Structure and Dynamics in Solids As Probed by Optical Spectroscopy

Skinner, James; Moerner, W. E.

doi:10.1021/jp9601328

Cited by 122 publications

(84 citation statements)

References 133 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Because such an environment changes due to the lattice vibration of the surrounding atoms or molecules, the frequency fluctuates with time. [111][112][113][114][115][116] SMD can probe this stochastic trajectory of frequency without taking an ensemble average, which is now called spectral diffusion 115) Reilly and Skinner explained spectral diffusion using a model of a chromophore coupled to a collection of stochastic two-state jump systems. 116) In 2D spectroscopy, the multibody correlation functions of a molecular dipole or polarizability are measured using ultrashort pulses.…”

Section: Molecular Vibrational Spectroscopymentioning

confidence: 99%

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

2006

View full text Add to dashboard Cite

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, Mössbauer spectroscopy, neutron scattering, and linear and nonlinear laser spectroscopies. Following the summary of the advantage and limitation of the stochastic theory, we then derive a quantum Fokker-Planck equation and a quantum master equation from a system-bath Hamiltonian with a suitable spectral distribution producing a nearly Markovian random perturbation. By introducing auxiliary parameters that play a role as stochastic variables in an expression for reduced density matrix, we obtain the stochastic Liouville equation including temperature correction terms. The auxiliary parameters may also be interpreted as a random noise that allows us to derive a quantum Langevin equation for non-Markovian noise at any temperature. The results afford a basis for clarifying the relationship between the stochastic and dynamical approaches. Analytical as well as numerical calculations are given as examples and discussed.

show abstract

Section: Molecular Vibrational Spectroscopymentioning

confidence: 99%

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

2006

View full text Add to dashboard Cite

show abstract

“…This constitutes a result, which could have never been achieved using bulk, ensemble averaged methods. Single-molecule fluorescence approaches were also employed to probe crystals of organic molecules [34] and glassy materials [35] and related results have significantly contributed to the understanding of structure and dynamics of soft condensed matter. Lattice dynamics at low temperatures was investigated by following single molecule spectral diffusion or linewidth distributions and different explanations based on a two-level-system concept [36,37] were developed to account for the observed behavior [38][39][40][41].…”

Section: Introductionmentioning

confidence: 99%

Probing polymers with single fluorescent molecules

Tomczak¹,

Vallée²,

Dijk³

et al. 2004

European Polymer Journal

View full text Add to dashboard Cite

The use of single molecules to study local, nanoscale polymer dynamics is presented. Fluorescence lifetime fluctuations were used to extract the number of polymer segments (N s ) taking part in the rearranging volume around the probe molecule below the glass transition temperature. N s was dependent on the temperature and it decreased with increasing temperature. Above the glass transition, rotational motion of single molecules was followed in time and typical time-scales of the rotational diffusion were extracted. These two approaches allowed us to obtain non-averaged information about the heterogeneous dynamics present in polymer systems, on the nanoscale, above and below glass transition temperatures.

show abstract

Section: ͓S0163-1829͑99͒10907-x͔mentioning

confidence: 99%

“…For a bulk sample SD also leads to time-dependent line shapes, and time-frequency distributions in bulk materials have been studied intensively for more than 20 years. 7,8 Different from nonreproducible SM spectra, a time-frequency distribution for an ensemble of molecules is a reproducible macroscopic characteristic.It is important to emphasize that time and frequency obey the uncertainty principle and one can speak about timedependent ''spectra'' only when the measuring procedure is exactly described. There are few methods for measuring time-dependent spectra of ensembles.…”

mentioning

confidence: 99%

Time-dependent single molecule spectral lines

Plakhotnik

1999

Phys. Rev. B

View full text Add to dashboard Cite

A general conceptual problem of time-dependent single molecule spectra is discussed theoretically in the framework of recently developed intensity-time-frequency correlation spectroscopy. It is shown that the new method is closely related to a ''gedanken'' three-pulse photon echo experiment done on an ensemble of identical molecules interacting with statistically identical microscopic environments. The correlation function is an integral transform ͑under certain conditions a Fourier transform͒ of the echo amplitude as a function of the delay between the first and the second pulses. ͓S0163-1829͑99͒10907-X͔A common characteristic feature of single molecules, single quantum dots, or any other single quantum systems ͑later on all are referred to as SMs͒ is that each successive spectral measurement performed on the same SM can reveal a new ''spectrum'' even when the macroscopic conditions do not change. 1,2 In mathematics, such time-dependent spectra are called joint time-frequency distributions.3 The spectral dynamics result from fluctuations of the microscopic surroundings of each SM. These surroundings are sometimes simulated by a set of two-level systems ͑TLSs͒ interacting with a phonon bath.4,5 Each TLS is characterized by two parameters, the energy splitting E and the sum of downward and upward TLS flip rates K. The interaction between a SM and a TLS leads to a SM resonance frequency shift 2 when the TLS flips. These flips are random and are not correlated with flips of other TLSs. Thus the resonance frequency becomes a stochastic function of time.6 This effect is called spectral diffusion ͑SD͒. For a bulk sample SD also leads to time-dependent line shapes, and time-frequency distributions in bulk materials have been studied intensively for more than 20 years. 7,8 Different from nonreproducible SM spectra, a time-frequency distribution for an ensemble of molecules is a reproducible macroscopic characteristic.It is important to emphasize that time and frequency obey the uncertainty principle and one can speak about timedependent ''spectra'' only when the measuring procedure is exactly described. There are few methods for measuring time-dependent spectra of ensembles. These are two-and three-pulse photon echo 9-11 and ''hole burning. '' 12 Hole burning makes little sense for SMs. Hahn-echo-type experiments, which are limited by the lifetime of the exited state, can be done even on a SM, 13 but classical two-and three-pulse echoes require an ensemble. Strictly speaking, neither experimental methods nor even a consistent theoretical description for time-dependent reproducible spectral distributions for single molecules have existed. Only recently, a new approach called intensity-time-frequency correlation ͑ITFC͒ was suggested and demonstrated experimentally. 14 ITFC spectroscopy works in three steps: ͑a͒ N laser scans over the same spectral region are acquired and the SM luminescence intensity as a function of the laser frequency is measured, ͑b͒ a correlation function is calculated for each scan, and ͑c͒ thes...

show abstract

Structure and Dynamics in Solids As Probed by Optical Spectroscopy

Cited by 122 publications

References 133 publications

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

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

Probing polymers with single fluorescent molecules

Time-dependent single molecule spectral lines

Contact Info

Product

Resources

About