Cooperative emission from an ensemble of three-level Λ radiators in a cavity: An insight from the viewpoint of dynamics of nonlinear systems

Cooperative radiation emitted by an ensemble of three-level optical systems with a doublet in the ground state (Λ scheme), which is placed into a cyclic cavity, is studied theoretically. In contrast to the two-level model of emitters, this process with such a configuration of operating transitions may occur without population inversion in the whole, if the doublet is prepared at the initial instant in a superposition (coherent) state. In the ideal case of a Hamilton system, in which the cavity losses and relaxation in the radiator ensemble are disregarded, the conservation laws are derived, which allow a substantial reduction of the dimension of the phase space of the model (?¹¹ → ?⁵) and the application of methods of dynamics of nonlinear systems for analyzing the three-level superradiance under these conditions. The possibility of different (both quasiperiodic and chaotic) scenarios of the three-level superradiance is demonstrated on the basis of Poincaré’s mappings. Global bifurcation of the system upon a transition from the conventional superradiance regime to inversionless one is revealed. The effects of cavity losses, as well as homogeneous and inhomogeneous broadening in the system of radiators on the regularities found are also discussed.     

Inversionless superradiance of an ensemble of three-level atoms in a high-Q cavity

We analyze the possibility of superradiance in an ensemble of three-level atoms in the absence of population inversion. We show that in the case of a Λ configuration of the active transitions this effect can occur for an initially coherent superposition of the states of the lower doublet. We also study how splitting of the lower levels influences this effect and discuss ways of creating low-frequency coherence. Zh. éksp. Teor. Fiz. 115, 505–520 (February 1999)     

Effect of the near-lying level on the kinetics of the field of superradiance of a thin layer

The effect of the local field on the competition of transitions in the superradiance of an incompletely excited thin layer of three-level atoms (Λ-diagram of working transitions) is studied. Analysis is made for the conditions when one of the sublevels of the lower doublet is initially unpopulated. For an initially unpopulated upper sublevel of the lower doublet, a new superradiance regime is found.     

Effect of the near-lying level on the kinetics of populations in the superradiance of a thin layer: Local-field regime

The effect of the local field on the competition of transitions in the superradiance of an incompletely excited thin layer of three-level atoms Λ-diagram of working transitions) is studied. The analysis made proves that the upper sublevel of the lower doublet is initially unpopulated. It is shown that the Raman transition, in the local-field regime, is ahead of the development of the superradiance pulse and causes the transfer of populations between sublevels of the lower doublet.     

Superradiance and superradiance without inversion of a thin layer of three-level atoms: The consideration of the sample extent

The effect of the sample extent in the process of superradiance and superradiance without population inversion of a thin (L ≤ λ) layer of three-level atoms (Λ-configuration of working transitions) is investigated. The limits of applicability of the spatially homogeneous approximation are determined. The consideration of the extent is shown to introduce new effects into the kinetics of populations and the field.     

Inversionless superradiance of a thin layer of three-level atoms: Coherent Raman transition between sublevels of the lower doublet

The effect of a local field on the transition competition in the process of superradiance of a thin layer of three-level atoms (Λ-configuration of working transitions) in the presence of an initial coherence of the lower doublet is investigated. It is shown that under the action of a local field, a coherent Raman transition between sublevels of the lower doublet can take place.     

Self-induced three-level echo

A new type of three-level photon echo has been predicted and analytically described. In contrast to the conventional three-level echo, whose formation involves three resonant ultrashort excitation pulses spaced in time, two of which are resonant to different optically allowed and adjacent transitions with different frequencies, the echo predicted arises under the conditions of formation of the conventional two-pulse echo and requires only two pump pulses of the same frequency. A theory is developed for the conditions of experiments on generation of a superradiance pulse at the ³ P ₀-³ H ₆ transition in impurity praseodymium ions in the LaF₃ matrix upon ultrashort coherent excitation of the adjacent optically allowed ³ H ₄-³ P ₀ transition in praseodymium. It is shown that the superradiance pulse after its deexcitation does not polarize the medium at the ³ P ₀-³ H ₆ generation transition and completely eliminates polarization at the ³ H ₄-³ P ₀ excitation transition. However, simultaneously, the superradiance pulse transfers the optical coherence from the excitation transition to the optically forbidden ³ H ₆-³ H ₄ transition. Thus, the phase memory about the effect of the excitation superradiance pulse is retained in the medium within a time interval that is shorter than the irreversible relaxation time of the optically forbidden transition.     

