35th Winter Colloquium on The Physics of Quantum Electronics Snowbird, Utah -- January 2-6, 2005

1. 35th Winter Colloquium on The Physics of Quantum ElectronicsSnowbird, Utah -- January 2-6, 2005 Creating and Manipulating Electronic Coherences in Functionalized Semiconductor Nanostructures Sabas Abuabara, Luis G.C. Rego and Victor S. Batista Department of Chemistry, Yale University, New Haven, CT 06520-8107 TiO2-anatase semiconductor nanostructure functionalized with catecholadsorbates

2. Aspects of Study • Interfacial Electron Transfer Dynamics • Relevant timescales and mechanisms • Dependence of electronic dynamics on the crystal symmetry and dynamics • Effect of nuclear dynamics • Whether nuclear motion affects transfer mechanism or timescale • Implications for quantum coherences • Hole Relaxation Dynamics • Decoherence timescale • Possibility of coherent control L.G.C. Rego, S.T. Abuabara and V.S. Batista, J. Chem. Phys., submitted (2004) L.G.C. Rego, S.T. Abuabara and V.S. Batista Quant. Inform. Comput., submitted (2004) S. Flores and V.S. Batista J. Phys. Chem. B 108 ,6745 (2004) L.G.C. Rego and V.S. Batista, J. Am. Chem. Soc.125, 7989 (2003) V.S. Batista and P. Brumer, Phys. Rev. Lett.89, 5889 (2003), ibid. 89, 28089 (2003)

3. Model System – Unit Cell VASP/VAMP simulation packageHartree and Exchange Correlation Interactions: Perdew-Wang functional Ion-Ion interactions: ultrasoft Vanderbilt pseudopotentials TiO2-anatase nanostructure functionalized by adsorbed catechol 124 atoms: 32 [TiO2] units = 96 catechol [C6H6-202] unit = 12 16 capping H atoms = 16

4. Phonon Spectral Density O-H stretch, 3700 cm-1 (H capping atoms) C-H stretch 3100 cm-1 C-C,C=C stretch 1000 cm-1,1200 cm-1 TiO2 normal modes 262-876 cm-1

5. Simulations of Electronic Relaxation • Accurate description of charge delocalization requires simulations in extended model systems. • Simulations in small clusters (e.g., 1.2 nm nanostructures) are affected by surface states that speed up the electron injection process • Periodic boundary conditions alone often introduce artificial recurrencies (back-electron transfer events). [-101] Three unit cells extending the system in [-101] direction [010]

6. Electronic Hamiltonian .. • H is the Extended Huckel Hamiltonian in the basis of Slater type atomic orbitals (AO’s) including • 4s, 3p and 3d AO’s of Ti 4+ ions • 2s and 2p AO’s of O 2- ions • 2s and 2p AO’s of C atoms • 1s AO’s of H atoms • 596 basis functions per unit cell • S is the overlap matrix in the AO’s basis set. How good is this tight binding Hamiltonian?

7. Electronic Density of States (1.2 nm particles) photoexcitation LUMO,LUMO+1 HOMO HOMO Band gap =3.7 eV Conduction Band Valence Band ZINDO1 Band gap =3.7 eV Exp. (2.4 nm) = 3.4 eV Exp. (Bulk-anatase) = 3.2 eV

8. Mixed Quantum-Classical Dynamics Propagation Scheme , where and with are the instantaneous MO’s obtained by solving the extended-Hückel generalized eigenvalue equation:

9. Which in t0 limit we approximate as Propagation Scheme

10. Propagation Schemecont’d Derive propagator for midpoint scheme: Hamiltonian changes linearly during time step / Forward and Backwards propagation equal

11. Injection from LUMO TiO2 system extended in [-101] direction with PBC in [010] direction Grey ‘Balloons’ are isosurface of electronic density Allow visualization of mechanism

12. Propagation Schemecont’d • With this scheme, we can calculate for all t>0 : • electronic wavefunction • electronic density • Define the Survival Probability for electron(hole) to be found on specific adsorbate molecule

13. PMOL(t) LUMO Injection

14. Relaxation Dynamics of Hole States Localized on Adsorbate Monolayer Compute Hole Population on each adsorbate t=15 ps Super-exchange hole transfer After photoinduced electron-hole pair separation due to electron injection Hole is left behind, off resonant w.r.t. conduction and valence bands Dynamics on Adsorbate Monolayer

15. Coherent Hole-Tunneling Dynamics PMOL(t) PMOL(t) (3) (1) (2)

16. Measure of Decoherence and Localization

17. Survival of Electronic Coherences

18. Inhibiting Hole Super-Exchange by multiple 2 p pulses We investigate the feasibility of manipulating the underlying hole relaxation dynamics by merely affecting the relative phases of the state components (e.g., by using femtosecond laser pulses) L C LUMO CB superexchange hole HOMO w12 2p pulses HOMO-1 VB TiO2 semiconductor Adsorbate molecules (C, L,…)

19. Inhibiting Hole Super-Exchange by multiple 2 p pulses, cont’d • Proposals for the Inhibition of Decay by Using Pulses: • G.S. Agarwal, M.O. Scully and H. Walther • (a) Phys. Rev. Lett.86, 4271 (2001); • (b) Phys. Rev. A63, 44101 (2001) • L. Viola and S. Lloyd Phys. Rev. A58, 2733 (1998), • L. Viola, E. Knill and S. Lloyd Phys. Rev. Lett.82, 2417 (1999) • D. Vitali and P. Tombesi Phys. Rev. A59, 4178 (1999) • W.M. Itano, D.J. Heinzen, J.J. Bollinger and D.J. Wineland • Phys. Rev. A41, 2295 (1990)

20. Inhibiting Hole Super-Exchange by multiple 2 p pulses, cont’d t = 200 fs, w12 t= k*t Apply pulsed radiation tuned to frequency w21 2-p pulses (200 fs spacing)

21. Investigation of Coherent-Control cont’d 2-p pulses (200 fs spacing) 14 fs 60 fs

22. 2-p pulses (200 fs spacing) 2 fs 42 fs Investigation of Coherent-Control cont’d

23. Conclusions • We have investigated interfacial electron transfer and hole tunneling relaxation dynamics according to a mixed quantum-classical approach that combines ab-initio DFT molecular dynamics simulations of nuclear motion with coherent quantum dynamics simulations of electronic relaxation. • We have investigated the feasibility of creating entangled hole-states localized deep in the semiconductor band gap. These states are generated by electron-hole pair separation after photo-excitation of molecular surface complexes under cryogenic and vacuum conditions. • We have shown that it should be possible to coherently control superexchange hole-tunneling dynamics under cryogenic and vacuum conditions simply by applying a sequence of ultrashort 2p-pulses with a frequency that is resonant to an auxiliary transition in the initially populated adsorbate molecule. • We conclude that large scale simulations of quantum dynamics in complex molecular systems can provide valuable insight into the behavior of the quantum coherences in exisiting materials which might be essential to bridge the gap between the quantum information and quantum control communities.

24. Acknowledgment • NSF Nanoscale Exploratory Research (NER) Award ECS#0404191 • NSF Career Award CHE#0345984 • ACS PRF#37789-G6 • Research Corporation, Innovation Award • Hellman Family Fellowship • Anderson Fellowship • Yale University, Start-Up Package • NERSC Allocation of Supercomputer Time • PQE XXXV Organizers:     M. Scully, G. R. Welch, M. S. Zubairy, P. Brumer • Thank you !