Population Relaxation Rate Research Articles

μ POP Clock: A Microcell Atomic Clock Based on a Double-Resonance Ramsey Scheme

We demonstrate and study a microcell microwave atomic clock based on optical-microwave double resonance (DR) interrogation operated in a pulsed Ramsey scheme, called the \ensuremath{\mu}POP clock, based on a microfabricated Rb vapor cell and a micro-loop-gap microwave resonator. For the mm-scale dimensions of this cell, the population and coherence relaxation rates of the Rb clock transition are on the order of 4--5 kHz, which puts constraints on the useful Ramsey times and overall pulse sequence in view of optimized clock performance. Our proof-of-principle demonstration of the \ensuremath{\mu}POP clock shows that the pulsed DR approach is nevertheless feasible and results in a short-term clock stability of 1 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}11}$ \ensuremath{\tau}${}^{\ensuremath{-}1/2}$ and reaching the \ensuremath{\le}2 \ifmmode\times\else\texttimes\fi{} ${10}^{\ensuremath{-}12}$ level at timescales of 1000 s to one day. The short-term instability budget established for the \ensuremath{\mu}POP clock shows that the main limitation to the short-term stability arises from the detection noise. Thanks to the pulsed Ramsey scheme, light-shift effects are strongly reduced in the \ensuremath{\mu}POP clock, which opens perspectives for further improvements of long-term clock stability, in view of future generations of miniature vapor-cell clocks with enhanced performances based on the DR scheme.

Vibration-mediated energy transport in bacterial reaction center: Simulation study.

Exciton energy relaxation in a bacterial Reaction Center (bRC) pigment-protein aggregate presumably involves emission of high energy vibrational quanta to cover wide energy gaps between excitons. Here, we assess this hypothesis utilizing vibronic two-particle theory in modeling of the excitation relaxation process in bRC. Specific high frequency molecular vibrational modes are included explicitly one at a time in order to check which high frequency vibrations are involved in the excitation relaxation process. The low frequency bath modes are treated perturbatively within Redfield relaxation theory. The analysis of the population relaxation rate data indicates energy flow pathways in bRC and suggests that specific vibrations may be responsible for the excitation relaxation process.

Two-dimensional infrared study of the C[sbnd]D and C[dbnd]O stretching vibrations in strongly hydrogen-bonded complexes

We report a study of the CD and CO stretching modes of formyl deuterated formic acid (DCOOH) hydrogen bonded to nitrogenous bases. These modes are spectators to the hydrogen bond itself but are sensitive to the strength of that interaction. Using 2D IR spectroscopy, we show that in strongly hydrogen bonded complexes the CD stretching vibration becomes anharmonically coupled to low-order combination states leading to strong state mixing resulting in Fermi resonance transitions in the 2D IR spectra. In contrast, the CO vibrations show multiple peaks as a result of conformational heterogeneity associated with internal rotation about the hydrogen bond. For both modes, the population relaxation rates tend to be quite short, ∼1 ps or less. Having characterized the vibrational spectroscopy of these spectator vibrations, we conclude that they are quite sensitive to details of the hydrogen bonding interactions though their utility is limited by spectral complexity and short population lifetimes.

Flux Noise in a Superconducting Transmission Line

We study a superconducting transmission line (TL) formed by distributed LC oscillators and excited by external magnetic fluxes which are aroused from random magnetization (A) placed in substrate or (B) distributed at interfaces of a two-wire TL. Low-frequency dynamics of a random magnetic field is described based on the diffusion Langevin equation with a short-range source caused by (a) random amplitude or (b) gradient of magnetization. For a TL modeled as a two-port network with open and shorted ends, the effective magnetic flux at the open end has non-local dependency on noise distribution along the TL. The flux-flux correlation function is evaluated and analyzed for the regimes (Aa), (Ab). (Ba), and (Bb). Essential frequency dispersion takes place around the inverse diffusion time of random flux along the TL. Typically, noise effect increases with size faster than the area of TL. The flux-flux correlator can be verified both via the population relaxation rate of the qubit, which is formed by the Josephson junction shunted by the TL with flux noises, and via random voltage at the open end of the TL.

On the accuracy of the LSC-IVR approach for excitation energy transfer in molecular aggregates.

