Virtual photon exchange,intermolecular interactions and optical response functions

According to molecular quantum electrodynamics, coupling between material particles occurs due to an exchange of one or more virtual photons. In this work, the relationship between polarisability and hyperpolarisability tensors of atoms and molecules that feature in linear and nonlinear optical processes, and their analytically continued form in the complex frequency domain that appear in formulae describing fundamental inter-particle interactions, is studied. Examples involving a single virtual photon exchange, which are linearly proportional to electric dipole moments at each centre, include the electrostatic energy and the resonant transfer of excitation energy. The Casimir–Polder dispersion potential, and its discriminatory counterpart applicable to coupled chiral molecules, are used to illustrate response properties depending on the exchange of two virtual photons. Meanwhile, the energy shift between two hyperpolarisable species, a higher order discriminatory contribution to the dispersion potential, is employed to represent forces arising from the three virtual photon exchange. It is shown that for energy shifts that are quadratic or bilinear or cubic in the transition dipole moment, it is necessary to account for all two- and three-photon optical processes, such as absorption, emission and linear and nonlinear scattering of light in order to arrive at the correct form of the molecular response tensor.     

Measurements of the QED structure of the photon

The structure of both quasi-real and highly virtual photons is investigated using the reaction , proceeding via the exchange of two photons. The results are based on the complete OPAL dataset taken at centre-of-mass energies close to the mass of the Z boson. The QED structure function and the differential cross-section for quasi-real photons are obtained as functions of the fractional momentum x from the muon momentum which is carried by the struck muon in the quasi-real photon for values of ranging from 1.5 to 400 GeV. The differential cross-section for highly virtual photons is measured for GeV and GeV, where and are the negative values of the four-momentum squared of the two photons such that . Based on azimuthal correlations the QED structure functions and for quasi-real photons are determined for an average of 5.4 GeV. Received: 8 February 1999 / Published online: 28 September 1999     

From Faraday rotation to “Faraday oscillation”: Coherence effect between real and virtual excitons

This work provides the microscopic mechanisms responsible for circular birefringence changed into linear birefringence when the polarization of the excitons present in a semiconductor sample goes from circular to linear. This change shows up as Faraday rotation turning to “Faraday oscillation”: The probe polarization plane oscillates instead of rotates while the polarization goes from linear to elliptical and linear again. This oscillation, which reduces to zero when the probe polarization is parallel or perpendicular to the exciton polarization, comes from a non trivial coherence effect between real excitons present in the sample and virtual excitons coupled to unabsorbed photons. While Faraday rotation mainly follows from one single carrier exchange between composite excitons in the absence of Coulomb interaction, Faraday oscillation requires two Coulomb interactions plus a double carrier exchange, the virtual excitons coupled to the unabsorbed “in” and “out” photons being made with different electrons and holes, as nicely revealed by Shiva diagrams which visualize the many-body physics taking place in composite-exciton systems.     

Estimation of photonic multipolar coupling ranges among quantum dots on the basis of time–energy uncertainty

We give a real use of the time–energy uncertainty principle for nanostructure circuit design consideration. The range of virtual as well as real photons mediating interactions among nanostructures is estimated as the product of the photon lifetime and its velocity, as in the meson exchange model for nucleon. This gives a new vista for near field interactions of electric nature in a solid, especially for the nonradiative internal energy transfer, which may be called the resonance dynamic multipole–multipole interaction (RDMMI). The length of the transition dipole is deduced from the 0.3 meV fine structure in our microphotoluminescence spectra of an individual coupled GaAs asymmetric quantum dots. Various multipoles and their potentials are estimated employing this dipole length. Then the ranges and lifetimes of the RDMMI are derived and plotted, together with the spatiotemporal consideration and the provisional structure of quantum circuits.     

