To use SMPP to make the first ultra-fast single-molecule measurements of energy transfer ... Radiationless transfer of energy from an absorbing donor to an acceptor molecule ...
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Energy Transfer at the Single Molecule Level
PI: Jennifer Ogilvie
Topograph of LH2.
Ring Diameter ~ 65 Å
D:B800 - aqua A:B850 - yellow
intramolecular energy redistribution and energy transfer within the different regimes of weak (Förster) to strong (exciton) donor-acceptor coupling
Absorption Transitions - τ~10-15s
Internal Conversion - τ~10-12s
Fluorescence - τ~10-8s
Eadweard J. Muybridge 1879
Radiationless transfer of energy from an absorbing donor to an acceptor molecule
where is the decay time of the donor in absence of an acceptor, r is the donor acceptor distance, and is the distance at which RET is 50% efficient.
For τDer< τ< τET, molecules relax to the D10 state and ET is unlikely. Stimulated emission from D10,further reduces ET, and the FP decreases towards the 50% probe contribution.
For τET< τ< τAf, the A11 is excited by ET if the donor is excited, 50%. If not, the probe can excite the acceptor, thus FP =50% +50%*50% = 75%
Given a saturating pump or probe pulse, stimulated absorption and emission of the D00-D11 or A00-A11 transitions balance, so there is a 50% chance of excitation.
At τ = 0, if the probe did not excite A00-A11 and the pump excites D00-D11, then energy transfer (ET) excites A00-A11. So, Fluorescence Probability FP = 50%+ 50%*50% = 75%.
The SMPP experiment:
The longer wavelengths traverse more glass.
Rich Trebino, GIT & Hecht, Optics, 2001
Brandon Bachler, Liz Auto, &
Mode-locking : How short pulses are achieved. The Fourier transform (spectrum) of a plane wave is a delta function at the single frequency at the wave. A Gaussian pulse is the opposite extreme from a plane wave, and thus its Fourier transform is made of many different frequencies.
Fig 1 Synthesis of a periodic pulse train by superposition of sinusoidal oscillations, corresponding to different axial resonator modes in a mode-locked laser. There is a fixed phase relationship between these modes.
Fig2 Temporal evolution of the intracavity field in a laser, once with a fixed phase
relationship between the modes (mode-locked state), once with random phases.
GVD (or 2nd-order dispersion) is defined as
The Group Delay Dispersion (GDD) is defined as GVD*Length of material.
R.L. Folk, O.E. Martinez, J.P. Gorden, Optics Letters, Vol 9, No. 5 (1984)
A Michelson Interferometer splits the beam and it travels a path length differing by d in the two arms. Thus it outputs two beams separated by τ = d/c. A two-photon dye is used such that the dye fluoresces at the second harmonic frequency??, and it will only fluoresce when two photons are incident at the same time, i.e. about τ = 0.
A slow detector then records G2(t’) the second order interferometric correlation.
For delay times τof more than the total pulse length the two pulses are no longer
overlapping and the SOIC shows a constant
background signal. The wings are due to higher order dispersion terms.
For a delay increment of one-half light period, the two light fields add with opposite phase resulting in a near-zero signal, giving the fringes which contain pulse shape and phase info.
Van Dijk, et. al. P.R.L.94, (2005) – measured ultrafast energy redistribution
Rabi oscillations (stimulated emission by the pump pulse) in a realistic molecule with in homogeneously broadened line widths are super-damped due to dephasing between the molecule and a strong exciting field of duration longer than the dephasing time(~20fs)
Thus our pulses leave the molecule with an equal probability of being in the ground or excited state
At τ= 0, the S0-S11 is saturated by the pulse, thus the probe has no effect.
FP = Pump + Probe = 50% +0%
As τincreases, the molecule relaxes (via IC) to the S10 state and reducing stimulated emission. If the molecule is not excited by the pump, 50%, then there is a 50% chance the probe will excite it. Thus
FP = Pump + Probe = 50% +50%*50% = 75%
Traditionally, coupled differential rate equations are used to describe the energy transfer in an ensemble. Transition rates, absorption cross sections, Populations - deterministic.
A Monte Carlo approach was used to model a single molecule.
An large array of decay times following an exponential distribution are specified. The “experiment” is performed 10,000 with randomly chosen decay times. Stochastic.