We investigate the applicability of the linearized semiclassical initial value representation (LSC-IVR) method to excitation energy transfer (EET) problems in molecular aggregates by simulating the EET dynamics of a dimer model in a wide range of parameter regime and comparing the results to those obtained from a numerically exact method. It is found that the LSC-IVR approach yields accurate population relaxation rates and decoherence rates in a broad parameter regime. However, the classical approximation imposed by the LSC-IVR method does not satisfy the detailed balance condition, generally leading to incorrect equilibrium populations. Based on this observation, we propose a post-processing algorithm to solve the long time equilibrium problem and demonstrate that this long-time correction method successfully removed the deviations from exact results for the LSC-IVR method in all of the regimes studied in this work. Finally, we apply the LSC-IVR method to simulate EET dynamics in the photosynthetic Fenna-Matthews-Olson complex system, demonstrating that the LSC-IVR method with long-time correction provides excellent description of coherent EET dynamics in this typical photosynthetic pigment-protein complex.

Theory of saturated-absorption cavity ring-down: radiocarbon dioxide detection, a case study

The theoretical bases of saturated-absorption cavity ring-down (SCAR) spectroscopy are treated and described in detail in different transition broadening regimes. All the approximations that are introduced to achieve a model as simple and accurate as possible are discussed. In the Voigt broadening regime, a calibration factor that relates the measured spectral areas in the saturated and linear absorption regimes is retrieved. A relevant application of this technique to the measurement of radiocarbon dioxide concentration at both enriched and natural abundance (∼10−12) is presented. The population relaxation rate of one ro-vibrational state of the ν3 band is measured for this highly diluted CO2 isotopologue.

Vibrational dephasing in ionic liquids as a signature of hydrogen bonding.

Understanding both structure and dynamics is crucial for producing tailor-made ionic liquids (ILs). We studied the vibrational and structural dynamics of medium versus weakly hydrogen-bonded CH groups of the imidazolium ring in ILs of the type [1-alkyl-3-methylimidazolium][bis(trifluoromethanesulfonyl)imide] ([Cn mim][NTf2 ]), with n=1, 2, and 8, by time-resolved coherent anti-Stokes Raman scattering (CARS) and quantum-classical hybrid (QCH) simulations. From the time series of the CARS spectra, dephasing times were extracted by modeling the full nonlinear response. From the QCH calculations, pure dephasing times were obtained by analyzing the distribution of transition frequencies. Experiments and calculations reveal larger dephasing rates for the vibrational stretching modes of C(2)H compared with the more weakly hydrogen-bonded C(4,5)H. This finding can be understood in terms of different H-bonding motifs and the fast interconversion between them. Differences in population relaxation rates are attributed to Fermi resonance interactions.

Heterogeneity in (2-butoxyethanol + water) mixtures: Hydrophobicity-induced aggregation or criticality-driven concentration fluctuations?

Micro-heterogeneity in aqueous solutions of 2-butoxyethanol (BE), a system with closed loop miscibility gap, has been explored via absorption and time-resolved fluorescence measurements of a dissolved dipolar solute, coumarin 153 (C153), in the water-rich region at various BE mole fractions (0 ≤ XBE ≤ 0.25) in the temperature range, 278 ≤ T/K ≤ 320. Evidences for both alcohol-induced H-bond strengthening and subsequent structural transition of H-bond network have been observed. Analyses of steady state and time-resolved spectroscopic data for these aqueous mixtures and comparisons with the results for aqueous solutions of ethanol and tertiary butanol indicate that alcohol aggregation in BE/water mixtures is driven by hydrophobic interaction with no or insignificant role for criticality-driven concentration fluctuations preceding phase separation. Excitation energy dependence of fluorescence emission of C153 confirms formation of aggregated structures at very low BE mole fractions. No asymptotic critical power law dependence for relaxation rates of the type, k ∝ (|T - Tc|/Tc)(γ), with γ denoting universal critical constant, has been observed for both solute's rotational relaxation and population relaxation rates in these mixtures upon either approaching to critical concentration or critical temperature. Estimated activation energies for rotational relaxation rate of C153 and solution viscosity have been found to follow each other with no abrupt changes in either of them at any mixture composition. In addition, measured C153 rotation times at various compositions and temperatures reflect near-hydrodynamic viscosity coupling through the dependence,〈τr〉∝ (η/T)(p), with p = 0.8-1.0, suggesting solute's orientational relaxation dynamics being, on an average, temporally homogeneous.

