quantum decoherence of excited states of optically active biomolecules ross mckenzie

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Quantum decoherence of excited states of optically active biomolecules Ross McKenzie

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Page 1: Quantum decoherence of excited states of optically active biomolecules Ross McKenzie

Quantum decoherence of excited states of optically

active biomolecules

Ross McKenzie

Page 2: Quantum decoherence of excited states of optically active biomolecules Ross McKenzie

Outline• Optically active biomolecules as complex

quantum systems

• A minimal model quantum many-body Hamiltonian

• Spectral density for system-environment interaction is well characterised.

• Observing the ``collapse’’ of the quantum state!

• Ref: J. Gilmore and RHM, quant-ph/0609075

Page 3: Quantum decoherence of excited states of optically active biomolecules Ross McKenzie

Some key questions concerning biomolecular functionality

Which details matter?

• What role does water play?

• Do biomolecules have the optimum structure to exploit dynamics for their functionality?

• When is quantum dynamics (e.g., tunneling, coherence) necessary for functionality?

Page 4: Quantum decoherence of excited states of optically active biomolecules Ross McKenzie

Photosynthetic Light harvesting complexes

Quantum coherence over large distances?

Why should quantum physicists be interested in biomolecules?

• Retinal, responsible for vision– Single photon detector– Quantum dynamics when the

Born-Oppenheimer approx. breaks down

- Entanglement of electrons & nuclei

- Effect of decoherence on Berry’s phase

Photo-active biomolecules are tuneable systems at the quantum-classical boundary

Page 5: Quantum decoherence of excited states of optically active biomolecules Ross McKenzie

Quantum biology at amazon.com?

Page 6: Quantum decoherence of excited states of optically active biomolecules Ross McKenzie
Page 7: Quantum decoherence of excited states of optically active biomolecules Ross McKenzie

A complex quantum system: Photo-active yellow protein

Quantum system =

Ground + electronic

excited state of

chromophore

Environment =

Protein +

Water bound to

Protein +

Bulk water

Page 8: Quantum decoherence of excited states of optically active biomolecules Ross McKenzie

Seeking a minimal model for this quantum system and its environment

• Must capture and give insights into essential physics.

• Tells us which physical parameters lead to qualitative changes in quantum dynamics.

Page 9: Quantum decoherence of excited states of optically active biomolecules Ross McKenzie

• Chromophore is two level system (TLS).

• The environment is modelled as an infinite bath of harmonic oscillators.

• Effect of environment on quantum dynamics of TLS is completely determined by the spectral density:

Independent boson model Hamiltonian

Page 10: Quantum decoherence of excited states of optically active biomolecules Ross McKenzie

Leggett’s important idea• We don’t need to know all the microscopic

details of the environment, nor its interaction with the system. Only need J( ).

• Spectral density can be determined from measurements of the classical dynamics.

• Most spectral densities are ``ohmic’’, i.e., J( ) ≈ for <

1/ is relaxation time of the bath.• For > 1 quantum dynamics is incoherent.

Caldeira and Leggett, Ann. Phys. (1983); Leggett, J. Phys.: Cond. Matt. (2002).

Page 11: Quantum decoherence of excited states of optically active biomolecules Ross McKenzie

Quantum dynamics of TLSTLS is initially in a coherent superposition state uncoupled from the bath. Reduced density matrix of TLS is

Decay of coherence

Spectral diffusion

Page 12: Quantum decoherence of excited states of optically active biomolecules Ross McKenzie

``Collapse’’ of the wave function

• Zurek (`82), Joos and Zeh (`85), Unruh (`89)• Environment causes decay of the off-diagonal

density matrix elements (decoherence)• ``Collapse’’ occurs due to continuous

``measurement’’ of the state of the system by the environment.

• What is the relevant time scale for these biomolecules?

h/(kBT α) ~ 10 fsec

Page 13: Quantum decoherence of excited states of optically active biomolecules Ross McKenzie

Spectral density can be extracted from ultra-fast laser

spectroscopy• Measure the time dependence of the

frequency of maximum fluorescence (dynamic Stokes shift)

• Data can be fit to multiple exponentials.

• Fourier transform gives spectral density!

Page 14: Quantum decoherence of excited states of optically active biomolecules Ross McKenzie

Pal and Zewail, Chem. Rev. (2004)

Page 15: Quantum decoherence of excited states of optically active biomolecules Ross McKenzie

An example

• ANS is

chromophore

Pal, Peon, Zewail, PNAS (2002)

Page 16: Quantum decoherence of excited states of optically active biomolecules Ross McKenzie

Femtosecond laser spectroscopy: Measurement of the time-dependent spectral shift of a chromophore in a solvated protein

• Increasing pH unfolds (denatures) protein and exposes chromophore to more solvent.

