Population Relaxation Time Research Articles

Effects of laser-beam temporal pulse shape on signal strength and spectral line shape of forward degenerate four-wave mixing

We investigate the effects of the input laser beam’s temporal pulse shape on a forward degenerate four-wave mixing (FDFWM) signal, assuming two-level saturable absorbers. Under conditions in which the coherence time is far shorter than the pulse-duration, we can calculate the signal easily in the time and frequency domains. From this result it is shown that, when the pulse duration is longer than ten times the population relaxation time, the calculated signal intensity is almost the same as that obtained by assuming a steady state throughout duration of the laser pulse. With this assumption, we obtain the signal by summing all the steady-state signals at each time-domain grid point during the pulse. The calculation is performed with three input beam temporal pulse shapes: square, Gaussian, and typical Q-switched pulses. After reaching a maximum, the signal intensity decreases. The rates of the signal increase and decrease depend strongly on the temporal shape of the input beam. For the same average power, the square-pulse input saturates the absorber faster than the other pulses. These results indicate that the weak part of the pulse input plays an important role in generating the signal, yielding differences in saturation behavior of the signal intensity and the spectral line shape. We compare the calculations with experiments by fitting the saturation curve of the FDFWM signal of argon atoms in a radio frequency inductively coupled plasma. Also, the spectral line shape of the DFWM signal is fitted with the calculation by use of published experimental data.

Potential applications of dark resonance to subpicosecond optical switches in hyper-terahertz repetition rates

Subpicosecond optical switching in hyper-terahertz repetition rates is numerically demonstrated using dark resonance based two-photon coherence swapping. The switching time and repetition rate demonstrated are one tenth the population relaxation time T1, and it is a breakthrough in the critical limitation of current technologies of optical switches. This demonstration implies potential applications of ultrafast optical switches to ultrahigh-capacity fiber-optic communications.

Excited state dynamics in tetra tolyl porphyrins studied using degenerate four wave mixing with incoherent light and ps pulses

We present our experimental results on the excited state dynamics in several tetra tolyl porphyrins (with different central metal-ions) studied using degenerate four wave mixing with nanosecond incoherent light (DFWM-IL) and picosecond time-resolved four wave mixing (DFWM-PS). Incoherent light studies indicate three lifetimes, which have been attributed to different excited states. The shortest component with a decay constant of <170 fs is due to the vibrational relaxation in the higher excited singlet states S n( T 2 ) , 3–6 ps component is due to the vibrational relaxation of the Franck-Condon states in S 1( τ vib ) , and the long component of 20–100 ps is due to the population relaxation ( T 1 ) from S 1 to S 0. The population relaxation times obtained from time-resolved DFWM studies using a picosecond laser substantiates these results.

A mixed quantum-classical molecular dynamics study of vibrational relaxation of a molecule in solution

An application of mixed quantum-classical molecular dynamics to vibrational relaxation of the solute molecule in the solution has been investigated. In the present paper, we demonstrate that mean field approximation, rather than surface hopping approximation, works satisfactorily well for the vibrational relaxation of, at least, the CN− ion in the aqueous solution, where the potential surface of the solvent water depends little on the vibrational quantum state of the solute. The calculated relaxation time is in good correspondence to those obtained from other two different methods based upon the same potential model, i.e., Fermi’s Golden Rule with classical force autocorrelation function and path integral influence functional theory in its classical bath limit. The present method gives some interesting findings for the relaxation. For example, the energy relaxation time may be longer than the population relaxation time. With respect to the coupling to the solvent, water molecules in the first hydration shell make a leading contribution to the relaxation of the solute.

