Two-time Correlation Functions Research Articles

Quantum trajectory analysis of single-photon control from a single-molecule source

We investigate theory of single-photon control from a two-level single-molecule source irradiated by laser pulses of various shapes and pulse durations in terms of quantum trajectories which link stochastic dynamics of the radiating source with quantum measurement theory. Using Monte Carlo wave function simulation, we analyze the detailed dissipative dynamics of the single-molecule source and the photon statistics as revealed by repeated Gedanken photon measurement on the single radiating source. We show that much of the photon statistics from the two-level single-molecule single-photon sources, including few-photon emission probability, waiting time distribution, and two-time correlation function of the fluorescent light, can be understood qualitatively from the simple picture of Rabi nutation and pi pulse in terms of pulse areas.

Li jump process inh−Li0.7TiS2studied by two-timeLi7spin-alignment echo NMR and comparison with results on two-dimensional diffusion from nuclear magnetic relaxation

xTiS2 x = 0.7. Two-time correlation functions were recorded for fixed evolution times as a function of mixing time at temperatures within the 7 Li rigid-lattice regime. The corresponding decay rates were identified as Li jump rates �1 ranging from 10 �1 to 10 3 s �1 between temperatures T = 148 K and 213 K. The jump rates obtained directly from spin-alignment echo NMR and those from diffusion induced maxima of spin-lattice relaxation peaks, monitored in the laboratory as well as in the rotating frame, are consistent with each other and follow an Arrhenius law with an activation energy of 0.411 eV and a preexponential factor of 6.31 10 12 s �1 . Altogether, a solitary Li diffusion process was found between 148 and 510 K. Li diffusion was investigated in a dynamic range of about 10 orders of magnitude, i.e., 0.1 �1 7.8 10 8 s �1 . Additionally, the analysis of final-state echo amplitudes of the two-time correlation functions revealed information about the Li diffusion pathway in Li0.7TiS2. Obviously, a two-site jump process is present, i.e., besides the regularly occupied octahedral sites also the vacant tetrahedral ones within the van der Waals gap are involved in the overall two-dimensional diffusion process. DOI: 10.1103/PhysRevB.77.024311

Ultrafast Optical Spectroscopy of Spectral Fluctuations in a Dense Atomic Vapor

Transient four-wave mixing experiments with 100 fs pulses in a dense potassium vapor probe the electronic energy fluctuations that lead to optical decoherence. Echo-peak shift experiments yield a biexponential two-time correlation function of energy level fluctuations. Molecular dynamics simulations show that the slow component is a many-body excitonic contribution arising from long-range resonant interactions. The decay of the correlation function occurs on comparable time scales in theory and experiment.

Scaling and aging in the homogeneous cooling state of a granular fluid of hard particles

The presence of the aging phenomenon in the homogeneous cooling state (HCS) of a granular fluid composed of inelastic hard spheres or disks is investigated. As a consequence of the scaling property of the N-particle distribution function, it is obtained that the decay of the normalized two-time correlation functions slows down as the time elapsed since the beginning of the measurement increases. This result is confirmed by molecular dynamics simulations for the particular case of the total energy of the system. The agreement is also quantitative in the low density limit, for which an explicit analytical form of the time correlation function has been derived. Moreover, the reported results provide support for the existence of the HCS as a solution of the N-particle Liouville equation.

Observable coherence theory for statistically periodic fields

The framework of cyclostationary random processes is used to develop classical coherence theory for the measurement of statistically periodic stochastic optical fields, such as those produced by pulsed lasers. Cycloergodicity is invoked to show that precise and accurate inferences of the nonstationary process statistics can be made from a single field realization. In particular, many-pulse observations using nonlinear and/or nonstationary techniques, such as spectral shearing interferometry, can be used to fully characterize the standard two-time correlation function of a statistically periodic source. The theory is demonstrated through the simulation of spectral shearing interferometry and frequency-resolved optical gating measurements.

THE AGING BEHAVIOR OF THE RANDOM n-VECTOR MODEL WITH LONG-RANGE INTERACTION

The aging behavior of the random n-vector model with long-range interaction decaying as r-(d+σ) (where d is the dimensionality), is investigated by the theoretic renormalization-group approach. The system initially disordered at a high temperature is firstly quenched to the critical temperature T c and then released to an evolution with model A dynamics. The aging properties are studied by the short-time expansions. The scaling behavior of two-time response and correlation functions are obtained in a frame of the expansion in ∊ = 2σ-d. In dimensions d < 2σ, the long-time limit of the critical fluctuation dissipation ratio X∞ is calculated up to one-loop order. The simulation of X∞ is discussed.

Multimode analysis of the light emitted from a pulsed optical parametric oscillator

We present a multimode treatment of the optical parametric oscillator, which is valid for both pulsed and continuous-wave pump fields. The two-time correlation functions of the output field are derived, and we apply the theory to analyze a scheme for heralded production of nonclassical field states that may be subsequently stored in an atomic quantum memory.

