Chair for Laser and X-ray Physics E11 Prof. Reinhard Kienberger reinhard.kienberger@tum.de PD. Hristo Iglev hristo.iglev@ph.tum.de Dr. Wolfram Helml Wolfram.Helml@tum.de Ultrafast physics II SS 2018 Thursday, 10:15 11:45 h PH II 127, Seminarraum E11 Lecture notes: https://campus.tum.de/tumonline/ 0000003402 Ultrakurzzeitphysik 2 (2SWS VO, SS 2018) 25. & 26. June: Excursion Switzerland IBM Research Laboratory Zurich Chair of Ultrafast Physics ETH Paul Scherrer Institut Villigen 2
Modern Methods in Ultrafast Spectroscopy Literature: Laser Spectroscopy W. Demtröder, 4th Edition, Springer-Verlag, 2008 Fundamentals of Photonics B. E. A. Saleh and M. C. Teich, Wiley, 2007 Femtochemistry: Ultrafast dynamics of chemical bond A. Zeweil, World Scientific, 1994 3 Ultrafast Phenomena 8 fs: One H-H oscillation of the H2-molecule 10 fs: Average time between collisions of electrons and metal lattice 100 fs: Collisions between molecules in liquids at room temperature à the same timescale for numerous processes in the liquid phase 200 fs: Formation and breaking of chemical bonds 500 fs Bacteriorhodopsin switches from cis to trans conformation 10 1000 ps: Fluorescence and biologically relevant processes 4
"Snapshots" of Molecular Motion Transient Absorption Spectroscopy High excitation densities Measurable depopulation of the ground state the evolution of the excited state is monitored by measuring the absorption change 5 Pump-Probe (Transient Absorption) Spectroscopy Measuring the relaxation dynamics with sub-100 fs time-resolution Generated data sets: transient absorption spectra and signal transients Application of various excitation pulses with different wavelengths and temporal delays Processes running parallel may complicate the data interpretation Spectral regions: FIR (> 10 µm): Rotations, librations (intermolecular vibrations), H-bonds, free charges MIR (2 10 µm): Intramolecular vibrations NIR (780 nm 2 µm): Overtones VIS (390 780 nm): Electronic transitions within molecules UltravUV (3 nm 380 nm): Electronic transitions within atoms and molecules, transitions of the subshell electrons 6
Pump-Probe Spectroscopy on Dye Molecules Transient absorption spectroscopy on dye molecules Nile blue à Pump-off Pump-on Signal transients: DOD = Log (T/T0) Probe-transmission with pump D(Optical Density) = Log Probe-transmission without pump Wave packet dynamics in the excited state Optical control of the wave packet dynamics Prof. M. Motzkus, Uni Heidelberg 7 Coherent Control of Chemical Reactions Through excitation with optical pulses in a special temporal progression of phase and frequency, electronic and vibrational transitions can be induced in a certain order, which raises the quantum yield of certain reaction products. 8
Coherent Control of Chemical Reactions M. Aeschlimann et al. Adaptive subwavelength control of nano-optical fields, Nature 446 (2007) 301. à A polarization shaper for ultrashort laser pulses controls the temporal evolution of the vectorial electric field E(t) on a femtosecond timescale. 9 Pump-Repump-Probe Spectroscopy Pump-repump-probe allows optical manipulation of charge transfer reactions and provides additional information about "hidden" relaxation mechanisms and intermediate products. t23 = 150 ps Through the re-excitation (repump), intermediate steps in the relaxation dynamic are blocked/skipped and the quantum yield of the final products is modified in a controlled way à ( OD) at long delay times provides information about "hidden" relaxation dynamics Iglev, Fischer, Glisering, Laubereau, JACS 133 (2011) 790. B.J. Schwartz et al, Science 239, 462-465 (2001); 321, 1817-1822 (2008) 10
Phase sensitive transient absorption (PHASTA) PHASTA setup with few-cycle CEP-stable pulses. Typical interference pattern produced by the TWIN-unit with tlo = 800 fs. 11 Phase sensitivity via Fourier transform spectral interferometry! "#$%& ' = 0,5!, -./0 '1 23 + 0,5! 1, -./0 ' + ' 56 23 1 1 Inverse FT FT Cut + shift to t=0 12
Fourier transform spectral interferometry - simulations Identical LO and probe pulse: absorption @ 0.18 PHz in the probe Probe phase of + π Chirped probe pulse (10 mm fused silica) 13 PHASTA spectroscopy with few-cycle CEP-stable pulses Excitation conditions: 4.5 fs, 650 nm, 30 TW/cm 2 à Multiphoton and above threshold ionization of 2.5 µm liquid water sheet Transient absorption at 1900 nm 0.2 parallel othogonal Coherent oscillations most probably due to interference of probe pulse with pump-induced polarization in the sample "OD 0.1 2Tcoh = 70 fs 0 0 200 400 600 800 time delay [fs] Anisotropic signaled indicate an polarization dephasing time Tcoh 35 fs 14
