Bath Correlation Time Research Articles

Stimulated Raman adiabatic passage in the presence of dephasing

The prospect of employing the stimulated Raman adiabatic Passage (STIRAP) technique under the influence of pure dephasing is explored. A general analysis of how decoherence influences the performance of STIRAP is provided. Starting from a general and fully quantum-mechanical system–bath Hamiltonian, we derive a quantum master equation (QME) that describes the reduced dynamics of a dissipative STIRAP system. The derivation is based on the standard assumptions of (1) weak system–bath coupling; (2) Markovity, in the sense that the relaxation times are long in comparison to the bath correlation time, τc; and (3) weak field–matter interaction, in the sense that the Rabi period of the driving laser fields, Ω−1, is longer than τc. The dissipative term in this QME is the same as it would have been in the absence of the driving fields, because of the assumption of weak field–matter interaction. This type of uncontrollable dephasing is seen to diminish the efficiency of STIRAP, although the actual loss strongly depends on the specific dephasing mechanism. We also derive a more general QME, which is applicable to driving fields of arbitrary intensity. The dissipative term in the new QME is explicitly dependent on the driving fields, and therefore controllable. Intense fields are shown to effectively slow down the dephasing when Ωτc>1, which suggests that it may be possible to use STIRAP in order to transfer population between the quantum states of a solute molecule embedded in a solvent.

Non-Markovian effects on quantum optimal control of dissipative wave packet dynamics

Optimal control within the density matrix formalism is applied to the creation of a specified superposition state in condensed phases. The primary system modeled by a displaced harmonic oscillator is surrounded by a boson heat bath, the dynamics of which is described by a non-Markovian master equation. A newly developed monotonically convergent algorithm is used to solve the pulse design equations. The control mechanisms are strongly dependent on the bath correlation time that is characterized by the inverse of an exponential decay constant, γ. If the correlation time is shorter than the temporal width of a typical subpulse involved in an optimal pulse, the solution is reduced to that in the Markovian case. If we assume a longer correlation time, by weighing less physical significance on the penalty due to pulse fluence, an optimal pulse with high intensity is obtained, the temporal width of which approaches ∼1/γ. We also see considerable changes in the shape of the optimal pulse with increasing intensity, suggesting that strong fields open up control mechanisms that are qualitatively different from those in weak fields.

Time- and frequency-gated spontaneous emission as a tool for studying vibrational dynamics in the excited state

The theory of time- and frequency-gated (TFG) spontaneous emission (SE) spectra is elaborated. The present formulation generalizes previous derivations, clarifies the interrelations between different existing expressions, and establishes the validity of certain commonly assumed approximations. We obtain various explicit expressions for TFG SE spectra, which are suitable for performing actual calculations for nontrivial systems and which allow us to establish generic (that is, model-independent) properties of TFG spectra. The doorway-window picture of temporally and spectrally resolved spectra is further developed. It is shown that, to the leading order in the pump and probe pulses, the TFG SE signal is equivalent to the stimulated-emission contribution to the integral pump-probe spectrum in the case of nonoverlapping pulses. The theory is illustrated for the example of an electronic two-level system with a single Condon-active harmonic vibrational mode that is coupled to a thermal bath. The effect of imperfect time and frequency resolution is studied. It is pointed out that the TFG SE spectrum carries information not only on the strength of the system-bath coupling, but also on the relative magnitude of the bath correlation time.

Three-Pulse Photon Echo Measurements on the Accessory Pigments in the Reaction Center of Rhodobacter sphaeroides

Frequency-resolved, three-pulse photon echo peak shifts of the accessory pigments of the reaction center of Rhodobacter sphaeroides were recorded to study the ultrafast pigment−protein dynamics. For a qualitative understanding of the data, which includes an increase in rephasing capability after 1 ps, it is necessary to take into account the influence of the primary electron donor P on the 800 nm absorption band and direct electron transfer from the excited accessory bacteriochlorohyll BA. The peak shift data and the absorption spectrum are simulated via the time correlation function of the optical transition frequency. We observe subtle differences in the dynamics on the blue and red side of the absorption band, which may be related to differences in the environment between the BA and BB pigments, respectively. The bath correlation time is longer, ∼90 fs, at 810 nm than at 790 nm, where it is ∼60 fs. Since we conclude from our transient grating measurements that the time of energy transfer is 80 fs at 810 nm and 130 fs at 790 nm, this indicates that around 810 nm no significant nuclear relaxation takes place prior to energy transfer. On a longer time scale we observe coherent oscillations of low frequency, ∼3−4 and 36 cm-1, and a small ∼30 ps decay of rephasing capability.

The Integrated Photon Echo and Solvation Dynamics

The time-integrated three-pulse photon echo is discussed in terms of the line-shape functions which are shown to be directly related to the solvation dynamics. By using the short-time approximation to the line-shape function, an algebraic form of the three-pulse photon echo signal SPE (τ, T) is obtained as a function of two delay times, τ and T, between pulses. On the basis of the approximate form of the photon echo signal, the echo peak shift with respect to the second delay time (population evolution period) is derived and found to be linearly proportional to the time-dependent fluorescence Stokes shift function for times greater than the bath correlation time, τc. In the case of intermediate inhomogeneous broadening, the asymptotic echo peak shift magnitude is found to be useful in estimating the static inhomogeneous width. To illustrate the theoretical results, an analysis of the echo peak shift measurement of IR144 in a room temperature glass, PMMA, is presented.