Effects of the DNA state fluctuation on single-cell dynamics of self-regulating gene

A dynamical mean-field theory is developed to analyze stochastic single-cell dynamics of gene expression. By explicitly taking account of nonequilibrium and nonadiabatic features of the DNA state fluctuation, two-time correlation functions and response functions of single-cell dynamics are derived. The method is applied to a self-regulating gene to predict a rich variety of dynamical phenomena such as an anomalous increase of relaxation time and oscillatory decay of correlations. The effective "temperature" defined as the ratio of the correlation to the response in the protein number is small when the DNA state change is frequent, while it grows large when the DNA state change is infrequent, indicating the strong enhancement of noise in the latter case.

Coupled cavity QED for coherent control of photon transmission: Green-function approach for hybrid systems with two-level doping

This is the first one of a series of our papers theoretically studying the coherent control of photon transmission along the coupled resonator optical waveguide (CROW) by doping artificial atoms for various hybrid structures. We will provide the several approaches correspondingly based on Green function, the mean field method and spin wave theory et al. In the present paper we adopt the two-time Green function approach to study the coherent transmission photon in a CROW with homogeneous couplings, each cavity of which is doped by a two-level artificial atom. We calculate the two-time correlation function for photon in the weak-coupling case. Its poles predict the exact dispersion relation, which results in the group velocity coherently controlled by the collective excitation of the doping atoms. We emphasize the role of the population inversion of doping atoms induced by some polarization mechanism.

Microscopic Access to Long-Range Diffusion Parameters of the Fast Lithium Ion Conductor Li7BiO6 by Solid State 7Li Stimulated Echo NMR

Li self-diffusion in rhombohedral Li7BiO6, being a promising basic material for cathodes of rechargeable ion batteries, is studied by means of 7Li stimulated echo NMR. Using the pulse sequence introduced by Jeener and Broekaert, a spin-alignment echo is created whose amplitude decay is recorded as a function of mixing time. The so-obtained two-time correlation functions follow stretched exponential behavior and lead to decay rates which can be identified directly with microscopic Li motional correlation rates (tau(-1)). Using a jump distance of about 0.2 nm, this results in a diffusion coefficient (D) of about 0.5 x 10(-16) m(2) s(-1) at 294 K. The activation energy turned out to be 0.53(3) eV which is in very good agreement with recently obtained results by means of dc-conductivity measurements probing long-range diffusion parameters. This shows that stimulated echo NMR, due to its inherent time scale, gives microscopic access to long-range transport. The prefactor tau(0)(-1) of the corresponding Arrhenius law lies in the typical range of phonon frequencies, tau(0)(-1) = 3 x 10(12) s(-1).

Kinetics of the long-range spherical model

The kinetic spherical model with long-range interactions is studied after a quench to T < Tc or to T = Tc. For the two-time response and correlation functions of the order parameter as well as for composite fields such as the energy density, the ageing exponents and the corresponding scaling functions are derived. The results are compared to the predictions which follow from local scale invariance.

Nonexponential polymer segmental motion in the presence and absence of ions: H2 NMR multitime correlation functions for polymer electrolytes poly(propylene glycol)-LiClO4

The authors measure 2H NMR multitime correlation functions to investigate the segmental motion of poly(propylene glycol) containing various amounts of the salt LiClO4. 2H NMR two-time correlation functions indicate that addition of salt affects not only the time scale of the segmental motion, but also the degree of the nonexponential relaxation behavior. To quantify the origin of the nonexponential segmental motion, the authors analyze 2H NMR three-time correlation functions. In general, nonexponential relaxation can result from homogeneous dynamics, i.e., intrinsic nonexponentiality, and from heterogeneous dynamics, i.e., existence of a distribution of correlation times G(ln tau). For the studied high and low salt concentrations, including neat poly(propylene glycol), the analysis shows that both homogeneous and heterogeneous contributions are important. 2H NMR four-time correlation functions allow the authors to measure the lifetime of the dynamical heterogeneities. For the studied salt concentrations, the rate exchange occurs on the same time scale as the segmental motion, indicating short-lived dynamical heterogeneities. To arrive at these results, the authors reconsider the interpretation of (2)H NMR three-time correlation functions. Results of analytical calculations and computer simulations show that it is necessary to extend the previous way of analysis so as to include effects due to correlated back-and-forth jumps.

Ageing in one-dimensional coagulation–diffusion processes and the Fredrickson–Andersen model

We analyse the ageing dynamics of the one-dimensional Fredrickson–Andersen (FA) model in the nonequilibrium regime following a low temperature quench. Relaxation then effectively proceeds via diffusion-limited pair coagulation (DLPC) of mobility excitations. By employing a familiar stochastic similarity transformation, we map exact results from the free fermion case of diffusion-limited pair annihilation to DLPC. Crucially, we are able to adapt the mapping technique to averages involving multiple time quantities. This relies on knowledge of the explicit form of the evolution operators involved. Exact results are obtained for two-time correlation and response functions in the free fermion DLPC process. The corresponding long-time scaling forms apply to a wider class of DLPC processes, including the FA model. We are thus able to exactly characterize the violations of the fluctuation–dissipation theorem (FDT) in the ageing regime of the FA model. We find nontrivial scaling forms for the fluctuation–dissipation ratio (FDR) X = X(tw/t), but with a negative asymptotic value X∞ = −3π/(6π − 16) ≈ −3.307. While this prevents a thermodynamic interpretation in terms of an effective temperature, it is a direct consequence of probing FDT with observables that couple to activated dynamics. The existence of negative FDRs should therefore be a widespread feature in non-mean-field systems.

