Emergence of spectral line jumps and spectral diffusion in the two-photon correlator of a single impurity center

A dynamic theory of two-photon correlators for a single impurity center developed recently by the author [I. S. Osad’ko, Zh. éksp. Teor. Fiz. 113, 1606 (1998) [JETP 86, 875 (1998)] has been generalized to the case in which the center interacts with nonequilibrium two-level systems (TLSs) in polymers and glasses. Quantum tunneling transitions in TLS manifest themselves as random jumps of a spectral line of an impurity center. These jumps can be either spontaneous or light-induced. Interaction between the impurity center and many nonequilibrium TLSs, which exist in polymers, results in a time dependence of the optical dephasing rate 1/T ₂ of an impurity molecule, i.e., in spectral diffusion. This paper describes how the jumps of the spectral line manifest themselves in the two-photon correlator, which can be measured in experiments. Zh. éksp. Teor. Fiz. 116, 962–985 (September 1999)     

Anomalous scattered light correlator

The space-time correlation function of the scattered radiation intensity of atoms situated in an external field is investigated. This function includes contributions of the normal +E^–> and anomalous –E–> complex field amplitude correlator. These correlators have components due to scattering by density fluctuations and to collective, diffraction effects. The spatial structure of these correlators is studied and the conditions for the measurement of the anomalous correlator are derived. The temporal properties of the anomalous correlator and the effect of Doppler broadening on the correlation properties of scattered radiation are also considered. The investigation of the anomalous correlator is of interest in high-resolution spectroscopy and may also be useful in the study of nonresonant media.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 70–73, February, 1982.     

Singlet Oxygen Quantum Yield Determination for a Fluorene-Based Two-Photon Photosensitizer

The quantum yield, Φ_Δ, of singlet oxygen generation under two-photon excitation has been determined for a fluorene derivative. A photochemical method was developed using 1,3-diphenylisobenzofuran (DPBF), a chemical quencher of ¹O₂, and 2-(9,9-didecyl-7-nitrofluoren-2-yl)benzothiazole (1) as a two-photon photosensitizer (PS). The photochemical kinetics of the quencher was measured by two different fluorescence methods. Fluorene 1 exhibited relatively high singlet oxygen quantum yield, Φ_Δ ≈ 0.4 ± 0.1, and had a two-photon absorption cross-section of 28 ± 5 GM. Thus, 1 may have potential for use as a two-photon PS in the near-IR spectral region for biomedical applications.     

A study of the local dynamics of polymers using single impurity center spectroscopy (Review)

A review of one-and two-photon counting methods in single impurity center spectroscopy is reported, and advantages and drawbacks of these methods are discussed. The jumps of spectral lines, which are manifested as the so-called spectral trajectories, are discussed. Examples of the use of the theory of two-photon correlators and autocorrelation functions for experimental data processing are presented. Data are reported that demonstrate that the local dynamics of approximately 30% of single impurity centers cannot be described within the framework of the standard tunneling system model suggested by P. Anderson et al. to explain the low-temperature anomalies observed in glasses.     

Two-photon fluorescence spectrum in an atom + dielectric microsphere system

A strong resonant interaction of a two-level atom with a dielectric microsphere is studied on the basis of quantum electrodynamics. The initial condition considered is one in which the atom is initially excited and the resonant mode of the microsphere has been excited by a single photon. The spectrum of two emitted photons depends strongly on the method used to excite the microsphere, i.e., on the spatial distribution of the photon energy. The most characteristic feature of the two-photon fluorescence spectrum is a strong energy correlation of the emitted photons. This correlation is expressed in the fact that the energies of the emitted photons are related by the equation of an ellipse (ω+ω ₂−2ω _vA )²+3(ω ₁−ω ₂)²= 4Ω _Rabi ² . The relation between the results obtained and the predictions of the theory of dressed states is discussed. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 3, 192–197 (10 August 1999)     