Homogeneous linewidth measurements of Yb3+ ions in congruent and stoichiometric lithium niobate crystals

We report the result of a series of pump–probe spectral hole burning measurements on Yb3+ doped stoichiometric and congruent lithium niobate single crystal. The measurements were performed with a stabilized diode laser tuned to the ≈980nm transition of the dopant ions. The crystal samples were placed in a closed cycle helium cryostat, the experiments have been done in the temperature range 9–20K. The observed spectral holes have complex structure, at least two Lorentzian curves are needed to reproduce their shape (double spectral hole). A simple theoretical model has been developed to describe the line-shape resulting from the interaction between the light pulses and the dopant ions. Using the predictions of the theory, the homogeneous linewidths and the population relaxation rates have been estimated for both crystal samples. Using these results, the temperature dependence of the spectral hole widths and the spectral diffusion rates have also been determined. Some considerations are presented to explain the origin of the double spectral hole structure.

Saturated absorption and crossover resonances in a high-finesse cavity: Formalism and application to the hyperfine structure of jet-cooled NO2by saturated-absorption cavity-ring-down spectroscopy

The ${}^{q}{R}_{0}(0)$ rotational transition in the $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{A}{\phantom{\rule{0.16em}{0ex}}}^{2}{B}_{2}\ensuremath{\leftarrow}\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{X}{\phantom{\rule{0.16em}{0ex}}}^{2}{A}_{1}$ system of jet-cooled ${\mathit{NO}}_{2}$ located around $12\phantom{\rule{0.16em}{0ex}}536\phantom{\rule{0.16em}{0ex}}\phantom{\rule{0.16em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ is analyzed using a nonlinear-susceptibility formalism designed to describe the saturated absorption due to two identical counter-propagating radiations in an $n$-level system. An analytical solution of the equations of motion is obtained in the frequency space by considering the pertinent experimental conditions, mainly a high-finesse cavity and a slit-shaped supersonic expansion. Calculation of the nonlinear absorption coefficient requires the summing of all Zeeman-component contributions and a final numerical integration over the frequency detuning assuming a Maxwell-Boltzmann speed distribution. Determination of the experimental absorption coefficients is obtained by converting the shape of the temporal decay of the electromagnetic field amplitude initially captured inside the cavity. The molecular Hamiltonian includes both spin-rotation and hyperfine interactions. Molecular constants relative to the upper level are derived by exploiting Doppler-broadening-free so-called saturated-absorption cavity-ring-down spectroscopy. The dipole moment of the partially assigned hot band is obtained [${\ensuremath{\mu}}_{\mathrm{band}}=0.0047(12)$ D] together with the number density and the effective population relaxation rates. The model is validated by varying the intracavity power from 0 to 230 W (i.e., up to a maximum peak irradiance of $240\ifmmode\times\else\texttimes\fi{}{10}^{3}\phantom{\rule{0.28em}{0ex}}\mathrm{W}/{\mathrm{cm}}^{2}$), representing saturation coefficients up to 120. The experimental position, shape, and width of the Lamb and crossover dips are well reproduced. The spatial shape and modulation of the electromagnetic field are discussed.

Dissipation in molecular junctions

A recently developed theory that formulates the phenomena of inelastic transport and current-driven dynamics in molecular-scale electronics within a time-dependent scattering approach is extended to account for dissipation of the current-induced excitation through coupling to electrode phonons and electron-hole pairs. Our approach treats the electronic transport, the nuclear dynamics, and the energy and phase exchange between the electronic and the vibrational subspaces in the course of the inelastic scattering event within the Schrodinger picture, whereas the dissipation of the energy deposited in the nuclear modes is accounted for within a density matrix approach. Subsequent to formulation of the theory in terms of population relaxation and phase decoherence rates, we develop approaches for computing these rates, treating on equal footing the dissipation due to excitation of electron-hole pairs and that due to the interaction with phonons. Finally, we test the derived rates by application to the model problem of CO adsorbed on metal surfaces, an example that has been extensively studied previously and for which several experimental results are available for comparison.

