Part II Course Content

Transcription

1 Part II Course Content 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 Ultrafast optical Physics II 1

2 Outline Lecture 10 Elements of the last session 2-dimensional Fourier transform spectroscopy Time and Energy Scales Applications I: THz spectroscopy Applications II: Nonlinear infrared spectroscopy Applications III: 2D UV-vis spectroscopy Ultrafast optical Physics II 2

3 Nonlinear Spectroscopic Methods Pump-Probe Spectroscopy Quantum Beat Spectroscopy Photon-Echo Spectroscopy Peak Shift Spectroscopy Ultrafast optical Physics II 3

4 Frequency Correlations & Lineshapes Correlations of frequency fluctuations manifest in spectroscopic lineshapes within the second order approximation, one lineshape function describes all nonlinear signals of a given transition Ultrafast optical Physics II 4

5 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 Δ(t 1 ) with Δ(t 3 ) as a function of the waiting time t Ultrafast optical Physics II 5

6 2D Fourier Transform Spectroscopy E(t 1, t 2, t 3 ) = E(τ, T, t) R 2D-FT, dt 1 dt 3 E(ν 1, t 2,ν 3 ) = E(ν 1, T,ν 3 ) C Ultrafast optical Physics II 6

7 How to Measure 3 rd -Order Fields Use of a reference field (the local oscillator) for spectral interferometry T τ 3 τ 1 k LO, -k 1 + k 2 + k 3 Detector Array k LO Spectrograph Measured spectrograms for different time delays t 1 S(t 1,ν 3 ; T) τ 1 = τ 3-1 ν 3 ν 3 ν 3 Field extraction E(t 1,ν 3 ; T) Fourier transform E(ν 1,ν 3 ; T) Ultrafast optical Physics II 7

8 Phasing 2D Spectra Extraction of electric field by Fourier-filtering of spectrogram Contraction along ν 3 is equivalent to pump-probe spectrum Ultrafast optical Physics II 8

9 Double Resonance 2D-Spectra Double resonance spectroscopy Probe Fabry-Perot 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 T>0 Abssorption ν 1 Absorption ν 1 Detection ν 3 Detection ν Ultrafast optical Physics II 9

10 Outline Lecture 10 Elements of the last session 2-dimensional Fourier transform spectroscopy Time and Energy Scales Applications I: THz spectroscopy Applications II: Nonlinear vibrational spectroscopy Applications III: 2D UV-vis spectroscopy Ultrafast optical Physics II 10

11 Improving Shutter Speeds 1 Measurements of Brief Time Intervals 1 Time Interval (seconds) 10-3 milli 10-6 micro 10-9 nano pico <100 attoseconds atto =10-18 femto Camera Laser Ultrafast Processes Year 1/1000 1/1,000,000 1/1,000,000,000 1/1,000,000,000,000 1/1,000,000,000,000, Ultrafast optical Physics II 11

12 Energy & Time Scales 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 12

13 The Right Timing 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 A. Föhlisch, talk on hrixs, XFEL Feb. 12 E/ E For homogeneous lineshapes with Δν in energy units, the dephasing time is τ = h πππ h 4 ev fs in the non-relativistic limit, standard deviations for Energy & an observable O are linked as σ E σ O d O dt h 2 ma g ph 2 ph 1 bima g elast Energy Loss / ev Ultrafast optical Physics II 13

14 Outline Lecture 10 Elements of the last session 2-dimensional Fourier transform spectroscopy Time and Energy Scales Applications I: THz spectroscopy Applications II: Nonlinear infrared spectroscopy Applications III: 2D UV-vis spectroscopy Ultrafast optical Physics II 14

15 THz Generation via Antennas Based on dipole antennas Earliest implementation E TTT High-repetition rate Limited field strength with above-band gap excitation (damage threshold) Q Δτ 1 A From Terahertz Science Research Group, University of Fukui. See also M. van Exeter et al, Appl. Phys. Lett. 55, 337 (1989) Ultrafast optical Physics II 15

16 Antenna-THz Applications 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 Feurer group, U. Bern, Opt. Express 19, 7262 (2011) Schmuttenmaer group, Yale Univ., Nano Lett. 2, 983 (2002) Ultrafast optical Physics II 16

17 Optical Rectification ZnTe GaAs GaP Difference-frequency generation between low- & high-frequency parts of the driving pulse ω Spectral width of driving pulse determines THz spectrum Schmuttenmaer, Chem. Rev.. 104, 1759 (2004) Ultrafast optical Physics II 17

18 THz from Tilted Pulse Fronts 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 mpsd-cmd.cfel.de/research-met-thz-intensethz.html József András Fülöp and János Hebling, DOI / Ultrafast optical Physics II 18

19 THz from Tilted Pulse Fronts 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 Very high fields (>1MV/cm) Robust implementation But Need for amplified laser system Limited spectral width n gr vis =n ph THz nelson.mit.edu/blog/nonlinear-terahertz-spectroscopy József András Fülöp and János Hebling, DOI / Ultrafast optical Physics II 19

20 THz-gated Charge Transport Above E*, ω ~ E THz Cavalleri group, 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 20

21 2D-THz spectroscopy 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 Ultrafast optical Physics II 21