Correlations of polarizations and entangled states in the two-photon system

The correlations of the linear and circular polarizations in the system of two photons have been theoretically investigated. The polarization of a two-photon state is described by the one-photon Stokes parameters and by the components of the correlation “tensor” in the Stokes space. It is shown that in the case of two-photon decays π⁰ → 2γ, η → 2γ, K _L ⁰ → 2γ, K _S ⁰ → 2γ and the cascade process |0〉 → |1〉 + γ → |0〉 + 2γ(|0〉 and |1〉 are states with the spin 0 and 1, respectively) the final two-photon state represents a characteristic example of the entangled (nonfactorizable) state, and the correlations between the Stokes parameters in all these decays have the purely quantum character: the incoherence inequalities of the Bell type for the components of the correlation “tensor”, established previously for the case of classical “mixtures”, are violated. The general analysis of the registration procedure for two correlated photons by two one-photon detectors is performed.     

Mechanism of spontaneous radiation relaxation of an impurity atom in a photonic band-gap crystal

On the base of the concept of radiative interaction between atoms of two different species, a novel electric-dipole mechanism of spontaneous radiating relaxation of an impurity atom in a medium with a gap in the photonic density of states about the transition frequency has been suggested. A kinetic equation for an impurity atom has been derived, and polarizations of the photonic band-gap crystal and an induced electromagnetic wave at the spontaneous transition frequency due to the suggested mechanism have been investigated. The parameters of the induced wave are determined by those of the suggested mechanism, and this dependence can be used in experimental investigations of these parameters. Zh. éksp. Teor. Fiz. 116, 469–484 (August 1999)     

Glueballs,gluerings, and gluestars in the <Emphasis Type="Italic">d</Emphasis> = 2 + 1 <Emphasis Type="Italic">SU</Emphasis>(<Emphasis Type="Italic">N</Emphasis>) gauge theory

The 3d gluodynamics which governs the large-T quark—gluon plasma is studied in the framework of the field correlator method. Field correlators and spacial string tension are derived through the gluelump Green’s functions. The glueball spectrum is calculated both in C = −1 as well as in C = +1 sectors, and multigluon bound states in the form of “gluon rings” and “gluon stars” are computed explicitly. Good overall agreement with available lattice data is observed. The text was submitted by the author in English.     

Comparison of methods for calculating turbulent diffusion coefficients

Different methods for calculating the turbulent diffusion coefficient D _T of a passive scalar impurity in an infinite homogeneous isotropic stationary turbulent medium are examined. The values of D _T calculated by these methods are compared for two limiting types of turbulence, viz., turbulence with a δ-function spectrum and turbulence with a Kolmogorov-type spectrum. The temporal dependence of the velocity correlators is assumed to be exponential. It is shown that the most accurate method is based on the use of the solution of the nonlinear equation for the averaged Green’s function with consideration of the contribution from the four-point turbulent velocity correlators. A comparison with the results of other methods that are simpler from the mathematical standpoint shows that some of them also permit the calculation of D _T with relatively good accuracy. Zh. éksp. Teor. Fiz. 111, 871–881 (March 1997)     

Thick-target X-ray bremsstrahlung spectra produced in 6.5 keV and 7.5 keVe--Hf collisions

The absolute doubly differential cross-sections (DDCS) for production of the thick-target X-ray bremsstrahlung spectra in collisions of 6.5 keV and 7.5 keV electrons with thick Hf target are measured. The X-ray photons are counted by a Si(Li) detector placed at 90° to the electron beam direction. The bremsstrahlung spectra are corrected for various ‘solid-state effects’ namely, electron energy-loss, electron back-scattering, and photon-attenuation in the target, in addition to the correction for detector’s efficiency. The DDCS values after correction, are compared with the predictions of a most accurate thin-target bremsstrahlung theory [H K Tseng and R H Pratt,Phys. Rev. A3, 100 (1971); Kisselet al, Atomic Data Nucl. Data Tables 28, 381 (1983)]. Also, a dependence of the absolute DDCS on atomic numberZ of the targets (₄₇Ag,₇₉Au and₇₂Hf) at 7.0 keV and 7.5 keV electron energies has been studied. The agreement between experiment and theory is found to be satisfactory within 27% systematic error of measurements. However, an apparent systematic difference between experiment and theory in the region of low-energy photons has been explained qualitatively by considering the fact that the hexagonal atomic structure of Hf offers possibly a greater magnitude of ‘solid-state effects’ in respect of blocking the low-energy bremsstrahlung photons from coming out of the target surface than does the cubic-face centered structure of Ag and Au target in similar conditions of the experiment.     