Photon echo under superradiance

The dynamics of optical coherence and phase memory in three-level medium in conditions of superradiance pulse emission is considered. In the case of coherent excitation of the upper level in three-level system of lambda configuration it is shown that the superradiance eliminates optical coherence on the adjacent transitions of excitation and superradiance emission and induces optical coherence on the remain transition. This, in turn, makes it possible to observe new effects of photon-echo, simple example of which is described in the present Letter.     

Excited state dynamics of Eu3+ in the partially disordered crystals La3Ga5SiO14 and La3Ga5.5Ta0.5O14

The spectroscopic properties of two partially disordered crystals, langasite (LGS) and langatate (LGT), doped with Eu³⁺ were investigated. The fluorescence lifetimes of the ⁵D₀ and ⁵D₁ excited levels are measured. The spectral overlapping between the luminescence from the ⁵D₀ and ⁵D₁ levels was eliminated using pulsed excitation at 532 nm and suitable delays in order to improve the precision of the calculation of the spectroscopic figures of merit R₀, R₂ (the areas of the electric-dipole transitions ⁵D₀→⁷F₀ and ⁵D₀→⁷F₂, respectively, divided by the area of the magnetic-dipole one—⁵D₀→⁷F₁). The maximum splitting of the ⁷F₁ level (ΔE) is calculated from the luminescence spectra and the B₂₀ crystal field parameter is determined. We obtain R₀(LGS)>R₀(LGT), R₂(LGS)<R₂(LGT), and ΔE(LGS)>ΔE(LGT), and we discuss these results taking into account structural data, covalency and J-mixing effects.     

Delayed unitary cancellation and heavy particle effects in e+e−→W+W−

We examine one-loop radiative corrections to e⁺e⁻→W⁺W⁻ in the standard model with one Higgs doublet, concentrating on the effects of very heavy fermions. These disturb the delicate unitarity cancellation between s- and t-channel diagrams, raising the cross section even well below the fermion threshold and giving a clear experimental signature for the heavy sector.     

Superradiance of the system comprised of two parallel resonant thin layers

A cavity-like regime of superradiance for a double-layer medium populated by atoms with the A-scheme of transitions is considered in a semiclassical approximation under the condition that the layers are arranged symmetrically with respect to initial characteristics of the field and atomic system populating the layers. An analytical law for the linear stage of the superradiance process is found that agrees well with numerical solution of the differential equations of the model under consideration for any initial conditions nearly up to the peak of the appropriate characteristic of the field intensity module. For the case of degenerate lower doublet, the resonant character of the dependence of the superradiance pulse time delay on the distance between the layers is studied.     

Temperature dependence of superradiance intensity

Using the idea of exchange interaction in a system of two-level atoms participating in a superradiance process, we derive from first principles the superradiance Hamiltonian of such a system, which is found to be analogous to the Heisenberg Hamiltonian. We consistently calculate the coupling constant of the interaction that leads to the emergence of a superradiance state in the system. We also predict the existence of isospin excitations in the superradiance state, whose presence reduces the intensity of the corresponding superradiance pulse. Finally, we calculate the temperature dependence of the intensity of the superradiance pulse and find it be analogous to the Bloch T ^3/2-law for spin systems. Zh. éksp. Teor. Fiz. 116, 1148–1160 (October 1999)     

Model of stochastization of the oscillatory regime of superradiance

Based on the analysis of the experimental data on the observation of the fluorescence and superradiance of praseodymium ions in a matrix of lanthanum trifluoride, a model of superradiance of three-level radiators with two close upper levels is developed in the mean-field approximation and studied. The uppermost level is coherently pumped by an ultrashort pulse of electromagnetic field, after which the excitation is transferred to the close energy level, from which the superradiance transition occurs to the lower level. In limiting cases, the considered model is reduced to the known models of superradiance and describes the ordinary regimes of monopulse and multipulse (oscillatory) superradiance. However, in a certain region of parameters, the model under discussion describes such a multipulse superradiance signal in which electromagnetic field spikes composing it follow in time with random intervals and amplitudes, so that the regime of regular chaotic dynamics is demonstrated in a single superradiance signal. In a certain time interval, the proposed model can be described by the Lorenz equations with the parameters corresponding to the chaotic dynamics of spikes composing the superradiance signal. The presented results of the numerical simulation of the model equations qualitatively correspond to the picture of stochastic pulsations observed experimentally.     