Theory of energy- and time-resolved two-photon photoemission from metal surfaces - influence of pulse duration and excitation condition

The theory of energy- and time-resolved two-photon photoemission (2PPE) spectra of metal surfaces is presented using density matrix formulation for a three-level system consisting of an initial occupied, intermediate unoccupied and final photoelectron states. A perturbation expansion method is employed to calculate the energy-resolved 2PPE spectrum for continuous light beams. We have obtained analytical expressions of the 2PPE spectrum corresponding to a step-by-step one-photon process through the intermediate state and a direct two-photon-ionization process via virtual transition. It is demonstrated that the intermediate state can also be populated via the nonresonant virtual process. This indicates an absolute importance of “pure dephasing” associated with the transition between the initial and intermediate states. Evolution of the 2PPE spectrum as a function of the pump photon energy is calculated to demonstrate the conditions under which the intrinsic linewidth (total dephasing time) can be deduced from the lineshape analysis. It is also found that the intensity ratio of the two peaks due to the initial and the intermediate states in 2PPE spectrum can be used to estimate the pure dephasing time. Transient behavior of the excited-state population following pulse excitation is calculated with a focus on how the ultrafast relaxation times of the excited states such as image-potential states of metal surfaces are deduced from the transient 2PPE response observed with a pulse laser with much longer duration. The time-resolved 2PPE spectra are calculated for varying detuning from the resonant excitation from the initial state to the intermediate state. Transient responses of the 2PPE signal due to direct ionization and step-by-step processes are also calculated to demonstrate that the nonresonant former process has an influence on the analysis of the cross-correlation trace of the intermediate state, by which the population relaxation time is estimated. Attempts are also made to apply the present theory to a recent time-resolved 2PPE study of the relaxation dynamics of the image-potential states as well as hot electrons in Cu(100) and Ag(100) surfaces.

The intrasubband and intersubband relaxation of nonequilibrium electron populations in wide semiconductor quantum wells

The evolution of nonequilibrium electron distributions in wide GaAs quantum wells, driven by electron–electron scattering processes, is calculated through numerical integration of the Boltzmann collision integrals, by incorporating the multi-subband dynamically screened Coulomb interaction derived in the random phase approximation. We present results for the thermalisation and intersubband population relaxation times of these distributions, for different carrier densities and lattice temperatures, and for different fractions of the population excited into the upper subband, including the highly nonequilibrium case of a population inversion between the subbands. We compare the relative importance of electron–electron and electron–LO-phonon scattering processes in determining the intersubband population relaxation times. The role played by screening in intersubband transitions is discussed.

Two-Dimensional Line Shapes Derived from Coherent Third-Order Nonlinear Spectroscopy

Two-dimensional (2D) line shapes derived from four types of coherent third-order nonlinear spectroscopies as a function of two independent time or frequency variables are compared. The signals scattered into two wave-vector-matching directions in the limits of high-time or high-frequency resolution are calculated for an inhomogeneously broadened ensemble of two-level systems with phenomenological dephasing and population relaxation times. While one-dimensional (1D) line shape analysis for this model is ambiguous, the contours of these 2D line shapes are shown to be characteristic of the relative time scales of the three relevant line-broadening parameters. These broadening mechanisms are also apparent by comparing 2D spectral profiles along the diagonal and antidiagonal frequency axes. For time domain experiments, in analogy with NMR correlation spectroscopy, the radiated signal is observed as a function of the two coherence periods and is 2D Fourier transformed to obtain a line shape. For experiments bas...

Frequency-dependent vibrational population relaxation time of the OH stretching mode in liquid water

Abstract The vibrational population relaxation time has been measured across the inhomogeneously broadened OH stretching mode (ν3) of a 0.5% solution of HDO in D2O. Relaxation times vary from 0.5 ps at low frequency (3270 cm−1) to 1.0 ps at high frequency (3600 cm−1). This variation is attributed to a V–V transfer mechanism between ν3 and 2ν2.