PHASTA spectroscopy with few-cycle CEP-stable pulses "OD orthogonal Transient absorption (red) and phase (blue) at 1900 nm 0.2 0.1 0-0.1-0.2 65 fs 50 fs 165 fs 0 200 400 600 800 time delay [fs] The phase changes are negative à indication for free electrons 0.5 0.3 0.1-0.1-0.3-0.5 ") para [rad] Delayed signal increase with Tcoh = 37 fs (in agreement with the measured dephasing time of 35 fs) Both signals monitor different dynamics: - transient absorption à population of e pre - transient phase à electron localization phase par [a.u.] 0-0.5 Signal decay of Tlocalization = 48 fs à electron localization -1 37 fs 9 fs 48 fs H 2 O 0 100 200 300 time delay [fs] 15 Evaluation of the Lecture 0000003402 Ultrafast Physics 16
Optical Absorption and Fluorescence S2 Lifetime of higher vibrational states 10-12 s S1 Lifetime of excited electronic states (e.g. S1) 10-9 s S0 Fluorescence frequencies are smaller than the absorption frequencies "Stokes shift" Very fast relaxation into the lowest electronically excited state Kasha's rule: the fluorescence always occurs from the lowest electronically excited state 17 Fluorescence Spectra Fluorescence spectrum: Fluorescence intensity I(l) at a fixed excitation wavelength. Vibrational structure of S1 Vibrational structure of S0 Following Kasha's rule the Fluorescence always starts from S1 à Does not depend on the pump wavelength (Exception: very short laser pulses wave packet dynamic, or like Azulene Fluorescence from S1 and S2). Relaxation = Fluorescence + Non-radiative Transitions + InterSystem Crossing 18
Fluorescence vs. Phosphorescence Luminescence = Photon emission (in general) Fluorescence Phosphorescence Jablonski diagram Intersystem Crossing (ISC): S2 à T1 transition T1 à S1 Transition is forbidden, hence long phosphorescence lifetime 19 Relaxation Dynamic of Fluorescence and Phosphorescence The excitation pulse marks the "Start". A single luminescence photon turns off the detector and gives us the "Stop". The correlator measures the time difference between "Start" and "Stop". The measured times are depicted in a histogram. 20
Fluorescence Up-Conversion Fluorescence F F F Fluorescence (vis) Measured signal is proportional to the fluorescence intensity at td. The pulse duration of the gate pulses determines the time resolution. Only single SFG photons are detected à higher laser repetition rates Limited time window mechanical delay line (15 cm = 1 ns) 21 Pump-Dump Fluorescence Spectroscopy All photochemical reactions proceed within the first excited state. The wave packet dynamics provide vital information about S1 and lead to a change of the fluorescence characteristics. Pump-dump fluorescence spectroscopy provides information about the wave packet dynamics in S1. Cyanine Wei, Nakamura, Takeuchi, Tahara, JACS 133 (2011) 8205. 22
Kerr-Gate for fs Fluorescence Spectroscopy The gating of the fluorescence signal is realized through the Kerr-effect. +) transient fluorescence spectra are measured directly -) the gate pulse has to be much stronger in comparison to the up-conversion technique Prof. Peter Gilch, Uni Düsseldorf 23 Sum-Frequency Generation (SFG) Spectroscopy Surface-/interface sensitive method: for symmetry reasons SFG is forbidden in isotropic media (dipole approximation) SFG-Spectroscopy on surfaces and interfaces: Surface and bulk have different structure/symmetry 24
SFG Signal If ωpr = ωvib, or ωpr = ωel, SFG is resonantly amplified and hence yields surface-specific (spectroscopic) information Raman cross-section IR cross-section population density Resonant SFG-signal only if the vibration is Raman and IR-active at the same time Change of the Raman polarizability à Raman-active Change of the dipole moment à IR-active 25 Time- und Spectrally-Resolved SFG Spectroscopy +) Sub-monolayer sensitivity +) Surface-specific +) Well aligned output signal +) Non-destroying, in situ, +) High spatial, temporal and spectral resolution Unique application scenarios: Examination at wet interfaces Surface structure of polymers and liquids Ultrafast dynamics at interfaces Every interface accessible to light VIS Probe Pump SFG 26
Polarization-Resolved SFG Spectroscopy 3 (out of 8) SFG polarization combinations are non zero PPP and SSP yield information about rotations out of plane SPS yields information about rotations in plane 27 Resonant Light-Atom Interaction in Two-Level Systems Schrödinger equation: Free atom Light-atom interaction c1,2 : Time-dependent amplitudes of the two stationary eigenfunctions u1,2 Equations for the time-dependent amplitudes: Short: Definition: Resonant Rabi frequency Detuning of the light frequency with respect to the atomic resonance Rotating-Wave approximation 28
