Half century has past since the pioneering works of Anderson and Kubo on the stochastic theory of spectral line shape were published in J. Phys. Soc. Jpn. 9 (1954) 316 and 935, respectively. In this review, we give an overview and extension of the stochastic Liouville equation focusing on its theoretical background and applications to help further the development of their works. With the aid of path integral formalism, we derive the stochastic Liouville equation for density matrices of a system. We then cast the equation into the hierarchy of equations which can be solved analytically or computationally in a nonperturbative manner including the effect of a colored noise. We elucidate the applications of the stochastic theory from the unified theoretical basis to analyze the dynamics of a system as probed by experiments. We illustrate this as a review of several experimental examples including NMR, dielectric relaxation, Mossbauer spectroscopy, neutron scattering, and linear and nonlinear laser spectroscop...

Stochastic Liouville, Langevin, Fokker–Planck, and Master Equation Approaches to Quantum Dissipative Systems

Two-dimensional infrared (2D IR) vibrational spectroscopy is an experimental tool for investigating molecular dynamics in solution on a picosecond time scale. We present experimental and theoretical methods for obtaining a 2D IR correlation spectrum and modeling the underlying microscopic information. Fourier transform 2D spectra are obtained from heterodyne-detected third-order nonlinear signals using a sequence of broad bandwidth femtosecond IR pulses. A 2D IR correlation spectrum with absorptive line shapes results from the addition of 2D rephasing and nonrephasing spectra, which sample conjugate frequencies during the initial evolution time period. The 2D IR spectrum contains peaks with different positions, signs, amplitudes, and line shapes characterizing the vibrational eigenstates of the system and their interactions with the surrounding bath. The positions of the peaks map the transition frequencies between the ground, singly, and doubly excited states of the system and thus describe the anharmoni...

Coherent 2D IR Spectroscopy: Molecular Structure and Dynamics in Solution

Two-dimensional spectroscopy using diffractive optics based phased-locked photon echoes

Ultrafast solvent dynamics of room-temperature ionic liquids have been investigated by optical heterodyne-detected Raman-induced Kerr-effect spectroscopy (OHD-RIKES) by studying the effects of cation and anion substitution on the low frequency librational modes. The spectra of two series of imidazolium salts are presented. The first series is based on the 1-butyl-3-methylimidazolium salts [bmim]+ containing the anions trifluoromethanesulfate [TfO]−, bis(trifluoromethanesulfonyl)imide [Tf2N]−, and hexafluorophosphate [PF6]−. The second series is based on [Tf2N]− salts containing the three cations 1-butyl-2,3-dimethylimidazolium [bmmim]+, 1-methyl-3-octylimidazolium [omim]+, and [bmim]+. It is found in all five samples that the signal is due to libration of the imidazolium ring at three frequencies around 30, 65, and 100 cm−1 corresponding to three local configurations of the anion with respect to the cation.

The effects of anion and cation substitution on the ultrafast solvent dynamics of ionic liquids: A time-resolved optical Kerr-effect spectroscopic study

Two-dimensional electronic spectroscopy (2DES) reveals connections between an optical excitation at a given frequency and the signals it creates over a wide range of frequencies. These connections, manifested as cross-peak locations and their lineshapes, reflect the underlying electronic and vibrational structure of the system under study. How these spectroscopic signatures evolve in time reveals the system dynamics and provides a detailed picture of coherent and incoherent processes. 2DES is rapidly maturing and has already found numerous applications, including studies of photosynthetic energy transfer and photochemical reactions and many-body interactions in nanostructured materials. Many systems of interest contain electronic transitions spanning the ultraviolet to the near infrared and beyond. Most 2DES measurements to date have explored a relatively small frequency range. We discuss the challenges of implementing 2DES and compare and contrast different approaches in terms of their information content, ease of implementation, and potential for broadband measurements.

