Part II Course Content. Outline Lecture 9. Frequency Correlations & Lineshapes. Nonlinear Spectroscopic Methods
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1 Part II Course Content Outline Lecture 9 Optical Bloch equations Nonlinear polarizations in matter: the perturbative expansion approach. Ultrafast Fourier-transform spectroscopy: two and more dimensions. From THz to the ultraviolet: investigating transient states of matter with light More ways to see: Raman, CARS, & fluorescence - also good for imaging High harmonics and attosecond experiments: applications beyond the UV Ultrafast science with atomic resolution: the making of femtosecond molecular movies Applications II: Nonlinear infrared spectroscopy Applications III: 2D UV-vis spectroscopy Ultrafast optical Physics II Ultrafast optical Physics II 2 Nonlinear Spectroscopic Methods Frequency Correlations & Lineshapes Pump-Probe Spectroscopy Quantum Beat Spectroscopy Correlations of frequency fluctuations manifest in spectroscopic lineshapes Photon-Echo Spectroscopy k 2 Peak Shift Spectroscopy Sample k 1 k 1 +k 2 +k 3 k 3 +k 1 k 2 +k 3 Pulse sequence τ T within the second order approximation, one lineshape function describes all nonlinear signals of a given transition Ultrafast optical Physics II Ultrafast optical Physics II 4
2 2D Fourier Transform Spectroscopy 2D Fourier Transform Spectroscopy Third-order signals feature two periods of a coherent superposition in the probe oscillator which are separated by the population time interval. Just as the Fourier transform (FT) of the free induction decay yields A(ω), the 2D-FT of a third-order polarization decay along t 1 and t 3 is a 2D absorption spectrum, correlating (t 1 ) with (t 3 ) as a function of the waiting time t 2. E(t 1, t 2, t 3 ) = E(τ, T, t) R 2D-FT, t 1 dt 3 E(ν 1, t 2,ν 3 ) = E(ν 1, T,ν 3 ) C Ultrafast optical Physics II Ultrafast optical Physics II 6 T τ 3 τ 1 How to Measure 3 rd -Order Fields Use of a reference field (the local oscillator) for spectral interferometry k LO k LO, -k 1 + k 2 + k 3 Detector Array Spectrograph Phasing 2D Spectra Extraction of electric field by Fourier-filtering of spectrogram Signal intensity Re{E S,E* LO } Detection frequency ν 3 FT -1 I(τ, t) Time delay t FT Re{E S e iφ } Im{E S e iφ } Detection frequency ν 3 Contraction along ν 3 is equivalent to pump-probe spectrum Measured spectrograms for different time delays t 1 S(t 1,ν 3 ; T) τ 1 = τ 3-1 ν3 ν 3 ν 3 Field extraction E(t 1,ν 3 ; T) Fourier transform E(ν 1,ν 3 ; T) Absorbance difference (a) (b) (c) Solvent HAc, T=0fs HAc, T=400fs Detection frequency ν 3 / cm Ultrafast optical Physics II Ultrafast optical Physics II 8
3 Double Resonance 2D-Spectra Outline Lecture 9 Probe Fabry-Perot T=0 Abssorption ν 1 Double resonance spectroscopy T Pump Sample limitation: t 1 ν Detector linear abs. spectrum along diagonal excited state abs. shifted along ν 3 inhomogeneity elliptical lineshape couplings anti-diagonal signals T>0 Absorption ν 1 Applications II: Nonlinear vibrational spectroscopy Applications III: 2D UV-vis spectroscopy Detection ν 3 Detection ν Ultrafast optical Physics II Ultrafast optical Physics II 10 Improving Shutter Speeds Energy & Time Scales 1 Measurements of Brief Time Intervals 1 Time Interval (seconds) 10-3 milli 10-6 micro 10-9 nano Camera Laser pico Ultrafast Processes <100 attoseconds femto atto = Year 1/1000 1/1,000,000 1/1,000,000,000 1/1,000,000,000,000 1/1,000,000,000,000,000 hc = 1240 ev nm c = 300nm/fs } h 4 ev fs F. Krausz, M. Ivanov Review of Modern Physics 81, 163 (2009) Ultrafast optical Physics II Ultrafast optical Physics II 12
