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Photon Echo Technique

Photon Echo Technique. Quantum Mechanics of Ensembles. Described by the density matrix rather than a wavefunction. Calculating Nonlinear Signals. Time evolution of used to calculate the polarization P. Expand P as. Long and tedious expressions. Help is at hand!

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Photon Echo Technique

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  1. Photon Echo Technique

  2. Quantum Mechanics of Ensembles Described by the density matrix rather than a wavefunction.

  3. Calculating Nonlinear Signals Time evolution of used to calculate the polarization P Expand P as Long and tedious expressions. Help is at hand! For a two level system only 4 terms and their complex conjugates survive the definition of the density matrix Suggests we can represent these terms by diagrams in which we propagate the bra and ket separately.

  4. ks = -k1+k2+k3 k3 k2 k1 |g g| ks |e g| -k1 k3 |e e| ks k2 k2 |g e| -k1 k3 Feynman diagrams & the density matrix phase-matching direction energy |e |g time density matrix g| e| t d 0 1 |g T r = t d d 0 0 |e |g g|

  5. ks k3 k3 Geg(t3) Geg(t3) Gee(t2) Gee(t2) Geg(t1) Gge(t1) k2 k2 k1 R1 k1 R2 ks ks Geg(t3) Geg(t3) k2 k3 Ggg(t2) Ggg(t2) k3 k2 Gge(t1) Geg(t1) R3 R4 k1 k1 Two level systems are described by four Feynman diagrams and their complex conjugates ks If k3 = k2 (same pulse) ks= k1 for R1 and R4 ks = 2k2-k1 for R2 and R3

  6. Echo-Inhomogeneous broadening from Erwin Hahn and Chris Noble

  7. Lens Analogy for Photon Echoes After the first interaction we have a superposition oscillating at the energy difference between and . Inhomogeneous contribution leads to rephasing (3) Optical frequency (1) Homogeneous dephasing (2) (3) Define electronic phase factor Linear with slope determined by inhomogeneous parameter For N molecules we get N lines with different slopes Width amount of inhomogeneity

  8. The second interaction produces a population—no ε-term in difference between |e> and |e> Rephasing response function Now the third pulse phase factor is (sign change because now Ee-Eg not Eg-Ee), so now the slope of each ray will change sign but have the same magnitude.

  9. Non-rephasing response function 2 PE t1 t2 Dephasing Spectral diffusion Dephasing Refocusing gets poorer and poorer as t1, t2 increased. t1 t3 t2

  10. Photon Echoes 1 2 3 echo Pulse 2 creates population (|g> OR |e>) Pulse 1 creates coherence (|g> AND |e>) Pulse 3 creates another coherence Oscillatory term during first (second) coherence: e -(+)iωegt Slope of rays depends on ωeg in oscillator term

  11. Top: CO asymmetric stretch of W(CO)6 in 2 methyl pentane. Bottom: CO asymmetric stretch of W(W)6 in dibutyl phthalate. The beats are at the anharmonic vibrational splitting, and arise because the pulsewidth (0.7ps) is less than in the top figure.

  12. Figure 3. Temperature dependence of the homogeneous line widths of the T|u CO stretching mode of W(CO)6 in 2-MTHF, 2-MP, and DBP determined from infrared photon echo experiments using eq 9b.arrows mark the glass transition temperatures. Note the different temperature and line width scales.

  13. W(CO)6 in 2-MP Tokmakoff….Fayer J. Phys. Chem, 99 13310 (1995). Absorption Linewidth

  14. Two Pulse Electronic Echoes HITCI in glycerol/water (70/30) 2k2-k1 2k1-k2 20 fs transform limited pulses Deconvolution 20 fs decay

  15. Exciton Dephasing in Semiconducting Carbon Nanotubes ~800 nm Homogeneouscontribution ~0.75 nm • Only the (6,5) type SWNTs are resonantly excited, and the resulting 2-pulse photon echoes (2PEs) decays are measured • 2PEs provides a direct method to determine dephasing times • At RT, the FWHM of the inhomogeneous processes are ~6X the homogeneous width

  16. 2D Spectroscopy of Aggregates MOLECULAR AGGREGATES WEAKLY COUPLED STRONGLY COUPLED Absorption spectra of BIC monomer and J-aggregates LH2 Complex Two-exciton Band 2e Linear chain of 2 level molecules with electrostatic dipole-dipole interaction One-exciton Band 1e Ground state g

  17. SITE BASIS: J-AGGREGATE HAMILTONIAN Diagonal Electron-Phonon Off-diagonal Electrostatic EXCITON BASIS: EXCITON WAVEFUNCTIONS Diagonal Exciton-Phonon Off-Diagonal Exciton-Phonon Renormalization Factors Cause Exchange Narrowing Overlap Factors Define Relaxation • Higher Exciton States are Strongly Delocalized • Exchange-Narrowing is Stronger for Higher • (More Delocalized) Exciton States • Relaxation is Faster for Higher Exciton States