Experimental Implementations of Two-Dimensional Fourier Transform Electronic Spectroscopy

This work exploits the passive phase stabilization of diffractive optics to implement heterodyne detection of the complete χ(5) tensor of liquid CS2 as an example of a simple liquid. This approach permits the use of two different colors for the excitation, probe, and detection beam protocols and enables full optimization of the signal with respect to discrimination against lower order cascaded third-order responses. This work extends the previous study of polarization selectivity, in combination with heterodyne detection, to all independent polarization components to provide further insight into the origins of the fifth-order response and its connection to the multitime correlation of the liquid dynamics. The characteristic feature that clearly distinguishes the direct fifth-order response from lower order cascades is the pronounced ridge along the τ4 axis (probe pulse delay) with very rapid decay along the τ2 axis (excitation pulse delay). This observation is in contrast to recent related work using one-...

Diffractive optics-based six-wave mixing: Heterodyne detection of the full χ(5) tensor of liquid CS2

Diffractive optics based two-color six-wave mixing: phase contrast heterodyne detection of the fifth order Raman response of liquids

Diffractive optics are applied to six-wave mixing processes to provide a single optic approach to attaining the required, relatively complex, phase-matching geometry to discriminate against lower-order nonlinear responses. The diffractive optics were designed specifically for broad-bandwidth operation and passive phase locking of the appropriate pulse pairs for use in femtosecond two-dimensional Raman studies of the dynamic structure of liquids. The fifth-order signal was studied in liquid CS2; two different colors were used for the excitation and the probe to reduce background scatter, as were two different phase-matching geometries with different degrees of suppression of cascaded third-order processes.

Diffractive optics implementation of six-wave mixing.

Summary form only given. With a single diffractive optic it is possible to create a beam geometry which significantly phase mismatches the cascaded intermediates while maintaining near-perfect phase matching of the direct, fifth-order signal. Additionally, the diffractive optic provides passive phase-locking (/spl sim//spl lambda//50) necessary to implement heterodyne detection by interfering a reference local oscillator with the generated signal field. We present studies of liquid CS/sub 2/ where, in addition to the phase-contrast inherent in a heterodyne measurement, the effects of other variables, such as polarization and pathlength, distinguish the direct fifth-order response from the lower-order cascades.

Diffractive-optics based fifth-order Raman spectroscopy of ultrafast liquid dynamics

Summary form only given. Biological systems constantly transduce various forms of chemical energy into functions in which the inherent response of the system operates at the edge of stability. Excursions from the stability region lead to denaturation; whereas small fluctuations about the stability point lead to highly correlated responses that behave in a deterministic fashion with respect to the function of the system. Exactly how is the bond energy directed in such a complex system and how has the system evolved to minimize entropic losses in conversion efficiency? We have used the oxygen binding heme proteins as model systems for studying the coupling of reaction forces to functionally relevant motions; i.e., structural transitions important to the self regulation of oxygen binding and transport. Since the forces involved become spatially distributed over an enormous number of degrees of freedom, the net relative motions can be exceedingly small (<.1 /spl Aring/). A very sensitive method is needed to detect these motions and the time resolution must be sufficient to follow from the very first events of bond breaking to full relaxation. The use of diffractive optics for the implementation of heterodyne detected grating spectroscopy has recently been demonstrated. The diffractive optic also generates tilted phase fronts to provide true femtosecond time resolution in noncollinear geometries. This approach has sufficient time resolution and sensitivity to follow the mass displacement, as connected through changes in the material index of refraction, to address this issue.

V. Astinov

Papers

Diffractive optics-based six-wave mixing: Heterodyne detection of the full χ(5) tensor of liquid CS2

Diffractive optics based two-color six-wave mixing: phase contrast heterodyne detection of the fifth order Raman response of liquids

Diffractive optics implementation of six-wave mixing.

Diffractive-optics based fifth-order Raman spectroscopy of ultrafast liquid dynamics

Diffractive optics-based nonlinear spectroscopy: application to the study of deterministic protein motion