22 Collinear vs. Noncollinear Geometries 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 22

23 Extraction of Nonlinear Signals Differential measurements allow to extract the nonlinear THz field by synchronized light modulators (a - c). 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 23

24 2D-THz spectroscopy of Graphene 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 ) = Ultrafast optical Physics II 24

25 2D-THz spectroscopy of Graphene 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 M. Woerner et al., New. J. Phys. 15, (2013) Ultrafast optical Physics II 25

26 Outline Lecture 10 Elements of the last session 2-dimensional Fourier transform spectroscopy Time and Energy Scales Applications I: THz spectroscopy Applications II: Nonlinear vibrational spectroscopy Applications III: 2D UV-vis spectroscopy Ultrafast optical Physics II 26

27 Optical Parametric Generation White light Ti:sapphire CPA system BBO OPG Signal BBO OPG Signal + Idler AgGaS 2 DFG MIR few-cycle pulses noise suppressing scalable 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. Kaindl et al., J. Opt. Soc. Am. B 17, 2086 (2000) P. Hamm et al., Opt. Lett. 25, 1798 (2000) Ultrafast optical Physics II 27

28 Supercontinuum Generation Smooth spectra spanning hundreds of nanometers in the visible to infrared range Supercontinuua are fully coherent and compressible The resulting wide-bandwidth pulses are used for seeding in OPAs, probing absorption changes, and high-harmonic generation (HHG) DOI: /OE Butcher&Arrigoni, LaserFocusWorld 07/2010 DOI: /S (01) Ultrafast optical Physics II 28

29 The Structure and Dynamics of Water The complex and rapidly fluctuating hydrogen bond network in water is responsible for the many anomalies that this solvent of life exhibits. Vibrational spectroscopy has been used for a century to unravel some of the underlying reasons Copyright: David Prendergast & Giulia Gallis, UC Davis & Lawrence Livermore National Laboratory Ultrafast optical Physics II 29

30 Real-Time Energy Dissipation S. Ashihara et al. studied energy dissipation by the probing characteristic response of librations upon excitations of vibrations Vibrational excitations relax very efficiently in a cascade of coupled degrees of freedom, leading to ultrafast energy dissipation due to ultrafast population of extended (and hence low-frequency) modes. Change of Absorbance (mod) a E ex =1350 cm -1 b E ex =1650 cm -1 <100fs 200fs 170fs 170fs -1 DOI: /jp c E ex =3150 cm Delay Time (fs) Ultrafast optical Physics II 30

31 Delocalization without Relaxation Signal ~ E sample r pppp ppppp = A A A + 2 A Signal ~ I sample r ttttt. gggg = I I I + 2 I Transient population grating (t 1 = 0) similar to pump-probe signal Population relaxation with a lifetime of 200 fs 1 T 2 3 Anisotropy decay with time constants of 80 fs Ultrafast optical Physics II 31

32 Delocalization without Relaxation 0 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 32

33 Coherent Motions in Water The complex hydrogen bond network of water leads to a wide distribution of structures and hence large inhomogeneity in absorption lineshapes. One important question was whether coherent motions via creation of wavepackets would be possible in such a rapidly fluctuating liquid. Echo peak shift measurements by Tokmakoff s group indeed suggested this possibility due to observation of a clear recurrence, attributed to low-frequency excitations, possibly O O stretching modes. However, 2DIR spectroscopy did not seem to see such coherences Energy E(Q i ) n fast = 1 n fast = 0 DOI: /science Slow mode coordinate Q i Ultrafast optical Physics II 33

34 Ultrafast Inhomogeneity Decay in Water ν 1 (cm -1 ) T=0fs T=50fs ν 3 (cm -1 ) τ T=0 fs ν 3 (cm -1 ) -1 τ T=50 fs -1 LO time LO time Cowan et al., Nature 2005, DOI: /NMAT Ultrafast optical Physics II 34

35 Inhomogeneity in Water 3500 T=0fs T=50fs 1 ν 1 (cm -1 ) ν 3 (cm -1 ) ν 3 (cm -1 ) -1-1 Frequency correlation: < ω(0) ω(t) > decays within 100 fs Microscopic origin: librational modes with ω > ω(o...o) Ultrafast optical Physics II 35

36 Coherent Motions in Water Upon close inspection of better quality 2D spectra one finds indeed that a recurrence due to underdamped oscillations of coherent excitations is likely. While 2D spectra reveal a lot of information, echo peak shift measurements may reveal certain dynamics more favorably. DOI: ypnas Ultrafast optical Physics II 36

37 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. DOI: /ja Ultrafast optical Physics II 37

38 Revealing Chemical Shifts 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 Ultrafast optical Physics II 38

39 Outline Lecture 10 Elements of the last session 2-dimensional Fourier transform spectroscopy Time and Energy Scales Applications I: THz spectroscopy Applications II: Nonlinear vibrational spectroscopy Applications III: 2D visible spectroscopy Ultrafast optical Physics II 39

40 Resonant Energy Transfer (cont d) Fenna Matthews Olson (FMO) photosynthetic light-harvesting protein Fleming Group, Nature 2005, DOI: /nature03429 Page 40

41 Resonant Energy Transfer (cont d) Page 41

42 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 42