  18. Photon Echo Technique

  19. Integrated Three Pulse Photon Echo: Nile Blue in Acetonitrile

  20. Origin of the Peak Shift Rephasing side as spectral diffusion occurs will become more and more like non- rephasing side Non-rephasing side not influenced by spectral diffusion Eventually the echo signal will become symmetric around τ=0

  21. Measuring inhomogenous broadening Peakshift tracks the surface denoted by the blue line

  22. IR 144 τ*(T) vs. T • Finite long • time peak shift • Inhomogeneous • broadening • Timescales of • fluctuations in • transition frequency. 32K 294K Ethanol 294K

  23. What is the Peak Shift? At high temperature it relates to the Stokes shift dynamics and the ratio of dynamical and static contributions to the spectral broadening. The long time value allows the inhomogeneous width to obtained: The time dependence gives inhomogeneous width Stokes Shift obtain inhomogeneous width, M. Cho

  24. Solvation Dynamics IR144 in acetonitrile Correlation function Peak Shift Spectral Density

  25. Instantaneous Normal Mode Spectral Density CH3CN

  26. Solvation Spectral Density for Acetonitrile

  27. Dielectric Response of Aqueous Proteins Lysozyme with eosin bound in the ‘hydrophobic box’ Eosin/lysozyme/water Eosin/water

  28. LH1 and Reaction Center of Purple Bacteria Roszak, Howard, Southhall, Gardiner, Law, Isaacs & Cogdell Science, 302, 1969 (2003).

  29. Structure of the LH3 Complex K. McLuskey et al.: Biochemistry 40, 8713 (2001). Rhodopseudomonas acidophila Strain 7050

  30. Photon Echo Peak Shift Measurements LH1 of Rb. sphaeroides vs. the B820 Subunit of LH1 of Rs. rubrum Same parameters as LH1 except no 90 fs EET component B820 subunit of LH1 Peak Shift (fs) Inhomogeneous broadening 90 fs energy transfer timescale LH1 T(fs)

  31. Light Harvesting Complex II Absorbance (norm.) Wavelength/nm

  32. Bacterial Light Harvesting Hu, et al. J. Phys. Chem. B (1997) 101 3854 Bahatyrova, et al. Nature (2004) 430 1058

  33. Peak Shift on the B850 band of LH2 membranes (Rps. acidophila) Membrane samples Intra-complex exciton relaxation or energy transfer Solubilized samples In collaboration with C. N. Hunter, Sheffield Energy Transfer between the complexes Membrane samples Solubilized samples Since the Peak Shift carries information abut the inter-complex energy transfer dynamics, we can say that the individual rings do not have the full disorder distribution that is observed in the absorption spectrum.Energy Transfer between the rings is estimated to be ~ 5 ps at room temperature.

  34. Pump Probe (Transient Absorption) IR144 in MeOH

  35. Pump-Probe (Transient Absorption) k1and k2 come from same pulse ks = -k1 + k1 + k3 = k3 signal along probe direction P(3) heterodyned with probe field. ks gg k3 eg ee ge k2 • Measurement time window (t’) determined by the • pulse duration of the probe. • If the probe is short rephasing may not be • detected. • M(t) reflected in pump-probe signal • (may be difficult to extract quantitatively). • “coherence” spike not a coherent effect. • Arises from dynamics. gg k1 rephasing diagram Probe Detector Pump

  36. Contributions to Pump-Probe Signal

  37. Pump Probe Signals (Calculation)

  38. Transient Absorption

  39. Coworkers Taiha Joo Minhaeng Cho Yutaka Nagasawa Sean Passino Matt Lang Xanthipe Jordanides Xeuyu Song

  40. Peak Shift IR144 in MeOH

  41. 1-Color Transient Grating Signals Time unit: ps.

  42. Two Color Transient Grating Signals Positive Negative At the probe is at the bottom of the excited state well. For large detuning the birefringent contribution becomes similar to the dichroic contribution (at short times).

  43. Two Color Transient Grating Signals. Homodyne Detection Detuning = 800cm-1 Maximum correlates well with Gaussian time constant,

  44. Experimental 1-Color and 2-Color TG Signals for DTTCI in MEOH Downhill. Detuning = Probe close to minimum of excited state surface.

  45. Experimental One-Color and 2-Color TG Signals for IR144 in MEOH 1C 750nm 2C 750, 750 800nm (downhill)

  46. Two-Color three-pulse Photon Echoes IR144 in Methanol DTTCI in Methanol

  47. IR144 Methanol 750, 750, 800

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