Yoshitaka Tanimura

Two‐dimensional femtosecond vibrational spectroscopy of liquids

The nonlinear optical response of liquids subjected to a series of N femtosecond laser pulses is calculated using a multimode harmonic model for nuclear motions, with nonlinear coupling to the radiation field through the coordinate dependence of the electronic polarizability. Using electronically off‐resonant optical fields, this multidimensional spectroscopy is shown to provide direct information regarding the homogeneous or the inhomogeneous nature of the spectral density obtained from optical birefringence measurements. Complementary information can be obtained using infrared pulses where the multiple time correlation functions of the nuclear dipole moment (rather than the electronic polarizability) are being probed.

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

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...

Time Evolution of a Quantum System in Contact with a Nearly Gaussian-Markoffian Noise Bath

A test system is assumed to interact with a heat bath consisting of harmonic oscillators or an equivalent bath with a proper frequency spectrum producing a Gaussian-Markoffian random perturbation. The effect of reaction of the test system to the bath is considered in the high temperature approximation. Elimination of the bath using the influence functional method of Feynman and Vernon yields a continuous fraction expression for the reduced density matrix of the test system. The result affords a basis to clarify the relationship between the stochastic and the dynamical approaches to treat the problem of partial destruction of quantum coherence of a system interacting with its environment.

Quantum Dynamics of System Strongly Coupled to Low-Temperature Colored Noise Bath: Reduced Hierarchy Equations Approach

Reduced equations of motion for a two-level system strongly coupled to a harmonic oscillators bath are constructed by extending the hierarchy of equations introduced by Tanimura and Kubo [J. Phys. ...

Femtosecond two-dimensional spectroscopy from anharmonic vibrational modes of molecules in the condensed phase

We have developed a theory of the fifth-order off-resonant spectroscopy to study the effect of anharmonicity of molecular vibrational modes. The anharmonicity, as well as nonlinear dependence of polarizability on nuclear coordinates, can be the origin of the fifth-order Raman signal. A profile of the signal varies depending on the relative importance of the two effects—the anharmonicity and the nonlinearity. The anharmonicity of a potential can be distinguished from the other effects such as the nonlinearity or the inhomogeneity of vibrational modes. In order to carry out calculations analytically, we employ the multimode Brownian oscillator model and treat anharmonicity as perturbation to the harmonic vibrational modes. A simple analytical expression for the fifth-order polarization is obtained through a diagrammatic technique, called Feynman rule on the unified time path. Physical pictures for the analytical expression are given for a single mode system through numerical calculations and through double-...

Non-Markovian Entanglement Dynamics in the Presence of System-Bath Coherence

A complete treatment of the entanglement of two-level systems, which evolves through the contact with a thermal bath, must include the fact that the system and the bath are not fully separable. Therefore, quantum coherent superpositions of system and bath states, which are almost never fully included in theoretical models, are invariably present when an entangled state is prepared experimentally. We show their importance for the time evolution of the entanglement of two qubits coupled to independent baths. In addition, our treatment is able to handle slow and low-temperature thermal baths.

The (2n+1)th-order off-resonant spectroscopy from the (n+1)th-order anharmonicities of molecular vibrational modes in the condensed phase

Assuming that the polarizability is a linear function of the nuclear coordinate, i.e., α(q)=α0+α1q, we obtain analytical expressions of the (2n+1)th-order signals and show that the leading order of the signals (n>1) is proportional to gn+1, where gn+1 is the coefficient of the anharmonic potential V(q)=g3q3/3!+g4q4/4!+⋅⋅⋅. In other words, detection of the (2n+1)th-order signal implies the direct observation of the (n+1)th-order anharmonicity within the approximation. Based on this fact we discuss a possibility to detect the (n+1)th-order anharmonicity directly from the (2n+1)th-order experiment. Calculations are made by using novel Feynman rules for the nonequilibrium multitime correlation functions relevant to the higher-order off-resonant spectroscopy. The rules have been developed by the authors and are presented compactly in this paper. With the help of a conventional double-sided Feynman diagram, we draw physical pictures of higher-order off-resonant optical processes. Representative calculations for...

Multistate quantum Fokker–Planck approach to nonadiabatic wave packet dynamics in pump–probe spectroscopy

The quantum Fokker–Planck equation of Caldeira and Leggett is generalized to a multistate system with anharmonic potentials and a coordinate dependent nonadiabatic coupling. A rigorous procedure for calculating the dynamics of nonadiabatic transitions in condensed phases and their monitoring by femtosecond pump–probe spectroscopy is developed using this equation. Model calculations for a harmonic system with various nonadiabatic coupling strengths and damping rates are presented. Nuclear wave packets in phase space related to electronic coherence are shown to provide an insight into the mechanism of nonadiabatic transitions. The Green’s function expression for these wave packets is used to explore possible algorithms for incorporating electronic dephasing in molecular dynamics simulations of curve crossing processes.

Modeling vibrational dephasing and energy relaxation of intramolecular anharmonic modes for multidimensional infrared spectroscopies

Starting from a system-bath Hamiltonian in a molecular coordinate representation, we examine an applicability of a stochastic multilevel model for vibrational dephasing and energy relaxation in multidimensional infrared spectroscopy. We consider an intramolecular anharmonic mode nonlinearly coupled to a colored noise bath at finite temperature. The system-bath interaction is assumed linear plus square in the system coordinate, but linear in the bath coordinates. The square-linear system-bath interaction leads to dephasing due to the frequency fluctuation of system vibration, while the linear-linear interaction contributes to energy relaxation and a part of dephasing arises from anharmonicity. To clarify the role and origin of vibrational dephasing and energy relaxation in the stochastic model, the system part is then transformed into an energy eigenstate representation without using the rotating wave approximation. Two-dimensional (2D) infrared spectra are then calculated by solving a low-temperature corrected quantum Fokker-Planck (LTC-QFP) equation for a colored noise bath and by the stochastic theory. In motional narrowing regime, the spectra from the stochastic model are quite different from those from the LTC-QFP. In spectral diffusion regime, however, the 2D line shapes from the stochastic model resemble those from the LTC-QFP besides the blueshifts caused by the dissipation from the colored noise bath. The preconditions for validity of the stochastic theory for molecular vibrational motion are also discussed.

The interplay of tunneling, resonance, and dissipation in quantum barrier crossing: A numerical study

We discuss the interplay of various quantum effects on barrier crossing for a one‐dimensional system with dissipation. This is based on a numerical study using a hierarchy of kinetic equations introduced by Tanimura and Kubo. The numerical work uses a grid in phase space for the Wigner distribution and deals with both the classical limit and the tunneling regimes.