Mixed Frequency/Time Domain Optical Analogues of Heteronuclear Multidimensional NMR

Ultrafast spectroscopy is dominated by time domain methods such as pump-probe and, more recently, 2D-IR spectroscopies. In this paper, we demonstrate that a mixed frequency/time domain ultrafast four wave mixing (FWM) approach not only provides similar capabilities, but it also provides optical analogues of multiple- and zero-quantum heteronuclear nuclear magnetic resonance (NMR). The method requires phase coherence between the excitation pulses only over the dephasing time of the coherences. It uses twelve coherence pathways that include four with populations, four with zero-quantum coherences, and four with double-quantum coherences. Each pathway provides different capabilities. The population pathways correspond to those of two-dimensional (2D) time domain spectroscopies, while the double- and zero-quantum coherence pathways access the coherent dynamics of coupled quantum states. The three spectral and two temporal dimensions enable the isolation and characterization of the spectral correlations between different vibrational and/or electronic states, coherence and population relaxation rates, and coupling strengths. Quantum-level interference between the direct and free-induction decay components gives a spectral resolution that exceeds that of the excitation pulses. Appropriate parameter choices allow isolation of individual coherence pathways. The mixed frequency/time domain approach allows one to access any set of quantum states with coherent multidimensional spectroscopy.

OH-Stretch Vibrational Relaxation of HOD in Liquid to Supercritical D2O

The population relaxation of the OH-stretching vibration of HOD diluted in D2O is studied by time-resolved infrared (IR) pump-probe spectroscopy for temperatures of up to 700 K in the density range 12 <or= rho <or= 58 mol/L. For selected state points of the fluid solution, transient IR spectra were recorded following resonant excitation of the v = 0 --> 1 OH stretching transition with a 200 fs laser pulse centered at approximately 3500 cm(-1). Above 400 K these spectra show no indication of spectral diffusion after pump-probe delays of 0.3 ps. Over nearly the entire density range and for sufficiently high temperatures (T > 360 K), the vibrational relaxation rate constant, kr, is strictly proportional to the dielectric constant, epsilon, of water. Together with existing molecular dynamics simulations, this result suggests a simple linear dependence of kr on the number of hydrogen-bonded D2O molecules. It is shown that, for a given temperature, an isolated binary collision model is able to adequately describe the density dependence of vibrational energy relaxation even in hydrogen-bonded fluids. However, dynamic hydrogen bond breakage and formation is a source of spectral diffusion and affects the nature of the measured kr. For sufficiently high temperatures when spectral diffusion is much faster than energy transfer, the experimentally observed decays correspond to ensemble averaged population relaxation rates. In contrast, when spectral diffusion and vibrational relaxation occur on similar time scales, as is the case for ambient conditions, deviations from the linear kr(epsilon) relation occur because the long time decay of the v = 1 population is biased to slower relaxing HOD molecules that are only weakly connected to the hydrogen bond network.

Constraints on relaxation rates forN-level quantum systems

We study the constraints imposed on the population and phase relaxation rates by the physical requirement of completely positive evolution for open N-level systems. The Lindblad operators that govern the evolution of the system are expressed in terms of observable relaxation rates, explicit formulas for the decoherence rates due to population relaxation are derived, and it is shown that there are additional, non-trivial constraints on the pure dephasing rates for N>2. Explicit experimentally testable inequality constraints for the decoherence rates are derived for three and four-level systems, and the implications of the results are discussed for generic ladder-, Lambda- and V-systems, and transitions between degenerate energy levels.

Vibrational Dynamics of Terminal Acetylenes: III. Comparison of the Acetylenic C−H Stretch Intramolecular Vibrational-Energy Redistribution Rates in Ultracold Molecular Beams, Room-Temperature Gases, and Room-Temperature Dilute Solutions

The population relaxation rate of the first excited state of the acetylenic C−H stretch is compared for a series of isolated and solvated terminal acetylenes. The isolated molecule relaxation rate for ultracold molecules is measured using high-resolution infrared spectroscopy in a molecular beam. These measurements use a microwave−infrared double-resonance technique to obtain rotationally resolved spectra that originate in the vibrational ground state. The relaxation rates in room-temperature gas and dilute CCl4 solution (0.05 M) are measured using two-color transient absorption picosecond spectroscopy. Although the molecule-dependent contribution to the total relaxation rate in solution is proportional to the population relaxation rate measured for the isolated molecule under molecular-beam conditions, a large scale factor (27) is required to reach quantitative agreement. Part of the reason a large IVR scaling rate is observed can be attributed to the fact that the intramolecular vibrational-energy redis...

