Resonant optical rectification. Theory and application to bacteriorhodopsin

Transcription

1 Resonant optical rectification. Theory and application to bacteriorhodopsin Institute of Biophysics Biological Research Centre of the Hungarian Academy of Sciences Szeged, Hungary Laboratory for Optical Biosciences INSERM U451 - CNRS UMR7645 Ecole Polytechnique Palaiseau, France Géza Groma Anne Colonna Manuel Joffre Marten Vos Jean-Louis Martin Supported by the ESF Femtochemistry and Femtobiology Programme.

2 Bacteriorhodopsin Single protein in the purple membrane of Halobactrium salinarium Forms hexagonal D crystal in the membrane Utilizes light energy by pumping protons across the membrane

3 Pt + ITO BR native rise time: 3-5 ps Light-induced electric response signal of oriented purple membrane sample

4 What is the real primary charge separation process? Traditional idea: charge separation by all-trans 13-cis isomerization of the retinal chromophore still popular questioned by studies on artificial pigments of locked isomerization

5 µ 11 excited state µ 00 µ 11 µ 00 = 1 D ground state Mathies & Stryer, PNAS 73, 169 (1976) Upon excitation a huge change of dipole moment takes place. According to the Maxwell theory this is a source of electromagnetic radiation. What kind of optical phenomenon could describe this radiation?

6 The expected radiation rises instantaneously with absorption decays with excited state = aperiodic, no carrier freqency observable only on oriented (noncentrosymmetric) sample can not be a first order optical process resonant dominated by T 1 relaxation fundemental nd order processes second harmonic generation optical rectification no resonant theory! (popular χ expressions are singular)

7 Theory of resonant optical rectification (based on Mukamel s method), = 1, 1,, P r t dt dt S t t E r t t E r t t t second-order polarisation () i S t t1 V t t1 ρ (, ) = << G VG Va >> two-point transfer function h G i t A t H A t h () θ () exp [, ] Liouville-space Green function V = µ a>< b ab, ab µ =< av b> ab Hilbert-space dipole operator V A = [ V, A] Liouville-space dipole operator 1 χ ω ω ω ρ ω ω ω ( ;, ) = S ( +, ) () () s p second-order susceptibility

8 Specification of the (tetradic) relaxation matrix: Γ γ aa, bb ( a b) ab Γ γ Γ aa, aa a bb, aa b ( a) 1 Γ = ( γ + γ ) Γˆ Γ ab, ab a b ab ab In earlier work the offdiagonal elements were neglected Γ = aa, bb ( a b) 0 simpler formula lack of conservation of the probability () singularity in χ ( ω ; s ω, 1 ω) for ω = ω 1

9 For a two-level system with complete T 1 relaxation matrix: 1 1, 1 = 1 e cos 1+ T µ 10 ( µ 11 µ 00 ) θ θ { ω1 0 S t t P 0 P 1 t t t t h t t 1 T1 T + e e cos ω t } t + t 10 1 ω10 T1 T transition frequency population relaxation time coherence relaxation time 0< T <= T 1

10 incident light: = cos( ω ) E t Env t t polarisation: () 0 = (, ) cos ω cos ω P t dt dt S t t Env t t t t Env t t t t t t () () OR SH P t = P t + P t optical rectification: ( ) OR () = (, ) P t dt dt S t t Env t t Env t t t 1 S ( t, t ) = S t, t cos t ( ) ( ω ) ()

11 Simulations 1.4 w0 = 3000 THz w10 = 500 THz h = 10 fs T1 = 00 fs T = 400 fs population coherence intensity 60 w0 = 3000 THz w10 = 3000 THz h = 10 fs T1 = 00 fs T = 400 fs population coherence classical Time (fs) Time (fs) off-resonant excitation resonant excitation

12 Simulations 0.10 w0 = 3000 THz w10 = 100 THz h = 10 fs T1 = 00 fs T = 400 fs population coherence Time (fs) envelope resonance

13 Scheme of the setup for coherent IR emission measurement cm -1 (Ecole Polytechnique, Palaiseau)

14 A Time (fs) Coherent infrared emission signal from br and GaAs Groma et al. PNAS 101: 7971 (004)

15 B Frequency (cm-1) Power spectrum of br and GaAs coherent infrared emission signal

16 A 1.0 Signal Intensity (a.u.) intensity dependence Time (fs) B visible pump IR HV s p VV p p VH p s HH s s polarisation dependence Time (fs)

17 Frequency (cm-1) Time (fs) Power spectrum of the oscillation region.

18 Conclusions The theory of optical rectification was extended to the resonant case with complete relaxation matrix. The existence of the optical rectification process in bactriorhodopsin was experimentally confirmed. We assume that this second order process is the primary reason of the further proton motions, that is the functional motor of the protein. P = χ E the function is linear in light intensity The optical rectification process is accompanied by multimodal coherent vibration. causal relation? functionally important vibrations?