On the theory of vibronic superradiance

The Dicke superradiance on vibronic transitions of impurity crystals is considered. It is shown that parameters of the superradiance (duration and intensity of the superradiance pulse and delay times) on each vibronic transition depend on the strength of coupling of electronic states with the intramolecular impurity vibration (responsible for the vibronic structure of the optical spectrum in the form of vibrational replicas of the pure electronic line) and on the crystal temperature through the Debye-Waller factor of the lattice vibrations. Theoretical estimates of the ratios of the time delays, as well as of the superradiance pulse intensities for different vibronic transitions well agree with the results of experimental observations of two-color superradiance in the polar dielectric KCl:O ₂ ^? . In addition, the theory describes qualitatively correctly the critical temperature dependence of the superradiance effect.     

Hadronic gauge couplings in meson decays

The branching ratiosR(J→ππρ)≡Γ(J→ππρ)/Γ(J→ππ) for naturalJ ^P mesons have been evaluated under the assumption that theT(J→ππρ) amplitudes are generated by the gauge principle for ρ-mesons originally proposed by Sakurai in his approach to VMD. The ratios are predicted to increase withJ and are compatible with the present-day data. This suggests that the hadronic interactions of the photon proceed exclusively through its hadronic (VMD) component.     

Measurement ofR ine + e − annihilation for\sqrt s between 7.4 and 9.4 GeV

The rationR=σ(e ⁺ e ^?→hadrons)/σ(e ⁺ e ^?→ µ⁺ µ^?) was measured with the LENA detector at DORIS in a scan between 7.40 and 7.48 GeV and between 8.67 and 9.43 GeV center of mass energies. Corrected for QED radiative effects,R is found to be constant with an average value ofR=3.37 ±0.06_stat±0.23_syst. No narrow resonances withΓ _ee (Γ _had/Γ _tot)?0.30 keV (95% C.L.) and no steps have been observed. Based on this value ofR, revised values for υ(1S) resonance parameters are presented.     

High Pressure effect on fluorescence lifetime τ for magnetic dipole 5D0→5F1 transitions in YAG:Eu3+

The fluorescence lifetime for magnetic dipole ⁵D₀→⁷F₁ transition in yttrium aluminum garnet doped with Eu³⁺ (YAG:Eu³⁺) crystal was studied under the pressure of up to 10.4?GPa at room temperature. The fluorescence lifetime τ (⁵D₀→⁷F₁ transition) slowly decreased with pressure. The pressure effect on τ (⁵D₀→⁷F₁ transition) was explained with a model which considered pressure effect on line position: inter-ionic distance, ion volume, molecular volume, ion polarizability, molecular polarizability, sample refractive index, and surrounding hydrostatic medium refractive index. The fluorescence lifetime τ calculated by the presented model was in close correspondence with the experimental values.     

Exclusive semileptonic heavy meson decays including lepton mass effects

We discuss the exclusive semi-leptonic (s.l.) bottom meson decaysB→D(D ^*)+l+v where we include non-zero lepton mass effects in the kinematics and dynamics. We develop the general formalism for the non-zero lepton mass case. We then look at how rates, spectra and angular correlations are affected by non-zero lepton masses in the context of a specific spectator quark model. Numerical results are presented for s.l. decays involving thee-, μ- and τ-leptons. We also discuss the s.l. decaysB→π(ρ),D→K(K ^*) and the free quark decay model.     

DIRECT UPCONVERSION SENSITIZATION LUMINESCENCE OF Ho(0.1)Yb(5):OXYFLUORIDE VITROCERAMICS

This paper studies the upconversion luminescence phenomenon of the Ho,Yb co-doped oxyfluoride vitroceramics. There is one group of strong upconversion luminescence lines positioned at 536.5nm, 18639cm^-1; 540.5nm, 18501cm^-1; 544.0nm, 18399cm^-1, which is easily identified as the transitions of ⁵S₂→⁵I₈. There are other splendid upconversion luminescence lines, which are ⁵S₂→⁵I₇,⁵F₅→⁵I₈,⁵G₆→⁵I₈, (⁵G³G)₅ →⁵I₈,(³F³H⁵G)₄→⁵I₇,⁵G₄→⁵I₈ and (⁵G³H)₅→⁵I₈. It is also found that an interesting kind of upconversion cooperative radiation fluorescence comes from a kind of coupling state of clusters consisting of two Yb³⁺ ions.