On the dominant role of two-photon relaxation in photonic crystals in external fields

It is shown that resonant interaction of a coherent wave with impurity atoms leads to filling of levels of an impurity atom that lie in the gap in the photon density of states and do not belong to resonant transitions, while the interaction of impurity atoms with a nonresonant coherent wave results in effective deactivation of the indicated levels. The main mechanism determining the pumping and decay of an impurity level in a gap are two-photon radiative relaxation processes previously investigated by the present author (Zh. éksp. Teor. Fiz. 102, 1126 (1992) [Sov. Phys. JETP 75, 611 (1992)]). Pis’ma Zh. éksp. Teor. Fiz. 70, No. 7, 434–438 (10 October 1999)     

Two-photon cooperative decay in a cavity in the presence of a thermalized electromagnetic field

We study the cooperative two-photon spontaneous decay of an excited atomic system in a microcavity whose size is of the order of several wavelengths of atomic radiation. We show that a thermalized electromagnetic field in the microcavity strongly affects the two-photon cooperative spontaneous emission of radiation. The increase in the rate of spontaneous cooperative decay is due to the presence of a small number of thermalized photons in a microcavity mode. At low temperatures, the two-photon absorption probability is found to be a linear function of the two-photon flux, and photon superbunching is observed. Zh. éksp. Teor. Fiz. 115, 1153–1167 (April 1999)     

Resonant two-photon absorption in ZnSiP2

The complex of optical investigations into the intrinsic (I) and resonant (R) two-photon absorption (TPA) inZnSiP ₂ crystals of tetragonal modifications is performed by methods of amplitude laser-modulation spectroscopy. The ITPA of allowed-forbidden type and the two Lorentz spectral lines associated with coherent resonant two-photon transitions through impurity states of allowed-allowed type are found. The electron transverse relaxation time at the RTPA is determined, and the total absorption cross section of laser-radiation photons emitted at electron transitions between the valence band v, the conduction band c, and local centers that produce real states intermediate for the RTPA in the forbidden band is estimated. M. P. Dragomanov National Pedagogical University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 36–43, February, 2000.     

Heavy-to-light correlators beyond the light cone

We present the first systematic analysis of the off-light-cone effects in correlators relevant for the extraction of the heavy-to-light form factors within the method of light-cone sum rules. In a model with scalar constituents, the correlator is calculated in two different ways: (i) by performing the expansion of the Bethe-Salpeter amplitude of the light meson near the light cone x ² = 0 and (ii) by adopting the known solution for the Bethe-Salpeter amplitude which allows one to calculate the correlator without invoking any expansion. We demonstrate that the contributions to the correlator from the off-light-cone terms x ² ≠ 0 are not suppressed by any large parameter compared to the contribution of the light-cone term x ² = 0. For decays of heavy particles of mass in the range 1.5–5 GeV, the light-cone correlator is shown to systematically overestimate the full correlator, numerically the difference being 10–20%. The text was submitted by the authors in English.     