A Study of Vibrational Relaxation of B-State Carbon Monoxide in the Heme Pocket of Photolyzed Carboxymyoglobin

The vibrational energy relaxation of dissociated carbon monoxide in the heme pocket of sperm whale myoglobin has been studied using equilibrium molecular dynamics simulation and normal mode analysis methods. Molecular dynamics trajectories of solvated myoglobin were run at 300K for both the δ- and ∈-tautomers of the distal histidine, His64. Vibrational population relaxation times were estimated using the Landau–Teller model. For carbon monoxide (CO) in the myoglobin ∈-tautomer, for a frequency of ω0=2131cm−1 corresponding to the B1 state, T1∈(B1)=640±185 ps, and for a frequency of ω0=2119cm−1 corresponding to the B2 state, T1∈(B2)=590±175 ps. Although the CO relaxation rates in both the ∈- and δ-tautomers are similar in magnitude, the simulations predict that the vibrational relaxation of the CO is faster in the δ-tautomer. For CO in the myoglobin δ-tautomer, it was found that the relaxation times were identical within error for the two CO substate frequencies, T1δ(B1)=335±115 ps and T1δ(B2)=330±145 ps. These simulation results are in reasonable agreement with experimental results of Anfinrud and coworkers (unpublished results). Normal mode calculations were used to identify the dominant coupling between the protein and CO molecules. The calculations suggest that the residues of the myoglobin pocket, acting as a first solvation shell to the CO molecule, contribute the primary “doorway” modes in the vibrational relaxation of the oscillator.

Hot luminescence of Mn 2+ in ZnS nanocrystals

Time resolved emission spectra of Mn 2+ in ZnS nanocrystals were studied. Two split-pair bands at high- and low-energy sides of the peak position of the conventional Mn 2+ emission band were observed at short delay times. They emerge gradually into the conventional emission band of Mn 2+. These two bands were assumed to be hot luminescence which comes from the vibronic transitions from the vibrational states of the excited state of Mn 2+ to its ground state. The population and energy relaxation times of hot electrons were deduced.

Excited state dynamics of C 60 studied using incoherent light

Excited state dynamics of C 60 have been studied using backward degenerate four wave mixing with incoherent light. Estimates of the population relaxation time T 1 of the lower excited singlet state S 1 and phase relaxation time T 2 of the higher excited singlet state S n are obtained. The vibrational dephasing in the S 1 state is ∼5 ps. The results are in good agreement with those obtained using a fs laser. We also present Z-scan data at 600 nm.

Laser-induced long-lifetime electron tunnelling in biased asymmetric double quantum well

Laser (cw)-induced tunnelling dynamics of an electronic wavepacket in a biased asymmetric double quantum well (DWQ) structure is studied numerically, varying the quantum level alignment in the DQW. The Markoff master equation is used to determine the time evolution of the wavepacket that is initially created by a pump pulse. Laser-induced long-lifetime (practically equal to the population relaxation time) electron tunnelling is observed when the Rabi frequency is smaller in magnitude than the dephasing rate. It is shown that this laser-induced effect can be eradicated by adjusting the bias voltage to align the upper two electronic states in the narrow and wide wells.

Subpicosecond Time-Resolved Raman Studies of Non-Equilibrium Excitations in Wide Bandgap GaN

Non-equilibrium phonon dynamics in wurtzite GaN have been studied by subpicosecond time-resolved Raman spectroscopy. The population relaxation time of longitudinal optical phonons was directly measured to be τ ≅ (5 ± 1) ps at T = 25 K. The experimental results on the temperature dependence of the lifetime of longitudinal optical phonons suggest that the primary decay channels for these phonons are the decay into (i) one transverse optical phonon and one high energy, longitudinal or transverse acoustical phonons; and (ii) one transverse optical phonon and one E2 phonon.

