Population Decay Rate Research Articles

Bifurcation analysis of predator–prey model with time delay and harvesting efforts using interval parameter

This paper presents a prey–predator harvesting model with time delay for bifurcation analysis. We consider the parameters of the proposed model with imprecise data as form of interval in nature, due to the lack of precise numerical information of the biological parameters such as prey population growth rate and predator population decay rate. The proposed prey–predator harvesting model is presented with Holling type of predation and time delay under impreciseness of parameters by introducing parametric functional form of interval number. Our study reveals that along with delay and harvesting efforts role on the stability of the system, interval parameters also play a significant role. Computer simulations of numerical examples are given to explain our proposed imprecise model and for observing of chaotic behaviors.

The Lorenz model for single-mode homogeneously broadened laser: analytical determination of the unpredictable zone

Abstract We have applied harmonic expansion to derive an analytical solution for the Lorenz-Haken equations. This method is used to describe the regular and periodic self-pulsing regime of the single mode homogeneously broadened laser. These periodic solutions emerge when the ratio of the population decay rate ℘ is smaller than 0:11. We have also demonstrated the tendency of the Lorenz-Haken dissipative system to behave periodic for a characteristic pumping rate “2C P”[7], close to the second laser threshold “2C 2th ”(threshold of instability). When the pumping parameter “2C” increases, the laser undergoes a period doubling sequence. This cascade of period doubling leads towards chaos. We study this type of solutions and indicate the zone of the control parameters for which the system undergoes irregular pulsing solutions. We had previously applied this analytical procedure to derive the amplitude of the first, third and fifth order harmonics for the laser-field expansion [7, 17]. In this work, we extend this method in the aim of obtaining the higher harmonics. We show that this iterative method is indeed limited to the fifth order, and that above, the obtained analytical solution diverges from the numerical direct resolution of the equations.

Phase grating in a doubly degenerate four-level system

In this paper, we suggest a doubly degenerate four-level system, in which the transition takes place between the hyperfine energy 52S1/2 F = 1 and 52P3/2 F = 2 in rubidium 87 D2 line, for studying atomic phase grating based on the cross-Kerr and phase conjugation effects. The phase grating with high efficiency can be obtained by tuning phase shift Φ between the coupling and probe field, when the coupling intensity is much stronger than the strength of probe field. Under different coupling intensities, a high diffraction efficiency can be maintained. A new and simple way of implementing phase grating is presented. However, in such an atomic system, two main limitations must be taken into account. First, the independence between steady state probe susceptibility and the coupling intensity, when the population decay rate is larger than the Rabi frequency of the coupling field, cannot result in diffraction grating; second, the sample to be prepared should not be too long.

Correlation and dephasing effects on the non-radiative coherence between bright excitons in an InAs QD ensemble measured with 2D spectroscopy

Exchange-mediated fine-structure splitting of bright excitons in an ensemble of InAs quantum dots is studied using optical two-dimensional Fourier-transform spectroscopy. By monitoring the non-radiative coherence between the bright states, we find that the fine-structure splitting decreases with increasing exciton emission energy at a rate of 0.1μeV/meV. Dephasing rates are compared to population decay rates to reveal that pure dephasing causes the exciton optical coherences to decay faster than the radiative limit at low temperature, independent of excitation density. Fluctuations of the bright state transition energies are nearly perfectly correlated, protecting the non-radiative coherence from interband dephasing mechanisms.

Optimal harvesting of prey–predator system with interval biological parameters: A bioeconomic model

The paper presents the study of one prey one predator harvesting model with imprecise biological parameters. Due to the lack of precise numerical information of the biological parameters such as prey population growth rate, predator population decay rate and predation coefficients, we consider the model with imprecise data as form of an interval in nature. Many authors have studied prey–predator harvesting model in different form, here we consider a simple prey–predator model under impreciseness and introduce parametric functional form of an interval and then study the model. We identify the equilibrium points of the model and discuss their stabilities. The existence of bionomic equilibrium of the model is discussed. We study the optimal harvest policy and obtain the solution in the interior equilibrium using Pontryagin’s maximum principle. Numerical examples are presented to support the proposed model.

Spin dynamics in the optical cycle of single nitrogen-vacancy centres in diamond

We investigate spin-dependent decay and intersystem crossing (ISC) in the optical cycle of single negatively charged nitrogen-vacancy (NV) centres in diamond. We use spin control and pulsed optical excitation to extract both the spin-resolved lifetimes of the excited states and the degree of optically induced spin polarization. By optically exciting the centre with a series of picosecond pulses, we determine the spin-flip probabilities per optical cycle, as well as the spin-dependent probability for ISC. This information, together with the independently measured decay rate of singlet population, provides a full description of spin dynamics in the optical cycle of NV centres. The temperature dependence of the singlet population decay rate provides information about the number of singlet states involved in the optical cycle.

