Quantum Beating In Photosynthetic Systems using Noisy Light

Darin UlnessDepartment of ChemistryConcordia College, Moorhead, MN

Quantum Beating In Photosynthetic Systems using Noisy Light

Darin UlnessDepartment of ChemistryConcordia College, Moorhead, MN

Quantum Beating In Photosynthetic Systems using Noisy Light

Darin UlnessDepartment of ChemistryConcordia College, Moorhead, MN

Quantum BiologyMagneto-receptionOlfactationEnzymesPhotosynthesis

Green Sulfur Bacteria

Fenna-Matthews-Olson(FMO) Complex

Fenna-Matthews-Olson(FMO) Complex

Energy Transfer Funnel

Incoherent Energy TransferForster Resonant Energy Transfer

Incoherent Energy TransferForster Resonant Energy Transfer

Another routeCoherent Energy Transfer Quantum beating

wb

P(t) = ½ + ½cos(wbt)P(t)

t

Quantum beating

wb

P(t) = ½ + ½cos(wbt)P(t)

t

Quantum beating

wb

Quantum beating…in a bath

wbL

Quantum beating…in a bath

wbL

P(t)

t

L smallL large

Quantum coupling

Jwb wb

J = 0 J = small

J = med J = large

Local Basis Delocalized Basis

J = 0 J = large

Local Basis Delocalized Basis

J = 0 J = large

Local Basis Delocalized Basis

NN N NNN

J = 0 J = large

Local Basis Delocalized Basis

NN N NNN

J = 0 J = large

Local Basis Exciton Basis

J = 0 J = large

Local Basis Exciton Basis

J = 0 J = med

Local Basis Exciton Basis

t t

t

t

Ener

gy

J

Coherent Light

Phase locked

Incoherent “noisy” Light

Color Locked

Noisy Light: Definition•Broadband•Phase incoherent•Quasi continuous wave

Ele

tric

Fie

ld S

tren

gth

Time

Noi

sy L

ight

Spe

ctru

m

Frequency

Time resolution onthe order of the correlation time, tc

Sunlight is Noisy Light!

Nonlinear Spectroscopy

Signal

Material

Light field

Perturbation series approximation

P(t) = P(1) + P(2) + P(3) …

P(1) = c (1)E, P(2) = c (2)EE, P(3) = c (3)EEE

P= c E

Light source

Interferometer

Sample

Local Oscillator

(LO)

A, B, and C beams

Signal (S beam)

Homodyne intensity is observed

A

B C

S

s

t

z

k

λ = ±s or ±tφ = z or k

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

ConstructionRules

Physics

hard hard

easy

EvaluationRules

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

s

t

z

k

Optical coherence theory

Perturbation theory: Density operator

Noisy Light Spectroscopy

Construction of an FTC Diagram

A

B C

S

s

t

z

k

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

s

t

z

k

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

s

t

z

k

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

s

t

z

k

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

s

t

z

k

Optical coherence theory

Perturbation theory: Density operator

Noisy Light Spectroscopy

Construction of an FTC Diagram

Timeline for signal

Timeline for LO

One Example

A B C

A

B C

S

s

t

z

k

Optical coherence theory

Perturbation theory: Density operator

Noisy Light Spectroscopy

Construction of an FTC Diagram

Timeline for signal

Timeline for LO

One Example

A B C

A

B C

S

s

t

z

k

Optical coherence theory

Perturbation theory: Density operator

Noisy Light Spectroscopy

Construction of an FTC Diagram

Timeline for signal

Timeline for LO

One Example

A B C

A

B C

S

s

t

z

k

128 terms = 128 FTC diagrams

FTC diagrams

FTC diagrams

A

B C

S

s

t

z

k

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 !

Weak !

Analytic Results: Unrestricted

Strong SignalNo quantum beating

Analytic Results: Singly restricted

Weak SignalQuantum beating

Analytic Results: Doubly restricted

Weak SignalQuantum 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

FundingConcordia Chemistry Research FundStudent Government AssociationNSF STEP grantMinnesota Space Grant

PeopleDuffy Turner, U TorontoMark Gealy, PhysicsErika SutorRebecca HendricksonDylan Howey