Vibrational Dynamics of Terminal Acetylenes: I. Comparison of the Intramolecular Vibrational Energy Redistribution Rate of Gases and the Total Relaxation Rate of Dilute Solutions at Room Temperature

The population relaxation rate of the first excited state of the acetylenic C−H stretch is compared for room-temperature gas-phase and solution-phase samples of 10 terminal acetylenes. The gas-phase sample pressure is less than 1 atm for all measurements, ensuring that the dynamics occur under collision-free conditions. The relaxation rates are measured using two-color transient absorption picosecond spectroscopy. The population of the excited state is monitored directly through the anharmonically shifted v = 1−v = 2 excited-state transition. The relaxation rates of isolated and solvated molecules are strongly correlated and follow a relationship expected for a parallel relaxation process in solution: the total rate in solution is the sum of a molecule-dependent rate related to the isolated molecule dynamics and a molecule-independent solvent-induced relaxation rate. For the terminal acetylenes, the vibrational normal-mode frequencies of the acetylene chromophore and their anharmonic interactions are highly conserved for all terminal acetylenes. Therefore, the observation that a single solvent relaxation contribution to the total relaxation rate describes the solution dynamics for all terminal acetylenes is consistent with the idea that solvent-induced energy relaxation pathways are dominated by the vibrational motions that are in close proximity to the excited state.

Optically induced coherent intraband dynamics in disordered semiconductors

On the basis of a tight-binding model for a strongly disordered semiconductor with correlated conduction- and valence band disorder a new coherent dynamical intra-band effect is analyzed. For systems that are excited by two, specially designed ultrashort light-pulse sequences delayed by tau relatively to each other echo-like phenomena are predicted to occur. In addition to the inter-band photon echo which shows up at exactly t=2*tau relative to the first pulse, the system responds with two spontaneous intra-band current pulses preceding and following the appearance of the photon echo. The temporal splitting depends on the electron-hole mass ratio. Calculating the population relaxation rate due to Coulomb scattering, it is concluded that the predicted new dynamical effect should be experimentally observable in an interacting and strongly disordered system, such as the Quantum-Coulomb-Glass.

Semiclassical stability analysis of a two-photon laser including spatial variation of the cavity field

We investigate the dynamics of a two-photon laser under conditions where the spatial variation of the cavity field along the cavity axis is important. Main attention is paid to linear stability analysis and numerical investigation of a two-photon laser for the Maxwell-Bloch equations. The model assumes pumping to the upper state of the two-photon transition. We consider the Maxwell-Bloch equations on the basis of which we study the stability analysis of the steady state of the system. The system is taken to be contained in a ring-laser cavity. Asymptotic expansion of the eigenvalue and analytic information are obtained in some realistic limits, such as very large reflectivity, very small cavity losses, or very small population relaxation rate. The results are illustrated with an application to a specific atomic system (Potassium) as an amplifying medium.

Quantum Brownian motion on potential surfaces coupled via tunneling in an external electric field[-2mm

The present paper deals with the motion of a Brownian particle on two identical but shifted potential surfaces, coupled via a tunneling matrix element in an external electric field. Dissipation is induced by a heat bath represented by an infinite set of harmonic oscillators with a continuum range of frequencies. We derive a perturbative solution for the quantum coherence term of the particle system after performing a small-polaron-like transformation. This is subsequently necessary for the extraction of an equation that describes the reduced dynamics and the minimal action path of the Brownian particle. Finally we extract expressions for the population relaxation rate and the pure quantum-dephasing rate of the two-level system.

Selective excitation in pulsed EPR of spin-correlated radical pairs: electron–electron interactions, zero-, single-, and double-quantum relaxation and spectral diffusion

Experiments are described in which a low-amplitude microwave pulse excites only one out of four allowed transitions of a spin-correlated radical pair (SCRP). A second high-amplitude pulse produces an FID whose temporal shape is strongly modulated with frequencies determined by electron–electron spin-exchange and dipolar interactions. The dependence of the FID intensity on the delay between the two pulses is determined by the relaxation of populations of energy levels connected by allowed single-quantum transitions and by forbidden zero- and double-quantum transitions. The first direct measurement of the zero-quantum population relaxation rate for P + Q A − radical pairs in bacterial photosynthetic reaction centers shows it is temperature independent.