Quantum measurement and pure dephasing

The prerequisite of quantum measurement is a transformation of an initially off-diagonal density matrix ρmα;nβ describing an interacting measured object and measuring device into a diagonal density matrix ρmα;mαδmnδαβ . The latter density matrix describes a proper mixture of states having definitem-values. On the other hand, the irreversible relaxation (towards the thermodynamic equilibrium) is also characterized by transformation of an initially off-diagonal matrix into a diagonal one. It has been shown that the process of irreversible relaxation can be used to perform quantum measurement, provided the duration Δt of the measurement is much larger thanT 2, the phase relaxation time, and much smaller thanT 1, the population relaxation time:T 2 ≪ Δt ≪T 1. Agedanken experiment describing this kind of measurement is provided. Aπ/2-pulse transforms an initials z = −1/2 state into superposition ofs z = ±1/2 states. The irreversible relaxation leads to the proper mixture ofs z = 1/2 ands z = −1/2 state. Results of the measurements are verified by the second electromagnetic pulse.

Observation of narrow resonances inside homogeneously self-broadened lines in pump-probe reflection experiments

We report the experimental investigation of spectral hole burning and four-wave mixing at the interface of glass and a dense cesium vapor using two tunable diode lasers in a pump-probe experiment. Narrow spectral features were observed in the center of the strongly self-broadened ${\mathrm{D}}_{2}$ line at Cs number density from 9\ifmmode\times\else\texttimes\fi{}${10}^{15}$ to 2.8\ifmmode\times\else\texttimes\fi{}${10}^{16}$${\mathrm{ncm}}^{\mathrm{\ensuremath{-}}3}$. The origin of the resonances is associated with the coherent scattering of laser beams at a self-induced population grating, and their spectral widths reflect the relaxation rate of the population difference. A simple asymptotic expression is used to fit the spectral line shapes and to infer a population relaxation time of 3.7(2) ns, which is almost an order of magnitude shorter than natural lifetime of the excited state.

Power dependence of transient degenerate four-wave mixing in molecular systems

The object of this study is to quantitatively elucidate the laser-power dependence in transient degenerate four-wave mixing (DFWM) with an emphasis on the high laser-pump intensity region. We discuss our investigation on the power dependence of transient DFWM by taking gas-phase iodine (${\mathrm{I}}_{2}$) molecules as a testing example. The distinct physical feature is that in the high-power laser pump, where both laser-pulse duration and the inverse of pump rate are much shorter than the molecular population relaxation time, the steady-state DFWM theory of Abrams and Lind [Optical Phase Conjugation, edited by R. A. Fisher (Academic, New York, 1983), Chap. 8, pp. 211--284; Opt. Lett. 2, 94 (1978); 3, 205 (1978)] is not appropriate. The prediction by the steady-state theory has shown the DFWM to decrease with increasing laser-pump intensity as a function of 1/${\mathrm{I}}_{\mathrm{laser}}$, which disagrees with the saturation behavior observed in the experiment. To elucidate the dependence of DFWM on the laser pump intensity, a non-steady-state extension of the nonperturbative theory of Abrams and Lind is required. The non-steady-state theoretical result will be shown to be in good agreement with the experimental power dependence at resonance transient DFWM especially in the high-power pump region.

Neck flexor muscle strength, efficiency, and relaxation times in normal subjects and subjects with unilateral neck pain and headache.