4 The Right Timing Outline Lecture 9 The energy scale of an excitation limits the time scale of associated dynamics The required time-resolution to follow dynamics depends on the dephasing time of the initial excitation For homogeneous lineshapes with Δ in energy units, the dephasing time is τ = h 4 ev fs in the non-relativistic limit, standard deviations for Energy & an observable O are linked as h 2 A. Föhlisch, talk on hrixs, XFEL Feb. 12 mag ph2 ph1 bimag elast Energy Loss / ev E/ E Applications II: Nonlinear infrared spectroscopy Applications III: 2D UV-vis spectroscopy Ultrafast optical Physics II Ultrafast optical Physics II 14 THz Generation via Antennas Antenna-THz Applications Based on dipole antennas Earliest implementation Δ 1! High-repetition rate Limited field strength with above-band gap excitation (damage threshold) Protein-Water Dynamics upon Folding Phase Transitions in Molecular Crytals Gruebele & Havenith Groups, Angew. Chem. Int. Ed. 47, 6486 (2008) Helm group, U. Freiburg, J. Mol. Struct. 1006, 34 (2011) Size-Dependent Photoconductivity in CdSe NPs Nonlinear THz Generation in Nanostructures From Terahertz Science Research Group, University of Fukui. See also M. van Exeter et al, Appl. Phys. Lett. 55, 337 (1989) Schmuttenmaergroup, Yale Univ., Nano Lett. 2, 983 (2002) Feurer group, U. Bern, Opt. Express 19, 7262 (2011) Ultrafast optical Physics II Ultrafast optical Physics II 16
5 Optical Rectification THz from Tilted Pulse Fronts ZnTe GaAs GaP Difference-frequency generation between low- & high-frequency parts of the driving pulse ω ω: THz frequency d eff : second order nonlinearity L: phase-matched length I: laser intensity n v : optical group refractive index n THz : THz phase refractive index Spectral width of driving pulse determines THz spectrum mpsd-cmd.cfel.de/research-met-thz-intensethz.html n gr vis =n ph THz Schmuttenmaer, Chem. Rev.. 104, 1759 (2004) Ultrafast optical Physics II 17 JózsefAndrás Fülöpand JánosHebling, DOI / Ultrafast optical Physics II 18 THz from Tilted Pulse Fronts THz-gated Charge Transport Above E*, ω ~ E THz Very high fields (>1MV/cm) Robust implementation But Need for amplified laser system Limited spectral width ω: THz frequency d eff : second order nonlinearity L: phase-matched length I: laser intensity n v : optical group refractive index n THz : THz phase refractive index n gr vis =n ph THz nelson.mit.edu/blog/nonlinear-terahertz-spectroscopy JózsefAndrás Fülöpand JánosHebling, DOI /6914 Cavallerigroup, MPISD, Nature Photonics 5, 485 (2011) THz-induced superconductivity in High-Tc superconductors at room temperature d.c. resistivity vanishes for charge carriers between oxide places modulation of Im(σ C ) of conductivity σ C, Meissner effect appears: σ C 0 as ω 0) Ultrafast optical Physics II Ultrafast optical Physics II 20
6 2D-THz spectroscopy Collinear vs. Noncollinear Geometries THz fields can be measured easily in real time via the electro-optic effect. The THz field modulates the birefringence of a crystal which rotates the polarization of a short reference pulse, sampling the THz field. In non-collinear geometries, nonlinear signals of different order are spatially separated by different superpositions of wavevectors of the generating pulses. In collinear geometry, all nonlinear orders are present in the measured signal: Ultrafast optical Physics II Ultrafast optical Physics II 22 Extraction of Nonlinear Signals 2D-THz spectroscopy of Graphene Differential measurements allow to extract the nonlinear THz field by synchronized light modulators (a - c). Graphene which a vanishing energy gap between the highest valence and the lowest conduction bands with linear dispersion and massless charge carriers with velocities independent of energy. 2D-THz spectroscopy studies carrier dynamics on ultrafast time scales close to the Dirac points E(K) = E(K ) = 0. The signal is the nonlinear electric field emitted from the sample (e). A 2D-Fourier transformation provides all nonlinear signals at once. Depending on their nature, they will manifest in spectral regions. M. Woerner et al., New. J. Phys. 15, (2013) Ultrafast optical Physics II Ultrafast optical Physics II 24