Superfluidity of coherent light in self-focusing nonlinear waveguides

We establish the superfluidity theory of coherent light in waveguides made of nonlinear polar crystals.It is found that the pairing state of photons in a nonlinear polar crystal is the photonic superfluid state.The photon-photon interaction potential is an attractive effective interaction by exchange of virtual optical phonons.In the traveling-wave pairing state of photons,the photon number is conserved,which is similar to the Bose-Einstein condensation(BEC) state of photons.In analogy to the BCS-BEC crossover theory of superconductivity,we derive a set of coupled order parameter and number equations,which determine the solution of the traveling-wave superfluid state of photons.This solution gives the critical velocity of light in a self-focusing nonlinear waveguide.The most important property of the photonic superfluid state is that the system of photon pairs evolves without scattering attenuations.     

Superfluid state of coherent light in nonlinear waveguides

We establish the photonic superfluid theory in waveguides made of self-defocussing polar crystals. In quantum theory it is shown that photons can sense an attractive effective interaction by exchange of virtual optical phonons. Such an interaction leads to the photonic superfluid state, in which a propagating photon pair consists of a combination of two photons with opposite transverse wave vector and spins. The most important property of the photonic superfluid state is that the system of photon pairs evolves without scattering attenuations. The traveling-wave superfluid state has the squeezing property and the soliton effect.     

The problem of two electrons in an external field and the method of integral equations in optics

This paper solves the problem of the interaction, via the field of virtual photon field with the emission or absorption of a real photon, of two atomic electrons located at arbitrary distances from one another. The interaction is interpreted as a third-order QED effect in the coordinate representation. The role of intermediate states with positive and negative frequencies is studied. A general expression is derived for the matrix elements of the operator of the effective electron-electron interaction energy for different types of quantum transitions. The expression makes it possible to calculate the probabilities of the corresponding transitions and to examine various patterns of induction of polarizing fields by one atom at the point occupied by the other atom. The exchange of virtual photons between the atoms located at arbitrary distances from one another is shown to lead to additional terms in the operators of spin-orbit and spin-spin coupling of the atomic electrons, over and above those in the corresponding Breit operators. It is shown that there is an important difference between the induction of polarizing fields and the transfer of optical photons. In particular, it is found that when polarizing fields are induced, a situation may arise in which the disappearance (production) of a photon takes place at the point occupied by one atom, while absorption (emission) of the same photon occurs at the place occupied by the other atom. A block diagram of an experimental device that could be used to study this property of polarizing fields is presented. Finally, a method of deriving integral field equations is proposed. The method is based on allowing for polarizing fields, and its effectiveness is demonstrated by the example of electric dipole and spin transitions in the spectrum of interacting atomic electrons. Zh. éksp. Teor. Fiz. 114, 1555–1577 (November 1998)     

Exchange and dipolar interactions in solid organic radicals

Investigations of the E.S.R. linewidths of exchange narrowed lines from solid organic free radicals allow one to obtain information about both the exchange interaction and the electron-electron dipolar interaction in some instances. In cases in which the dipolar interaction is incompletely averaged by spin exchange one can use the frequency dependence of the E.S.R. linewidth to determine the magnitudes of the exchange frequency and the dipolar interaction. This paper reports results from a study of the frequency and temperature dependence of the linewidth of four solid organic radicals. The dipole-dipole interaction of the two nitroxide radicals included in this study was found to be temperature dependent, indicating changes in intermolecular spin separation with temperature. The exchange energy of these two radicals appeared to vary exponentially with the separation of the spins through most of the temperature interval which was investigated.     

Consequences of gravity-induced couplings in theories with many particle species

In theories with many copies of the Standard Model virtual black hole exchange may produce effective higher-dimensional operators that can be treated below the cutoff scale as fundamental vertices of interspecies non-gravitational interaction. We consider the vertex that couples fermions of one species through magnetic moment to photons of other species, and study the quantum corrections it generates. In particular, we find kinetic mixing between photons of different species produced via fermion loops. Diagonalization of gauge kinetic terms then renders the fermions millicharged under other species' electromagnetism. We explore some phenomenological consequences of such effects by considering possible observable signatures in collider experiments and constraining the interaction strength. The derived bounds are in agreement with non-democratic nature of micro black hole coupling.     