Short-time critical dynamics and aging phenomena in the two-dimensionalXYmodel

With Monte Carlo methods, we simulate dynamic relaxation processes of the two-dimensional XY model at the Berezinskii-Kosterlitz-Thouless phase transition temperature and below, starting from both ordered and disordered initial states. The two-time correlation function A(t',t) is measured, and aging phenomena are investigated. The power-law correction in the spatial correlation length xi(t) for relaxation with an ordered initial state and the logarithmic correction for relaxation with a disordered initial state are carefully analyzed. The scaling functions of A(t',t) are then extracted.

Dynamic photon-mode selection in Dicke superradiance

We examine the mode structures of photons emitted by collective spontaneous decay of N{sub A}>1 excited atoms confined in a small volume. By introducing the notion of dynamical modes, we show how the emission process selects a set of time-dependent mode functions in which photons are optimally occupied. In particular we show that the effective number of such dynamical modes is governed by the separability of the two-time correlation function of atomic dipoles. Due to the nonlinearity of atomic dipoles and quantum fluctuations, more than one mode can be involved even in the large-atom-number limit.

Correlation Length in the Rayleigh–Bénard Convection

A proposal from the viewpoint of the correlation length is given for the divergence of the viscosity coefficient in the Rayleigh-Benard convection. The divergence of the time integral for the two-time correlation function for the momentum flux is attributed to the increase of the correlation length. The divergence is assumed to occur when the correlation length becomes longer than the system size.

Time-resolved noise of adiabatic quantum pumps

We investigate quantum-statistical correlation properties of a periodically driven mesoscopic scatterer on a time scale shorter than the period of a drive. In this limit the intrinsic quantum fluctuations in the system of fermions are the main source of a noise. Nevertheless the effect of a slow periodic drive is clearly visible in a two-time current-current correlation function as a specific periodic in time modulation. In the limit of a strong drive such a modulation can change the sign of a current correlation function.

Probability Distribution of the Maximum of a Smooth Temporal Signal

We present an approximate calculation for the distribution of the maximum of a smooth stationary temporal signal X(t). As an application, we compute the persistence exponent associated with the probability that the process remains below a nonzero level M. When X(t) is a Gaussian process, our results are expressed explicitly in terms of the two-time correlation function, f(t)=X(0)X(t).

Ageing in the contact process: scaling behaviour and universal features

We investigate some aspects of the ageing behaviour observed in the contact process after aquench from its active phase to the critical point. In particular we discuss the scalingproperties of the two-time response function and we calculate it and its universalratio to the two-time correlation function up to first order in the field-theoreticalϵ-expansion(ϵ = 4−d). The scaling form of the response function does not fit the prediction of the theory oflocal scale invariance. Our findings are in good qualitative agreement with recent numericalresults.

Ion and polymer dynamics in polymer electrolytes PPO–LiClO4.II. H2 and Li7 NMR stimulated-echo experiments

We use H2 NMR stimulated-echo spectroscopy to measure two-time correlation functions characterizing the polymer segmental motion in polymer electrolytes PPO–LiClO4 near the glass transition temperature Tg. To investigate effects of the salt on the polymer dynamics, we compare results for different ether oxygen to lithium ratios, namely, 6:1, 15:1, 30:1, and ∞. For all compositions, we find nonexponential correlation functions, which can be described by a Kohlrausch function. The mean correlation times show quantitatively that an increase of the salt concentration results in a strong slowing down of the segmental motion. Consistently, for the high 6:1 salt concentration, a high apparent activation energy Ea=4.1eV characterizes the temperature dependence of the mean correlation times at Tg&amp;lt;T≲1.1Tg, while smaller values Ea≈2.5eV are observed for moderate salt contents. The correlation functions are most nonexponential for 15:1 PPO–LiClO4 whereas the stretching is reduced for higher and lower salt concentrations. This finding implies that the local environments of the polymer segments are most diverse for intermediate salt contents, and, hence, the spatial distribution of the salt is most heterogeneous. To study the mechanisms of the segmental reorientation, we exploit that the angular resolution of H2 NMR stimulated-echo experiments depends on the length of the evolution time tp. A similar dependence of the correlation functions on the value of tp in the presence and in the absence of ions indicates that addition of salt hardly affects the reorientational mechanism. For all compositions, mean jump angles of about 15° characterize the segmental reorientation. In addition, comparison of results from H2 and Li7 NMR stimulated-echo experiments suggests a coupling of ion and polymer dynamics in 15:1 PPO–LiClO4.