Rabi Oscillations Equations for new coefficients: In resonance: d = 0 à c1(0) = 1 c2(0) = 0 The system oscillates between ground state and excited state with Ω0 Highly nonlinear dynamic à higher light intensity = strong oscillations Pulse area A = Rabi frequency x Pulse duration à Pi-half pulse: A = p/2 à Starting with an atom in the ground state, a Pi-half pulse generates a coherent superposition between ground state and excited state. This state posses an oscillating maximum dipole moment. Pi-pulse: A = p : The amplitudes between the states 1> and 2> are swapped under the influence of a Pi-pulse. 29 Rabi Oscillations with Detuning Solution at d 0 Generalized Rabi frequency: Density matrix: Coherences of the system Populations and For pure quantum states the phase j between 1> and 2> is constant and controlled in the experiment! Example: For à ß Completely coherent superposition à ß Completely incoherent superposition 30
Optical Bloch Equations (OBE) ß Completely coherent ß Completely incoherent Experimental distinction between a completely coherent and a completely incoherent superposition: a suitable p/2-pulse can transfer a coherent system entirely into the eigenstate 1> or 2>. 2LS for the density matrix + spontaneous emission = Optical Bloch Equations (OBE) Definition: Bloch vector (u,v,w) ß Dispersive component ß Absorptive component ß Inversion Optical Bloch eq. à Dampening of the secondary-diagonal elements as the population from 2> is lost 31 Bloch Vectors and Bloch Sphere In case without dampening: Bloch sphere: Describes a precession movement of the Bloch vector around the axis (W0,0,-d) Precession frequency: (0,0,-1) (0,0,1) (0,-1,0) = Pulse area In case with dampening à the Bloch vector moves within the Bloch sphere with the frequency à 32
Photon echo Photon Echo Inhomogeneously broadened ensemble of two-level systems: transition frequencies distributed around w0 Systems are initially in the ground state 1> Excitation with p/2-puls generates state of maximum population After excitation: free precession in (u,v) plane, frequency in the rotating reference system is different for every single dipole d = wl - w0 System disperses out of phase è destructive interference in the sum P After time t: p-pulse in Bloch sphere exactly swaps around the precession direction of all the elementary dipoles! Re-phasing of all the elementary dipoles after expiration of another time interval t: constructive interference yields macroscopic polarisation P once again. à Emission of a coherent light pulse: photon echo Requirement for a perfect photon echo: Phase relaxation time Tph of the single dipole >> t Intensity of the photon echo: Iecho µ e -4bt 33 Photon Echo: Experimental Applications Application: Measuring the microscopic phase relaxation time Tph or rather the homogenous line width b in the inhomogeneously broadened ensemble 2 Pulse photon echo 3 Pulse photon echo Local oscillator (similar to "Signal" at parametric amplification) Kurnit, Abelle and Hartmann, PRL 13 (1964) 547 The theoretical formulation uses the Liouville formulism and double-sided Feynman diagrams Information about coherent effects like T2- dephasing, anharmonic coupling and spectral diffusion of vibrations 34
Applications: Atomic Clocks Definition: The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom. How can we capture the clock cycle of the atoms? Interaction of the atoms with microwave radiation at frequency wl (d = 0). Generates free 133 Cs-atoms with controlled velocity The Ramsey Method: two separated interaction-zones (interaction with p/2-pulses each time), between which the atoms require a time-of-flight T. The measurement accuracy is determined by the interaction time t. 35 Atomic Clocks 1) An atom leaves the oven in the ground state 2) Through the p/2-puls (0,0,-1) à (0,-1,0) 3) Free time-of-flight T (i) For resonant light-atom interaction d = 0 à no dynamics ( no light: W0 = 0, d = 0) (ii) With detuning d 0 à the Bloch vector rotates around the w-axis by an angle dt (special case: dt = p) 4) Through the p/2-puls: (i) (0,-1,0) à (0,0,1) (ii) (0,1,0) à (0,0,-1) Ramsey interferences The measurement accuracy is determined through the time-of-flight T. 36
Modern Atomic Clocks Atomic-Fountain (< 10 µk). Time-of-flight T ~ 1s Ramsey interferences State-selective detection (e.g.- Raman effect) Ch. Salomon, ENS Paris 37