A Study of Dipolar Interactions and Dynamic Processes of Water Molecules in Tendon byH andH Homonuclear and Heteronuclear Multiple-Quantum-Filtered NMR Spectroscopy

The effect of proton exchange on the measurement of¹H–¹H,¹H–²H, and²H–²H residual dipolar interactions in water molecules in bovine Achilles tendons was investigated using double-quantum-filtered (DQF) NMR and new pulse sequences based on heteronuclear and homonuclear multiple-quantum filtering (MQF). Derivation of theoretical expressions for these techniques allowed evaluation of the¹H–¹H and¹H–²H residual dipolar interactions and the proton exchange rate at a temperature of 24°C and above, where no dipolar splitting is evident. The values obtained for these parameters at 24°C were 300 and 50 Hz and 3000 s⁻¹, respectively. The results for the residual dipolar interactions were verified by repeating the above measurements at a temperature of 1.5°C, where the spectra of the H₂O molecules were well resolved, so that the¹H–¹H dipolar interaction could be determined directly from the observed splitting. Analysis of the MQF experiments at 1.5°C, where the proton exchange was in the intermediate regime for the¹H–²H dipolar interaction, confirmed the result obtained at 24°C for this interaction. A strong dependence of the intensities of the MQF signals on the proton exchange rate, in the intermediate and the fast exchange regimes, was observed and theoretically interpreted. This leads to the conclusion that the MQF techniques are mostly useful for tissues where the residual dipolar interaction is not significantly smaller than the proton exchange rate. Dependence of the relaxation times and signal intensities of the MQF experiments on the orientation of the tendon with respect to the magnetic field was observed and analyzed. One of the results of the theoretical analysis is that, in the fast exchange regime, the signal decay rates in the MQF experiments as well as in the spin echo or CPMG pulse sequences (T₂) depend on the orientation as the square of the second-rank Legendre polynomial.     

Canonical quantization of the electromagnetic field with Dirac's monopoles

From a lagrangian theory of charge-monopole electrodynamics which uses strings but is free from Dirac's veto, a hamiltonian theory is derived which describes the interaction between electric and magnetic point particles and photons.     

Electromagnetic interactions in liquid helium

The Hamiltonian of interaction of liquid helium with the quantized electromagnetic field plays an important role in such phenomena as Raman scattering, excitons, and possible cooperative effects of exchange of virtual photons. This interaction has been derived from first principles by application of an appropriate unitary transformation to the second-quantized Hamiltonian of nuclei and electrons interacting with the quantized radiation field. The transformation is chosen so that the atomic bound states appear explicitly in the relevant scattering and reaction terms of the transformed Hamiltonian.     

A study of dipolar interactions and dynamic processes of water molecules in tendon by 1H and 2H homonuclear and heteronuclear multiple-quantum-filtered NMR spectroscopy

The effect of proton exchange on the measurement of 1H-1H, 1H-2H, and 2H-2H residual dipolar interactions in water molecules in bovine Achilles tendons was investigated using double-quantum-filtered (DQF) NMR and new pulse sequences based on heteronuclear and homonuclear multiple-quantum filtering (MQF). Derivation of theoretical expressions for these techniques allowed evaluation of the 1H-1H and 1H-2H residual dipolar interactions and the proton exchange rate at a temperature of 24 degrees C and above, where no dipolar splitting is evident. The values obtained for these parameters at 24 degrees C were 300 and 50 Hz and 3000 s-1, respectively. The results for the residual dipolar interactions were verified by repeating the above measurements at a temperature of 1.5 degrees C, where the spectra of the H2O molecules were well resolved, so that the 1H-1H dipolar interaction could be determined directly from the observed splitting. Analysis of the MQF experiments at 1.5 degrees C, where the proton exchange was in the intermediate regime for the 1H-2H dipolar interaction, confirmed the result obtained at 24 degrees C for this interaction. A strong dependence of the intensities of the MQF signals on the proton exchange rate, in the intermediate and the fast exchange regimes, was observed and theoretically interpreted. This leads to the conclusion that the MQF techniques are mostly useful for tissues where the residual dipolar interaction is not significantly smaller than the proton exchange rate. Dependence of the relaxation times and signal intensities of the MQF experiments on the orientation of the tendon with respect to the magnetic field was observed and analyzed. One of the results of the theoretical analysis is that, in the fast exchange regime, the signal decay rates in the MQF experiments as well as in the spin echo or CPMG pulse sequences (T2) depend on the orientation as the square of the second-rank Legendre polynomial.     