Photon polarization in the two-photon decay of heavy hydrogen-like ions

We have applied the density matrix and second-order perturbation theory in order to re-analyze the two-photon decay of hydrogen-like ions for the polarization of emitted light. Special attention is paid to the linear polarization of one of the photons, while the spin state of the second photon is supposed to be unobserved. For such an “angle-polarization” correlation of the two photons we investigate the contributions that arise from non electric-dipole terms in the expansion of the electron-photon interaction. Detailed calculations are performed for the 2s_1/2 →1s_1/2 and 3d_5/2 →1s_1/2 transitions in neutral hydrogen as well as in hydrogen-like uranium.     

The physics of 2≠1+1

One of the most surprising consequences of quantum mechanics is the entanglement of two or more distant particles. In an entangled EPR two-particle system, the value of the momentum (position) for neither single subsystem is determined. However, if one of the subsystems is measured to have a certain momentum (position), the other subsystem is determined to have a unique corresponding value, despite the distance between them. This peculiar behavior of an entangled quantum system has surprisingly been observed experimentally in two-photon temporal and spatial correlation measurements, such as “ghost” interference and “ghost” imaging. This article addresses the fundamental concerns behind these experimental observations and to explore the nonclassical nature of two-photon superposition by emphasizing the physics of 2 ≠ 1 + 1.      

Two-photon Absorption Properties of 9,10-Disubstituted 2,6-Bis(p-dihexylaminostyryl)Anthracene Derivatives. Effect of 9,10-Substituents

A series of 2,6-bis(p-dihexylaminostyryl)anthracence derivatives having phenyl, styryl, and phenylethynyl groups at 9,10-positions (1−4) have been synthesized and their two-photon cross-sections were determined. Overall, the wavelengths of the longest wavelength absorption band and emission spectra increase with increase in the conjugation length and the electron withdrawing ability of the 9,10-substituents. All compounds show two-photon cross sections in the range of 740−3940 GM at 780−960 nm, which increase significantly by the donor and acceptor groups at 9,10-positions. In addition, Ph and phenylethynyl groups are better when compared to the styryl group at the 9,10-positions in terms of the two-photon action cross section. From a practical perspective, 1a, 2a–c, and 4b showed significant two-photon action cross-section and are most useful for applications that use two-photon excited fluorescence.     

Quantum optics in waveguides with resonant atoms: Multi-photon scattering

Quantum scattering of photons inside a one-dimensional waveguide caused by a number of closely located resonant two-level atoms is studied using the theory of integrable quantum systems. The multi-particle wave function of scattered photons is represented as a sum of terms of different degrees of “entanglement.” For two-photon scattering we discuss explicitly differences in photon correlations for the single two-level atom case and the case of several atoms.     

Resonant two-photon absorption in a tetragonal CdP2

Kinetic, spectral, intensity, angular, and polarization of resonant two-photon absorption (TPA) in β-CdP₂ has been investigated. Resonant TPA was observed for which the total energy of the two photons was 2.60 eV. It is shown that resonant TPA takes place via a real intermediate level d ₃ in the band gap at the depth E _c-0.86 eV. The electron transverse relaxation time for resonant TPA, the cross section for absorption of laser photons in d ₃→C transitions, the equilibrium population of d ₃ centers in a doped n-type sample, and the resonant TPA constant were determined as 4.3×10⁻¹⁴ s, 1.25×10⁻¹⁷ cm², 0.95, and 0.028 cm/MW, respectively. Fiz. Tverd. Tela (St. Petersburg) 40, 1252–1256 (July 1998)     

Two-Photon Absorption in Nanoheterostructures with <Emphasis Type="Italic">D</Emphasis><Superscript>(−)</Superscript>-Centers

A two-photon impurity absorption coefficient of the “quantum dot — D⁽⁻⁾-center” complexes synthesized in a transparent dielectric matrix is calculated within the model of zero-radius potential. The evolution of spectral dependence of the absorption coefficient of the nanoheterostructure based on semiconductor CdS _x Se _1−x glasses is studied versus the average quantum-dot radius. It is shown that the contribution of the two-photon impurity absorption to the exited two-photon luminescence is fairly significant at a reasonable quantum-dot concentration. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 46–50, July, 2005.