, 1/${\mathit{c}}^{3}$, it is found that the total energy of the atom and the electromagnetic field in the vicinity of the atom decreases at a rate that is given by the Larmor power formula (2${\mathit{e}}^{2}$/3${\mathit{c}}^{3}$)(d〈v〉/dt${)}^{2}$, where 〈v〉 is the quantum-mechanical expectation of the electron's velocity operator. This approximate formulation of semiclassical radiation theory is applied to semiclassical calculations of atomic radiative shifts. It is then shown that, if some retardation effects are included to all orders of 1/c in the vector potential, the semiclassical analysis provides a formula for radiative energy-level shifts that are time dependent and that contain coefficients similar to the starting point of the Bethe calculation of the Lamb shift. The incorporation of mass renormalization in semiclassical theory is then discussed.

Bifurcation phenomena in a system of two-level atoms in front of a phase-conjugate mirror

The coherent interaction between a sample of two-level atoms and a phase-conjugate mirror is studied using a model based on semiclassical radiation theory. We show that the dynamics of our model has an analogy with the dynamics of the classical one-dimensional motion in a potential well. When frequency chirping is taken into account we find different bifurcation phenomena. It is shown that periodic emission of radiation from the sample may occur involving only superradiant states.