Molecular dynamics calculation of the dielectric constant

Molecular dynamics (MD) simulations of an isolated dipolar system (made of Stockmayer molecules) has been performed. A two dimensional system has been adopted, using a ‘2-D electrostatics’ dipolar interaction.

The isolated system was a disc in vacuo. The autocorrelation function (ACF) of the moment of the disc was extracted from our runs, together with the ACF of the moment of a small inner disc (‘microscopic’ or ‘multimolecular’ ACF). Comparison of these two ACF has allowed us to compute the response function of the annulus between the two discs. The behaviour of the latter was that predicted by the theory of Fatuzzo and Mason. It is thus shown, for the first time, that one can obtain, by numerical simulation of a few hundred molecules, reliable values of the complex permittivity of highly polar fluids, despite the long range character of the dipolar interaction.

Its behaviour is surprisingly realistic when compared with that of real 3-D polar liquids.

Monomolecular ACF have also been extracted from the MD runs. They recall that of the Itinerant Oscillator model, the long time behaviour of <u(0). u(t)> being diffusive, but shorter-lived than that of the multimolecular ACF. Compared to the free rotation, the monomolecular orientational correlation time dt (u(0). u(t)> cannot be explained quantitatively using the theory of dielectric friction derived from the Onsager reaction field. Finally a comparison between this monomolecular correlation time and the multimolecular one is made: Models linking the ratio of these two times to the Kirkwood g _K factor are examined.     

Quantum phase transition between a Luttinger liquid and a gas of cold molecules

We consider cold polar molecules confined in a helical optical lattice similar to those used in holographic microfabrication. An external electric field polarizes molecules along the axis of the helix. The large-distance intermolecular dipolar interaction is attractive but the short-scale interaction is repulsive due to geometric constraints and thus prevents collapse. The interaction strength depends on the electric field. We show that a zero-temperature second-order liquid-gas transition occurs at a critical field. It can be observed under experimentally accessible conditions.     

The effect of the single-spin defect on the stability of the in-plane vortex state in 2D magnetic nanodots

The aim of this study is to analyse the stability of the single in-plane vortex state in two-dimensional magnetic nanodots with a nonmagnetic impurity (single-spin defect) at the centre. Small square and circular dots including up to a few thousand of spins are studied by means of a microscopic theory with nearest-neighbour exchange interactions and dipolar interactions fully taken into account. We calculate the spin-wave frequencies versus the dipolar-to-exchange interaction ratio d to find the values of d for which the assumed state is stable. Transitions to other states and their dependence on d and the vortex size are investigated as well, with two types of transition found: vortex core formation for small d values (strong exchange interactions), and in-plane reorientation of spins for large d values (strong dipolar interactions). Various types of localized spin waves responsible for these transitions are identified.     

Influence of cubic anisotropy in dipole-dipole interactions on structural phase transitions using the renormalization group transformation

The critical behaviour of ferroelectrics is studied forT>T _c and for zero electric field, by the renormalization group techniques ind=3 dimensions. The model hamiltonian we used contains an isotropic exchange coupling and a dipolar interaction with strong cubic anisotropy. A quadratic anisotropic fixed point is found to be stable for the cubic anisotropic scale field. Experiments on BaTiO₃ and KTaO₃ are compared with our results.Work supported by N.F.W.O.     

Collisional control of ground state polar molecules and universal dipolar scattering

We explore the impact of the short-range interaction on the scattering of ground state polar molecules and study the transition from a weak to strong dipolar scattering over an experimentally reasonable range of energies and electric field values. In the strong dipolar limit, the scattering scales with respect to a dimensionless quantity defined by mass, induced dipole moment, and collision energy. The scaling has implications for all quantum mechanical dipolar scattering. Furthermore the universal scattering regime will readily be achieved with polar molecules at ultracold temperatures.