To determine the test-retest reliability of a new method for measuring muscular strength, efficiency, and relaxation times of the neck flexor musculature of healthy adults, and to compare these neck flexor muscle properties in subjects who have unilateral neck pain and headache with those in controls. Subjects lay supine and isometrically flexed their necks against a force transducer attached to the back of a webbing and velcro helmet. Electromyograms (EMGs) were recorded from surface electrodes on the sternocleidomastoid (SCM) muscles. Two consecutive sessions of five contractions of varying levels of effort from minimal through moderate and maximal effort were analyzed. Ambulatory referral center. Volunteer control subjects (n = 10, 3 men and 7 women) were recruited from hospital and university personnel. Volunteer neck pain subjects (n = 10, 3 men and 7 women) were recruited from a physiatric chronic pain practice and a hospital outpatient physical therapy practice. In the controls, the intraclass correlation coefficients (ICCs) for the first two maximum neck flexion contractions were; peak force ICC = .81; peak force/body weight ICC = .75; average force ICC = .75; force relaxation time ICC = .73; SCM EMG relaxation times: right ICC = .60 and left ICC = .67. Comparing sessions 1 and 2 the intraclass correlations for SCM efficiencies were right ICC = .58 and left ICC = .97. The peak force in controls (mean = 45.3 +/- 17.6N) was reduced by 50% in the neck pain subjects (mean = 22.4 +/- 13.1N) (p = .004). Similarly, peak force/body weight in the neck pain subjects (X = 0.3 +/- 0.2N/kg) was 46% of control (mean = 0.7 +/- 0.2N/kg) (p = .001), and average force in the neck pain subjects (X = 12.1 +/- 7.5N) was 43% of controls (mean = 28.5 +/- 11.0N) (p = .001). In two neck pain subjects. SCM, EMG and force relaxation times were abnormally long in both the affected and the unaffected SCM muscles, exceeding the control values by greater than 3 standard deviations. The difference between the right SCM efficiency of the control subjects (mean = 0.3 +/- 0.2N/ microV) and the affected SCM efficiency of the neck pain subjects (mean = 0.1 +/- 0.1 N/microV) approached the p < .05 criterion for significance (p = .055). The technique was found to be highly reliable for the measurement of neck flexor peak force, peak force/body weight, average force, and force relaxation time, and moderately reliable for the quantitation of SCM EMG relaxation times and SCM efficiency. All force values were significantly lower in the neck pain population compared with the controls. In the neck pain population, force and SCM EMG relaxation times, as well as efficiencies, suggested abnormalities. Neck pain subjects showed no significant differences in SCM EMG relaxation time or SCM efficiency between affected and unaffected SCM muscles.

Intraband Energy Relaxation of Hot-Excitons Localized at a Stacking Disorder Plane inBiI3

We study the intraband energy-relaxation of excitons localized at a stacking fault interface in a layered crystal BiI 3 observing the temporal behavior of the luminescence. The relaxation processes in this system are investigated by analyzing the time-resolved luminescence of a phonon sideband which directly reflects the exciton distribution in the band. When the exciton is resonantly excited by a picosecond laser pulse, the exciton population reveals a `hot' distribution at an early stage. The effective temperature decreases immediately according to the intraband energy-relaxation via the interaction with phonons, and after ∼40 psec, the distribution almost reaches the thermal equilibrium with the lattice. We obtain the consistent population relaxation time ( T 1 ) from the three-beam degenerate four-wave mixing signals.

Nonequilibrium electron distributions and phonon dynamics in wurtzite GaN

We report experimental measurements of nonequilibrium electron distributions as well as phonon dynamics in wurtzite GaN by using subpicosecond time-resolved Raman spectroscopy. Our experimental results have demonstrated that for electron densities n≥5×1017 cm−3, the nonequilibrium electron distributions in wurtzite GaN can be very well described by Fermi–Dirac distribution functions with the temperature of electrons substantially higher than that of the lattice. The population relaxation time of longitudinal optical phonons was directly measured to be τ≂5±1 ps at T=25 K.

Picosecond Time-ResolvedRaman Studies of Confined and Interface Optical Phonons in Short-PeriodGaAs-AlAs Multiple Quantum Well Structures

Picosecond time-resolved Raman spectroscopy was used to measure the population relaxation time of various confined and interface optical phonon modes in a series of short-period GaAs–AlAs multiple quantum well structures. The results demonstrate that within the experimental accuracy, the lifetime of various confined and interface optical phonon modes in the GaAs layers does not depend upon the GaAs well width. This is in good agreement with recent calculations by Gupta and Ridley in which optical phonons were assumed to decay into bulk-like acoustical phonons. The results also suggest that the light-scattering mechanism in this experiment is the defect-induced Fröhlich mechanism.