Energy Transfer at the Single Molecule Level Kate Wooley 8/1/2007 PI: Jennifer Ogilvie Topograph of LH2. Ring Diameter ~ 65 Å Bacteriochlorophylls: D:B800 - aqua A:B850 - yellow
Technique: Single Molecule (two color) Pump-Probe(SMPP) Objectives Background My Work Future Work Conclusions
Objectives • To use SMPP to make the first ultra-fast single-molecule measurements of energy transfer • To probe the role of disorder in energy transfer in simple donor-acceptor pairs and in natural light-harvesting complexes • To examine the relationship between intramolecular energy redistribution and energy transfer within the different regimes of weak (Förster) to strong (exciton) donor-acceptor coupling
Fluorescence • Fluorescence is a radiative transition between an excited and ground state of the same spin multiplicity (i.e. singlet) • During Internal Conversion, energy is dissipated through vibrational motion. • Multiple decay channels in molecules Jablonski Diagram Absorption Transitions - τ~10-15s Internal Conversion - τ~10-12s Fluorescence - τ~10-8s
Pump-Probe Experiment • Processes occur faster than any detector can time- resolve • Problem: You have a Pinhole camera with a slow shutter (assume you don’t need long exposure time). You want time-resolved images of a horse galloping • Solution: “Pump-Probe” » Strobe Photography • Upon the first flash of light, the horse bolts into a gallop • After a known delay a flash in front of the camera briefly illuminates the galloping horse, exposing the film. • Repeat with a longer time delay to get a flip book movie. Eadweard J. Muybridge 1879
Resonance Energy Transfer (RET) Radiationless transfer of energy from an absorbing donor to an acceptor molecule • Förster (weak coupling) energy transfer mechanism describes RET via Coulomb dipole-dipole interactions. • Rate of energy transfer is 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. • depends on spectral overlap between donor emission and the acceptor absorption, quantum yield of the donor, and the relative orientation of donor and acceptor transition dipoles.
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%. Simulation
Experimental Setup The SMPP experiment: • PCF: photonic crystal fiber for broadening the bandwidth • Pulse picker reduces pulse repetition rate to 1MHz • F1, F2: filter to select appropriate pump and probe bandwidth, respectively • DC: dispersion compensation • DBS: dichroic beamsplitter to separate fluorescence from pump and probe • APD: avalanche photodiode.
The longer wavelengths traverse more glass. M Group Velocity Dispersion (GVD) Compensation with a Prism Compressor • GVD (or 2nd-order dispersion)is defined as • The effect of GVD is to create a “chirped pulse” in which larger (smaller) frequencies lead smaller (larger), called positive (negative) chirp. If a pulse is chirped, its pulse duration is lengthened. • The dispersion of our oil immersion objective is equivalent to 250m of air. Rich Trebino, GIT & Hecht, Optics, 2001
2nd Order Interferometric Autocorrelation • For delay times τof more than the total pulse length the two pulses are no longer overlapping and G2(τ) gives a constant background signal. The wings are due to higher order dispersion terms. • Need pulse length ~ 100fs.
LabView Timing Issues! • Trigger Data Acquisition and the Piezo Stage positioning and feedback voltage • Match the position of the stage to the PMT fluorescence data • Determine accuracy and repeatability of positioning
Next Steps • Supercontinuum generation with photonic crystal fiber – larger bandwidth for biological systems that absorb white light. • Single Photon Counter – to detect WEAK! signals from single molecules • Use fluorescent tagged DNA with known lengths between base pair donor-acceptor pairs to test setup. • Examine systems of interest such as LH2 http://www.lumerical.com/mode_solver_applications
Conclusions SMPP • We have demonstrated a method for measuring single molecule energy transfer • We were able to compensate 2nd order dispersion of the oil immersion objective • We have the resolution and accuracy to repeatedly find a single molecule
Thanks! Brandon Bachler, Liz Auto, & Questions?
Answers to Potential Questions 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. http://www.rp-photonics.com/encyclopedia.html • Laser – TiSaphire mode-locked 16nW, sub 20fs pulses • We only get ~1nW, dispersion broadens to 70fs, 800nm±50nm
Group Velocity Dispersion (GVD) Compensation with a Prism Compressor 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)
Dispersion Compensation • The Taylor coefficients, specifically the second-order dispersion is calculated using the Sellmeier Equation n2(λ) where the Bi and Ci coefficients are experimentally known material constants. • The zero-order term describes a common phase shift. • The first-order term contains the inverse group velocity and • describes an overall time delay without an effect on the pulse shape. • The second-order term contains the second-order dispersion • (or group delay dispersion per unit length):
Interferometric Autocorrelation 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. http://nanooptics.uni-graz.at/ol/work/fs_measure/fs-measure.html
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% One Color SMPP
0.75 2 ps 0.70 1 ps 670 fs Fluorescence Probability 0.65 0.60 delay (ps) 0 1 2 3 4 5 Simulation 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.
RET- Forster Theory • Förster theory - weak coupling between donor and acceptor results in incoherent energy transfer • Note: Förster theory is for ensembles, other theories for strong coupling • Fluorescent Resonance Energy Transfer (FRET) • Same ET process. • Use fluorescence lifetimes to determine if ET has occurred. • Strong D-A distance dependence = ruler http://www.plantmethods.com/content/2/1/12/figure/F1 http://micro.magnet.fsu.edu/primer/techniques/fluorescence/fret/fretintro.html