• Presence of protein reduces psec relaxation and adds ~50 psec relaxation.

• Pal, Peon, Zewail, PNAS (2002)

Page 17: Quantum decoherence of excited states of optically active biomolecules Ross McKenzie

Measured spectral densities

Three contributions of ohmic form•Bulk water (solvent) ss ~ 0.3-3 psec•Water bound to the protein, esp. at surfaceb ~ 10-100 b ~ 10-100 psec•Protein pp ~ 1-100 nsec

Page 18: Quantum decoherence of excited states of optically active biomolecules Ross McKenzie

Spectral density for diverse range of biomolecules & solvents

Page 19: Quantum decoherence of excited states of optically active biomolecules Ross McKenzie

Classical molecular dynamics simulations

C(t) for Trp (green) and Trp-3 in monellin (black) in aqueous solution at 300 KNilsson and Halle, PNAS (2005).

Page 20: Quantum decoherence of excited states of optically active biomolecules Ross McKenzie

Our continuum dielectric models for environment

• We have calculated J( for 5 models for environment

• Key feature is separation of time and distance scales: Protein much larger than chromophore

• Relaxation time of Protein >> Bound water >> Bulk solvent

• J( is sum of Ohmic contributions which we can identify with 3 different environments, protein, bound water, and bulk water

Page 21: Quantum decoherence of excited states of optically active biomolecules Ross McKenzie

Key physics behind decoherence• Most chromophores have a large difference

between electric dipole moment of ground and excited states.

• Water is a very polar solvent (static dielectric constant s = 80)

– Water molecules have a net electric dipole moment– Dipole direction fluctuates due to thermal fluctuations

(typical relaxation time at 300K is ~1 psec)

• Chromophore experiences fluctuating electric field

• Surrounding protein does not completely shield chromophore from solvent.

Page 22: Quantum decoherence of excited states of optically active biomolecules Ross McKenzie

What have we learned?

• Complete characterisation of system-environment interaction for biomolecular chromophores.

• These spectral densities can be used to make definitive statements about the importance of quantum effects in biomolecular processes.

• Due to their tuneable coupling to their environment biomolecular systems may be model systems to use to test ideas in quantum measurement theory.

• For chromophores the timescale of the ``collapse’’ is less than 100 fsec.

Page 23: Quantum decoherence of excited states of optically active biomolecules Ross McKenzie
Page 24: Quantum decoherence of excited states of optically active biomolecules Ross McKenzie
Page 25: Quantum decoherence of excited states of optically active biomolecules Ross McKenzie
Page 26: Quantum decoherence of excited states of optically active biomolecules Ross McKenzie
Page 27: Quantum decoherence of excited states of optically active biomolecules Ross McKenzie

Localised

t

Coherent

t

Incoherent

t

Location of excitation with time

Criteria for quantum coherent transfer of excitation energy between two chromophores

J. Gilmore & RHM, Chem. Phys. Lett. (2006)

Page 28: Quantum decoherence of excited states of optically active biomolecules Ross McKenzie

Realisation of spin-boson model for coupled chromophores

• Excitation can be on either of two molecules

• Each two energy levels

If only one excitation is present, effectively a two level system

What is the two level system?

Page 29: Quantum decoherence of excited states of optically active biomolecules Ross McKenzie

• Excitations transferred by dipole-dipole interactions (Forster)– Shine in blue, get out yellow!

– Basis of Fluorescent Resonant Energy Transfer (FRET) spectroscopy

– Used in photosynthesis to move excitations around

What is the coupling?

Realisation of spin-boson model for coupled chromophores

Page 30: Quantum decoherence of excited states of optically active biomolecules Ross McKenzie

Localised

t

Coherent

t

Incoherent

t

Location of excitation with time

Criteria for quantum coherent transfer of excitation energy between two chromophores

J. Gilmore & RHM, Chem. Phys. Lett. (2006)

Coherent for α<1

Page 31: Quantum decoherence of excited states of optically active biomolecules Ross McKenzie

Questions

• How unusual is to have a physical system where the system-bath interaction is so well characterised?

• What experiment would best elucidate the “collapse”?

Page 32: Quantum decoherence of excited states of optically active biomolecules Ross McKenzie
Page 33: Quantum decoherence of excited states of optically active biomolecules Ross McKenzie

A comparison: Retinal vs. Green Fluorescent Protein

• Green Fluorescent Protein – Excited state 10000x longer– Fluoresces with high quantum

efficiency

• Bacteriorhodopsin– Non-radiative decay in 200fs– Specific conformational change

Very different quantum dynamics ofChromophore determined by environment!

Page 34: Quantum decoherence of excited states of optically active biomolecules Ross McKenzie

Flouresence from differentamino acid residues within

protein Cohen et al, Science (2002)