Quantum Beating In Photosynthetic Systems using Noisy Light Darin Ulness Department of Chemistry Concordia College, Moorhead, MN

Quantum Beating In Photosynthetic Systems using Noisy Light Darin Ulness Department of Chemistry Concordia College, Moorhead, MN

Quantum Beating In Photosynthetic Systems using Noisy Light Darin Ulness Department of Chemistry Concordia College, Moorhead, MN

Quantum Biology Magneto-reception Olfactation Enzymes Photosynthesis

Green Sulfur Bacteria Fenna-Matthews-Olson (FMO) Complex

Fenna-Matthews-Olson (FMO) Complex

Energy Transfer Funnel

Incoherent Energy Transfer Forster Resonant Energy Transfer

Incoherent Energy Transfer Forster Resonant Energy Transfer Another route Coherent Energy Transfer Quantum beating

bb P(t) = ½ + ½cos(  b t) P(t) t Quantum beating

bb P(t) = ½ + ½cos(  b t) P(t) t Quantum beating bb

Quantum beating…in a bath bb 

bb  P(t) t  small  large

Quantum coupling J bb bb

J = 0J = small J = med J = large

Local BasisDelocalized Basis J = 0J = large

Local BasisDelocalized Basis J = 0J = large

Local BasisDelocalized Basis NN NN J = 0J = large

Local BasisDelocalized Basis NN NN J = 0J = large

Local BasisExciton Basis J = 0J = large

Local BasisExciton Basis J = 0 J = med

Local BasisExciton Basis t t t t Energy J

Coherent Light Phase locked

Incoherent “noisy” Light Color Locked

Noisy Light: Definition Broadband Phase incoherent Quasi continuous wave Noisy Light Spectrum Frequency Time resolution on the order of the correlation time,  c

Sunlight is Noisy Light!

Nonlinear Spectroscopy Signal Material Light field Perturbation series approximation P(t) = P (1) + P (2) + P (3) … P (1) =  (1) E, P (2) =  (2) EE, P (3) =  (3) EEE P =  E

Light source Interferometer Sample Local Oscillator (LO) A, B, and C beams Signal (S beam) Homodyne intensity is observed

A B C S     λ = ±  or ±  φ =  or 

Optical coherence theory Perturbation theory: Density operator Noisy Light Spectroscopy

Theoretical Challenges Complicated Mathematics Complicated Physical Interpretation Difficulty The cw nature requires all field action permutations. The light is always on. The proper treatment of the noise cross- correlates chromophores. Solution Factorized time correlation (FTC) diagram analysis

FTC Diagram Analysis Set of intensity level terms (pre-evaluated) Set of evaluated intensity level terms Messy integration and algebra Set of FTC diagrams Construction Rules Physics hard easy Evaluation Rules

Utility of FTC Diagrams Organize lengthy calculations Error checking Identification of important terms Immediate information of about features of spectrograms Much physical insight that transcends the choice of mathematical model.

A B C S     Optical coherence theory Perturbation theory: Density operator Noisy Light Spectroscopy Construction of an FTC Diagram

A B C S     Optical coherence theory Perturbation theory: Density operator Noisy Light Spectroscopy Construction of an FTC Diagram Timeline for signal Timeline for LO

A B C S     Optical coherence theory Perturbation theory: Density operator Noisy Light Spectroscopy Construction of an FTC Diagram Timeline for signal Timeline for LO Field Interactions

A B C S     Optical coherence theory Perturbation theory: Density operator Noisy Light Spectroscopy Construction of an FTC Diagram Timeline for signal Timeline for LO Material Response

A B C S     Optical coherence theory Perturbation theory: Density operator Noisy Light Spectroscopy Construction of an FTC Diagram Timeline for signal Timeline for LO Correlated Field Action

A B C S     Optical coherence theory Perturbation theory: Density operator Noisy Light Spectroscopy Construction of an FTC Diagram Timeline for signal Timeline for LO One Example AB C

A B C S     Optical coherence theory Perturbation theory: Density operator Noisy Light Spectroscopy Construction of an FTC Diagram Timeline for signal Timeline for LO One Example AB C

A B C S     Optical coherence theory Perturbation theory: Density operator Noisy Light Spectroscopy Construction of an FTC Diagram Timeline for signal Timeline for LO One Example AB C

A B C S     128 terms = 128 FTC diagrams FTC diagrams

A B C S     128 terms = 128 FTC diagrams FTC diagrams Only 3 topological classes!

Topological classes of FTC Diagrams Unrestricted Singly Restricted Doubly Restricted

Topological classes of FTC Diagrams Unrestricted Singly Restricted Doubly Restricted Strong ! Weak !

Analytic Results: Unrestricted Strong Signal No quantum beating

Analytic Results: Singly restricted Weak Signal Quantum beating

Analytic Results: Doubly restricted Weak Signal Quantum beating

Conclusions Coherent quantum beating is seen in excitonic systems, although very weak. Noisy light spectroscopy can be used to investigate these systems FTC diagram analysis can simply calculations and provide insight It is worthwhile to attempt a noisy light based experiment

Acknowledgements Funding Concordia Chemistry Research Fund Student Government Association NSF STEP grant Minnesota Space Grant People Duffy Turner, U Toronto Mark Gealy, Physics Erika Sutor Rebecca Hendrickson Dylan Howey