7 2D-THz spectroscopy of Graphene Outline Lecture 9 Both the induced absorption and the absence of the photon-echo signals are explained by a model using a pseudopotential bandstructure for graphene including the electron light coupling via the vector potential Applications II: Nonlinear vibrational spectroscopy Applications III: 2D UV-vis spectroscopy M. Woerner et al., New. J. Phys. 15, (2013) Ultrafast optical Physics II Ultrafast optical Physics II 26 Optical Parametric Generation Supercontinuum Generation White light Ti:sapphire CPA system BBO OPG Signal BBO OPG Signal + Idler AgGaS 2 DFG MIR few-cycle pulses noise suppressing scalable Smooth spectra spanning hundreds of nanometers in the visible to infrared range Supercontinua are fully coherent and compressible The resulting wide-bandwidth pulses are used for seeding in OPAs, probing absorption changes, and high-harmonic generation (HHG) Sapphire Fundamental input Idler Signa l White light BBO DFG MIR output pulse intensity (arb. u.) pulse intensity (arb. u.) cm -1 narrow absorption lines leakage of idler wave 2360 cm wavenumber (cm -1 ) R. A. Kaindlet al., J. Opt. Soc. Am. B 17, 2086 (2000) P. Hamm et al., Opt. Lett. 25, 1798 (2000) DOI: /OE Butcher&Arrigoni, LaserFocusWorld07/2010 DOI: /S (01) Ultrafast optical Physics II Ultrafast optical Physics II 28
8 Delocalization without Relaxation Delocalization without Relaxation Signal ~ E sample " #$%#&#'()* = / +2 / Signal ~ I sample " 1'234.&6'21 = 7 7 / / 0 fs Transient population grating (t 1 = 0) similar to pump-probe signal 1 T 2 3 Population relaxation with a lifetime of 200 fs Anisotropy decay with time constants of 80 fs Polarization anisotropy decay: HOD/D 2 O: τ = 700 fs dipole rotation 100 fs H 2 O: τ = 80 fs resonant energy transfer and delocalization Ultrafast optical Physics II Ultrafast optical Physics II 30 Revealing Chemical Shifts Revealing Chemical Shifts One more application using transient 2DIR spectroscopy concerns the understanding of how vibrations shift upon a photoinduced chemical reaction In the specific system it was not clear how to assign excited-state spectra which is crucial for verifying theoretical predictions. By photoinducing the chemical reaction and then probing the resulting structure via 2DIR spectroscopy it is also not obvious how the two peaks in question shift. But when reversing the order of UV and IR pump pulses, vibrational labeling allows to assign the excited-state absorption features to the right functional groups: the equatorial ν CO shifts from 1910cm -1 to 1950cm -1. DOI: /ja DOI: /ja Ultrafast optical Physics II Ultrafast optical Physics II 32
9 Outline Lecture 9 Resonant Energy Transfer (cont d) Fenna Matthews Olson (FMO) photosynthetic light-harvesting protein Applications II: Nonlinear vibrational spectroscopy Applications III: 2D visible spectroscopy Fleming Group, Nature 2005, DOI: /nature Ultrafast optical Physics II 33 Page 34 Resonant Energy Transfer (cont d) Resonant Energy Transfer (cont d) Fenna Matthews Olson (FMO) photosynthetic light-harvesting protein downhill energy transport among chromophores identification of energy flow maps energetic and spatial correlations current intense debate about nature of ps-long coherences (vibrational vs. electronic) in lightharvesting proteins Fleming Group, Nature 2005, DOI: /nature03429 Page 35 Page 36
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