Electron Correlation Effects on the Femtosecond Dephasing Dynamics ofE22Excitons in (6,5) Carbon Nanotubes

Highly nonlinear pump fluence dependence was observed in the ultrafast one-color pump-probe responses excited by 38 fs pulses resonant with the E(22) transition in a room-temperature solution of (6,5) carbon nanotubes. The differential probe transmission (ΔT/T) at the peak of the pump-probe response (τ = 20 fs) was measured for pump fluences from ∼10(13) to 10(17) photons/pulse cm(2). The onset of saturation is observed at ∼2 × 10(15) photons/pulse cm(2) (∼8 × 10(5) excitons/cm). At pump fluences >4 × 10(16) photons/pulse cm(2) (∼1.6 × 10(6) excitons/cm), ΔT/T decreases as the pump fluence increases. Analogous signal saturation behavior was observed for all measured probe delays. Despite the high exciton density at saturation, no change in the E(22) population decay rate was observed at short times (<300 fs). The pump probe signal was modeled by a third-order perturbation theory treatment that includes the effects of inhomogeneous broadening. The observed ΔT/T signal is well-fit by a pump-fluence-dependent dephasing rate linearly dependent on the number of excitons created by the pump pulse. Therefore, the observed nonlinear pump intensity dependence is attributed to the effects of quasi-elastic exciton-exciton interactions on the dephasing rates of single carbon nanotubes. The low fluence total dephasing time is 36 fs, corresponding to a homogeneous width of 36 meV (290 cm(-1)), and the derived E(22) inhomogeneous width is 68 meV (545 cm(-1)). These results are contrasted with photon-echo-derived parameters for the E(11) transition.

Spectroscopic and Photophysical Properties of ZnTPP in a Room Temperature Ionic Liquid

The steady-state absorption and emission spectra and the time-resolved Soret- and Q-band excited fluorescence profiles of the model metalloporphyrin, ZnTPP, have been measured in a highly purified sample of the common room temperature ionic liquid, [bmim][PF₆]. S₂-S₀ emission resulting from Soret-band excitation behaves in a manner completely consistent with that of molecular solvents of the same polarizability. The ionic nature of the solvent and its slow solvation relaxation times have no significant effect on the nature of the radiationless decay of the S₂ state, which decays quantitatively to S₁ at a population decay rate that is consistent with the weak coupling case of radiationless transition theory (energy gap law). The ratio of the intensities of the Qα:Qβ (0-0:1-0) bands is consistent with the solvatochromic shift correlation data obtained for molecular solvents. The temporal S₁ fluorescence decay profiles measured at a single emission wavelength are biexponential; the longer-lived major component is similar to that observed for ZnTPP in molecular solvents, and the minor shorter-lived component is attributed to solvent relaxation processes on a nanosecond time scale.

Photophysics of Soret-Excited Tetrapyrroles in Solution. IV. Radiationless Decay and Triplet−Triplet Annihilation Investigated Using Tetraphenylporphinato Sn(IV)

The S(2) population decay rates and triplet-triplet annihilation efficiencies of Sn(IV)Cl(2)TPP have been measured in fluid solutions using its weak S(2)-S(0) fluorescence as a metric. A detailed description of the excited-state photophysics of Sn(IV)Cl(2)TPP has allowed comparisons to be made between this rigid, D(4h) axially coordinated molecule and axially uncoordinated tetrapyrroles of greater flexibility and lower symmetry. S(2)-S(1) internal conversion is the major S(2) population decay path for Sn(IV)Cl(2)TPP as it is for the S(2) states of all other d(0) and d(10) metalated tetrapyrroles. The S(2) state of Sn(IV)Cl(2)TPP exhibits S(2)-S(1) relaxation rates that follow the energy gap law of radiationless transition theory and are only slightly faster than those exhibited by MgTPP and the weak coupling limit. Differences in S(2)-S(1) radiationless decay rates among the series MTPP (M = Mg, Zn, Cd, SnCl(2)) cannot be traced to differences in the displacements of the S(2) and S(1) potential surfaces. Instead, the most likely source of the large differences in S(2)-S(1) radiationless decay rates between CdTPP and Sn(IV)Cl(2)TPP is the lower symmetry of the former (near C(4v)), which permits a much larger number of vibrations to participate in S(2)-S(1) vibronic coupling. Triplet-triplet annihilation of the type 2T(1) --> S(2) + S(0) has been observed in Sn(IV)Cl(2)TPP for the first time, but is of substantially lower efficiency than seen in ZnTPP in noncoordinating solvents because of its shorter triplet lifetime and the shielding effects of its axial Cl ligands, which tend to block the short-range interaction needed for Dexter energy transfer.

