Quantum decoherence of excited states of optically active biomolecules

1. Quantum decoherence of excited states of optically active biomolecules Ross McKenzie

2. 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

3. 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?

4. Why should quantum physicists be interested in biomolecules? Photo-active biomolecules are tuneable systems at the quantum-classical boundary • 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 Photosynthetic Light harvesting complexes Quantum coherence over large distances?

5. Quantum biology at amazon.com?

7. A complex quantum system: Photo-active yellow protein Quantum system = Ground + electronic excited state of chromophore Environment = Protein + Water bound to Protein + Bulk water

8. 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.

9. Independent boson model Hamiltonian • 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:

10. 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/t • t is relaxation time of the bath. • For a > 1 quantum dynamics is incoherent. Caldeira and Leggett, Ann. Phys. (1983); Leggett, J. Phys.: Cond. Matt. (2002).

11. Quantum dynamics of TLS TLS is initially in a coherent superposition state uncoupled from the bath. Reduced density matrix of TLS is Decay of coherence Spectral diffusion

12. ``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

13. 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!

14. Pal and Zewail, Chem. Rev. (2004)

15. An example • ANS is chromophore Pal, Peon, Zewail, PNAS (2002)

16. 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)

17. Measured spectral densities • Three contributions of ohmic form • Bulk water (solvent) • as ~ 1-10 ts ~ 0.3-3 psec • Water bound to the protein, esp. at surface • ab ~ 10-100 tb ~ 10-100 psec • Protein • ap ~ 100-1000 tp ~ 1-100 nsec

18. Spectral density for diverse range of biomolecules & solvents

19. Classical molecular dynamics simulations C(t) for Trp (green) and Trp-3 in monellin (black) in aqueous solution at 300 K Nilsson and Halle, PNAS (2005).

20. Our continuum dielectric models for environment • We have calculated J(w) 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(w) is sum of Ohmic contributions which we can identify with 3 different environments, protein, bound water, and bulk water

21. 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.

22. 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.

27. Incoherent Coherent t t t Localised Criteria for quantum coherent transfer of excitation energy between two chromophores J. Gilmore & RHM, Chem. Phys. Lett. (2006) Location of excitation with time

28. Realisation of spin-boson model for coupled chromophores • Excitation can be on either of two molecules • Each two energy levels What is the two level system? If only one excitation is present, effectively a two level system

29. Realisation of spin-boson model for coupled chromophores • 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?

30. Incoherent Coherent t t t Localised Criteria for quantum coherent transfer of excitation energy between two chromophores J. Gilmore & RHM, Chem. Phys. Lett. (2006) Location of excitation with time Coherent for α<1

31. 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”?

33. 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 of Chromophore determined by environment!

34. Flouresence from differentamino acid residues withinprotein Cohen et al, Science (2002)