Yujun Zheng

Lie algebraic approach to potential energy surface for symmetric triatomic molecules

Potential energy surfaces play an important role in studying theoretical chemistry. In this work, the expression of the potential energy surface containing information about the bending motion of triatomic molecules is derived by using the semiclassical limit of the algebraic Hamiltonian with the dynamical symmetry group U1(4)⊗U2(4). And, we also obtain the force constants. The method can be applied to a number of stable triatomic molecules, such as, H2O, H2S.

Photon emission from driven single molecules

The detection of photons emitted from a single molecule under the influence of electromagnetic radiation is considered. Utilizing a generating function formalism, we derive several exact results for the statistics of such emitted photons within the framework of the temporally modulated optical Bloch equations. Additionally, it is shown how these results reduce to previously obtained limiting behaviors. An appealing feature of this formulation is the inclusion of both photon bunching and anti-bunching effects within a single theoretical framework that is well suited for numerical analysis. Several examples are considered to demonstrate the feasibility of the approach in calculations. In most cases, these results verify known phenomena. In one case, we report a result that was missed by prior approximate treatments. This new effect centers around the fact that a chromophore will display anti-bunching behavior in the limit of fast modulation of the resonant absorption frequency.

Single molecule photon emission statistics for non-Markovian blinking models

The statistics of photon emission from a single molecule under continuous wave excitation are considered. In particular, we study stochastic model systems where photon emission rates evolve in time with non-Markovian dynamics. Our calculations are based on the recently introduced generalized optical Bloch equation (GBE) formalism, but with numerical complications beyond those seen in previous Markovian stochastic models. A spectral representation is introduced to facilitate the numerical solution of the GBE equations for these more challenging cases.

Single molecule photon emission statistics of driven three-level systems

We study the statistics of photon emission from three-level single molecule systems. The generating function method [Y. Zheng and F. L. H. Brown, Phys. Rev. Lett. 90, 238305 (2003)] is used to calculate steady state absorption line shapes and Mandels Q parameter as a function of excitation frequency, as well as the time dependence associated with approach to the steady state. The line shape calculations confirm known results derived via other methods, while the Q parameter results display complex frequency dependences not amenable to simple interpretation. This study confirms the applicability of the generating function formalism to multilevel quantum systems, including the proper modeling of quantum coherence effects.

Single Molecule Photon Counting Statistics for Quantum Mechanical Chromophore Dynamics

We extend the generating function technique for calculation of single molecule photon emission statistics (Zheng, Y.; Brown, F. L. H. Phys. Rev. Lett. 2003, 90, 238305) to systems governed by multi-level quantum dynamics. This opens up the possibility to study phenomena that are outside the realm of purely stochastic and mixed quantum-stochastic models. In particular, the present methodology allows for calculation of photon statistics that are spectrally resolved and subject to quantum coherence. Several model calculations illustrate the generality of the technique and highlight quantitative and qualitative differences between quantum mechanical models and related stochastic approximations when they arise. Calculations suggest that studying photon statistics as a function of photon frequency has the potential to reveal more about system dynamics than the usual broadband detection schemes.

Single molecule photon emission statistics in the slow modulation limit

A framework for calculating photon emission statistics for single chromophores perturbed by slow environmental fluctuations is introduced. When internal chromophore dynamics are significantly faster than time scales for environmental modulation it becomes possible to invoke a type of adiabatic approximation, allowing for straightforward calculation of photon counting moments including explicitly quantum effects. Unlike previous exact treatments, the present methodology involves calculation of dynamics reflecting only the modulation characteristics of the environment and quantum dynamics of an isolated chromophore separately, i.e., the complicated intermingling of chromophore quantum dynamics and the environmental modulation are suppressed via the adiabatic approximation. This leads to significant conceptual and computational simplifications. Within its regime of applicability, the present approximation reproduces exact calculations quantitatively. We demonstrate this accuracy explicitly for the case of a two-level chromophore modulated by a number of different stochastic models.

Photon counting statistics of single molecule in solid matrix.

In this paper, we investigate the properties of photon emission statistics of single molecule in solid matrix. The influences of solid matrix surroundings on photon emission of single molecule system under the laser field and rf field for several examples, the single dibenzanthanthrene molecule in hexadecane, the spectral diffusion process, and the hidden two-state models and the Gaussian models of blinking behavior, are considered.

Single-molecule photon emission statistics for systems with explicit time dependence: Generating function approach

Generating function calculations are extended to allow for laser pulse envelopes of arbitrary shape in numerical applications. We investigate photon emission statistics for two-level and V- and Lambda-type three-level systems under time-dependent excitation. Applications relevant to electromagnetically induced transparency and photon emission from single quantum dots are presented.

H2O photodissociation in the first absorption band: Entangled trajectory molecular dynamics method

We investigate H(2)O photodissociation in its first absorption band using entangled trajectory molecular dynamics method. We compare our results of entangled trajectories with exact quantum mechanical calculations, the overall agreement with the exact results is reasonable. To help understanding we show the photodissociation process with our entangled trajectories and the effect of the entangled trajectories in the system.

Single molecule counting statistics for systems with periodic driving.

We extend the generating function approach for calculation of event statistics observed in single molecule spectroscopy to cases where the single molecule evolves under explicitly time-dependent and periodic perturbation. Floquet theory is used to recast the generating function equations for the periodically driven system into effective equations devoid of explicit time-dependence. Two examples are considered, one employing simple stochastic dynamics and the other quantum dynamics, to demonstrate the versatility and numerical accuracy of the methodology.