Optical properties of an N-type system in Doppler-broadened multilevel atomic media of the rubidium D2 line

We report the observations of Mollow sideband-like transparency windows in a Doppler-broadened four-level N-type system of the rubidium D2 line. A pair of enhanced transparency windows across an electromagnetically induced transparency line centre results from dressed state interactions of two coupling fields. The present observations have potential applications of using the symmetric transparency windows for optical quantum information processing such as multiple optical buffer memories and double slow-light-based enhanced cross-phase modulation. We also discuss the quantum coherent control of absorption cancellation, absorption enhancement and probe gain in a closed N-type four-level model introducing the atom flow rate determined by the population decay rate and control field intensity.

Photophysics of Soret-Excited Tetrapyrroles in Solution. II. Effects of Perdeuteration, Substituent Nature and Position, and Macrocycle Structure and Conformation in Zinc(II) Porphyrins

The steady-state absorption, fluorescence, and excitation spectra and upper excited-state temporal fluorescence decay profiles of 11 tetrapyrroles in several fluid solvents are presented and analyzed to ascertain the factors that control their S2 population decay times. The S2 lifetimes, which vary by more than 2 orders of magnitude, are controlled exclusively by their rates of radiationless decay. The only important electronic relaxation path is S2-S1 internal conversion, the efficiency of which is near 1.0 in all compounds studied (except CdTPP where it is 0.69). The rate of S1 population rise equals the rate of S2 population decay in all cases. Among the compounds studied, only MgTPP exhibits S2-S1 decay behavior that corresponds to the weak coupling limit of radiationless transition theory; all zinc metalloporphyrins exhibit intermediate to strong coupling. Perdeuteration of ZnTPP produces no significant change in the rate of S2 decay or in the quantum yield of S2-S0 fluorescence, indicating that in-plane C-C and C-N vibrations are the accepting modes in S1 with the largest Franck-Condon factors. The initial vibrational energy content of the S2 states (0 < E(vib) < 3500 cm(-1) over the range of compounds) plays no significant role in determining their overall population decay rates in solution. The S2 population decay rates of these tetrapyrroles are controlled by two factors: the Franck-Condon factor, which is inversely proportional to the exponent of the S2-S1 electronic energy spacing and the S2-S1 coupling energy. The S2-S1 electronic energy spacing is determined in solution by the difference in the polarizabilities of the S2 and S1 states and can be controlled by varying the polarizability of the solvent. The S2-S1 coupling energy is influenced by the nature, location, and effect of the substituents, with beta-alkyl substitution and reduction of symmetry in the tetrapyrrole--for example by loss of planarity--increasing the interstate coupling energy.

Nonradiative exciton energy transfer in hybrid organic-inorganic heterostructures

Nonradiative energy transfer from a GaAs quantum well to a thin overlayer of an infrared organic semiconductor dye is unambiguously demonstrated. The dynamics of exciton transfer are studied in the time domain by using pump-probe spectroscopy at the donor site and fluorescence spectroscopy at the acceptor site. The effect is observed as simultaneous increase in the population decay rate at the donor and of the rise time of optical emission at the acceptor sites. The hybrid configuration under investigation provides an alternative nonradiative, noncontact pumping route to electrical carrier injection that overcomes the losses imposed by the associated low carrier mobility of organic emitters.

Development of spatial turbulence from boundary-controlled patterns in class-B lasers

We report time-resolved measurements of transverse dynamics in a pulsed custom-made Nd:YAG (yttrium aluminum garnet) broad-area laser, where a dynamic transition from order to turbulentlike patterns appears, without the modification of the Fresnel number. To our knowledge, it is the first time this dynamical transition is observed in a class-B laser. Higher values of the pumping and a higher ratio between the electric field and the inversion population decay rates diminish the time at which the transition takes place. A theoretical model based on the adiabatic approximation allows us to explain the main features of the observed dynamics and to compare the results with those previously seen, especially in broad-area $\mathrm{C}{\mathrm{O}}_{2}$ lasers.

Relaxation process of coherent transients in the presence of an adjacent strongly driven transition

Coherent transient occurs when a two-level transition is subjected to pulsed laser excitation. The relaxation process of coherent transient depends on both the longitudinal and transverse relaxation parameters of the two-level transition, which is related to the population and coherence decay rates. In this paper we study relaxation process of a new type coherent transients observed by applying a pulsed laser excitation to a two-level transition in the presence of a second strong continuous-wave (cw) coherent field coupling one of the two levels to a third level, that is, in a three-level double-resonance configuration. The relaxation process of coherent transients is studied as a function of relaxation parameters of both the two-level transition excited by the pulsed laser field and the transition coupled by the cw laser field. It is shown that by involving a third level with coherent field the relaxation process of coherent transients of a two-level transition can be modified. Our study illustrates a new way of controlling relaxation process of coherent transients in a two-level transition by a second coherent laser and this has important implication for quantum information storage and quantum computing.