Relationship between a nonlinear response and relaxation induced by colored noise.

The nonlinear response to external disturbances of a system of interest scrA (the ``atom'') in contact with a thermal bath is studied. The central issue is the relationship between the nonlinear susceptibility and the equilibrium relaxation spectra of observables of scrA. Paralleling the results of the linear-response theory, the nth-order nonlinear susceptibility is factorized by quantum-mechanical arguments into two terms pertaining to the disturbances and the spin-bath system, respectively. The role of slow atom states, i.e., states relaxing on times T longer than the bath correlation time ${\mathrm{\ensuremath{\tau}}}_{\mathit{c}}$, is pointed out, by recurring to recent findings on their general features [Phys. Rev. A 46, 6222 (1992)]. In the frame of a stochastic picture of the bath and a multilevel scheme of the system scrA, the conditions under which the nonlinear susceptibility provides the spectrum of the slow atom states are clarified. Illustrations are drawn from magnetic resonance to demonstrate that techniques based on the nonlinear response of a spin system to multiple continuous waves compete favorably with pulsed techniques to provide information on longitudinal spin relaxation.

Memory kernel for a multilevel quantum system driven by colored thermal noise

The memory kernel appearing in a non-Markovian population equation for a multilevel quantum system stochastically coupled to a colored Gaussian bath is calculated on the basis of a fully quantum-mechanical treatment to construct the time autocorrelation function (TAF) associated to the system–bath interaction Hamiltonian. The limiting cases of high and low temperatures and white noise bath are also analyzed. These examples allow us to discuss in a very simple way the dependence of the memory kernel on the Bohr frequencies of the system, the intensity of the system–bath interaction, its correlation time, and the bath temperature. In particular, it is shown that a true Markovian population equation is only achieved at high temperatures with a bath correlation time much shorter than the relaxation process characteristic time.

Onset of non-Markovian behaviour in a harmonic oscillator stochastically coupled to a thermal bath

The influence of a finite bath correlation time and the bath temperature on the onset of a non-Markovian behaviour in the relaxation of a harmonic oscillator linearly coupled to a coloured thermal bath is analysed. A fully quantum mechanical treatment of the time autocorrelation function of the oscillator-bath interaction is made. Special attention is paid to the temperature dependence. In the low-temperature regime a non- exponential time decay of the mean number of quanta is found even though the correlation time associated with the oscillator-bath interaction is zero.

Vibrational dephasing in liquid nitrogen at high densities studied with time-resolved stimulated Raman gain spectroscopy

In highly compressed liquid nitrogen at 295 K we observe a sharp increase in the vibrational dephasing rate T−12 with increasing density, indicating that at high fluid densities (2.3 to 2.9×1022 cm−3) the modulation of the vibrational frequency shows a stronger density dependence than the bath correlation time due to the action of short range repulsive forces. The observed behavior shows good agreement with results of previously published molecular dynamics simulations and a fit to a binary interaction model. When the phase transition from the liquid to the solid state takes place we observe a sudden drop in T–12 by a factor of 4. We also present the variation of the Raman line shift of liquid and solid nitrogen with pressure over a region of 0.5 to 4.6 GPa at 295 K.

On “anomalous” free induction decay rate

Generalized non-markovian master equations, which take into account the nonvanishing bath correlation time τ c, are used to explain the “anomalous” (which cannot be described by the well-known Bloch master equations) behaviour of the optical free induction decay recently observed by DeVoe and Brewer [Phys. Rev. Lett. 50 (1983) 1269] for the Pr 3+: LaF 3 at T ≃ 1.6 K. We found τ c = 5 μs to be the best fit of our theory to the above experiment provided that T 1 = 100 μs, T 2 = 24 μs. New experimental tests of the non-markovian relaxation theory are proposed.

Non-Markovian theory of collisional dephasing in near resonance light scattering

We present a general microscopic theory for near resonance light scattering (RLS) from collisionally perturbed atoms and molecules. The theory is based on the tetradic scattering formalism of Fano and Ben-Reuven. We perform a systematic density expansion and show that the four-time, many-body, dipole correlation functions necessary for the evaluation of the RLS cross section may be rigorously expressed (to lowest order in pressure) in terms of three single-particle, two-time, correlation functions, two of which are associated with the absorption and emission line broadening and the third is a cross correlation function. Our most general expressions are valid for an arbitrary value of the bath correlation time (relative to the broadening), and interpolate smoothly all the way from the static limit of inhomogenous broadening up to the reverse, the Markovian (homogenous) limit. The stochastic Gaussian model of Takagahara, Hanamura, and Kubo is obtained also as a special case of the present formulation.