Probing dynamics of single molecules: Nonlinear spectroscopy approach

Abstract

A two level model of a single molecule undergoing spectral diffusion dynamics and interacting with a sequence of two short laser pulses is investigated. Analytical solution for the probability of n=0,1,2 photon emission events for the telegraph and Gaussian processes is obtained. We examine under what circumstances the photon statistics emerging from such pump-probe setup provides new information on the stochastic process parameters and what are the measurement limitations of this technique. The impulsive and selective limits, the semiclassical approximation, and the fast modulation limit exhibit general behaviors of this new type of spectroscopy. We show that in the fast modulation limit, where one has to use impulsive pulses in order to obtain meaningful results, the information on the photon statistics is contained in the molecule's dipole correlation function, equivalently to continuous wave experiments. In contrast, the photon statistics obtained within the selective limit depends on the both spectral shifts and rates and exhibits oscillations, which are not found in the corresponding line shape.

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

“…37,41,45 Although the framework of generating function calculations remains unchanged under pulsed excitation or more general timedependent perturbations, the resulting equations must be solved numerically; this has not previously been explored in any generality. ͑Barkai and co-workers 34,52,53 considered time-dependent excitations within the generating function and related frameworks, but these works were limited to idealized square pulses and/or slowly varying perturbations.͒ The present paper demonstrates that the generating function framework is well suited for numerical calculations involving general nonconstant excitation profiles. Several model calculations are presented related to the dynamics of twoand three-level chromophore systems.…”

Reconstruction of the environmental correlation function from single-emitter photon statistics: A non-Markovian approach

“…whereσ i denotes the Pauli matrices. Within the spectral diffusion approach the two-level system density operator ρ(t|η t ) is a function of a real process η t , and obeys a stochastic Liouville equation [23][24][25] d dtρ…”

“…where ω L and Ω 0 = − degE are the angular and the Rabi frequencies of the laser (d eg = d ge are the matrix elements of the off-diagonal electric dipole moment, and E is the laser amplitude). Switching to a rotating frame by the unitary transformation R(t) = exp i ωL 2 tσ z [25], allows eliminating the explicit time dependence, and yields…”

“…( 29), while the interaction with the thermal environment, described by η t and Υ Eq. ( 5), stays unaltered [23][24][25]. It is evident that by simple addition of a real random process to the unperturbed emitter transition frequency ω 0 , the phenomenological model independently imposes the rates of variation associated with the interaction with the thermal bath and the laser, as if each coupling acted alone.…”

“…Up to now, the theoretical investigations of SMS were mainly based on a phenomenological approach assuming that the coupling to a thermal bath may be imitated by a real noise η t artificially added to the unperturbed frequencies of the emitter [23][24][25].…”