Solvent-Polarity Tuning Excited-State Charge Coupled Proton-Transfer Reaction inp-N,N-Ditolylaminosalicylaldehydes

Detailed insight into the excitation behavior for charge versus proton transfer in p-N,N-ditolylaminosalicylaldehyde (Ia) has been gained via luminescence spectroscopy and femtosecond dynamics. In cyclohexane, following an ultrafast rate (2.0 10 12 s -1 ) of excited-state intramolecular proton transfer (ESIPT), fast equilibrium takes place between normal (N*) and tautomer excited states (T*), resulting in dual fluorescence maximized at 450 and 540 nm, respectively, with a common population decay rate of 360 ps -1 . The normal emission exhibits drastic solvent-polarity dependence and has been concluded to originate from a chargetransfer species incorporating excited-state intramolecular charge transfer from ditolylamine to carbonyl oxygen. In dipolar solvents, competitive rates between ESIPT and solvent relaxation were observed, and the solvated charge-transfer state is thermodynamically more favorable, so that the T* f N* reverse proton transfer takes places. Supplementary support was provided by the corresponding experiments for the methoxy derivative of Ia as well as other relevant analogues. The results shed light on detailed proton/charge transfer coupled dynamics as well as the associated solvent-relaxation dynamics at an early time domain.

Population shelved all-optical modulation

An all-optical modulation method is proposed and experimentally demonstrated to overcome the modulation bandwidth limitations, imposed by the excited-state population decay rate, in a conventional resonant optical modulator. In the experimental demonstration, we have observed an all-optical modulation bandwidth \ensuremath{\sim}200 times wider than the population decay rate. The enhancement of the modulation bandwidth is due to the fast spin dephasing caused by spin inhomogeneous broadening.

Ultrafast vibrational dynamics and stability of deuterated amorphous silicon.

Infrared four-wave mixing experiments performed upon deuterated amorphous silicon layers (a-Si:D) reveal profound differences in the dynamics of Si-D stretch vibrations compared to those of analogous Si-H vibrational modes in hydrogenated amorphous silicon (a-Si:H). Remarkably, transient-grating measurements of the population decay rate of the Si-D vibrations show single-exponential decay directly into collective modes of the a-Si host, bypassing the local bending modes of the defect into which the Si-H vibrations decay. Photon-echo measurements of the vibrational dephasing suggest at low temperature contributions from TO nonequilibrium phonons and at elevated temperatures elastic phonon scattering of TA phonons.

Electron Induced Collisional Population Decay Rates for Levels of 3p54s and 3p54p Manifolds of ArI in Plasma

Population decay rates due to collisions with electrons were calculated for levels belonging to 4s and 4p manifolds of ArI, for the electron temperature range from 7000 K to 21 000 K. These quantities are necessary to describe the signal received from the laser spectroscopy of argon plasmas as well as in plasma modelling. Discussion on the available theoretical and experimental data concerning cross sections required for calculation is presented. Consistency of the cross section data set was verified by comparing the measured Stark width and its temperature dependence for the 696.5 nm ArI line to the inelastic collisions contribution to this line width derived from calculated population decay rates.

Nonlinear decoherence in quantum state preparation of a trapped ion

We present a nonlinear decoherence model which models decoherence effect caused by various decohereing sources in a quantum system through a nonlinear coupling between the system and its environment, and apply it to investigating decoherence in nonclassical motional states of a single trapped ion. We obtain an exactly analytic solution of the model and find very good agreement with experimental results for the population decay rate of a single trapped ion observed in the NIST experiments by Meekhof and coworkers (D. M. Meekhof, {\it et al.}, Phys. Rev. Lett. {\bf 76}, 1796 (1996)).

Theory of exciton dephasing in semiconductor quantum dots

A resonant optical excitation creates an excited state population and also induces an optical polarization. Dynamics of this optical excitation is characterized by relaxation of the population as well as decay of the induced optical polarization. In lower dimensional semiconductors, electronic confinement leads to qualitative changes in population relaxation, including spontaneous emission and exciton-phonon scattering, as shown in extensive recent studies [1]. These population relaxation processes are expected to contribute to dephasing with a dephasing rate given by half the population decay rate. Pure dephasing processes that do not involve population or energy relaxation of excitons can also contribute to dephasing. Pure dephasing, which is a well-established concept for atomic systems, remains yet to be investigated in lower-dimensional semiconductors due to a lack of direct comparison between dephasing and population relaxation and between theory and experiment. Studies of pure dephasing processes in lower-dimensional semiconductors will renew and deepen our understanding of dephasing of collective excitations in solids, although several seminal studies were done on the exciton dephasing in quantum well (QW) structures [2–6].