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

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, (2003)

Model System – Unit Cell TiO 2 -anatase nanostructure functionalized by adsorbed catechol 124 atoms: 32 [TiO 2 ] units = 96 catechol [C 6 H ] unit = capping H atoms = 16 VASP/VAMP simulation package Hartree and Exchange Correlation Interactions: Perdew-Wang functional Ion-Ion interactions: ultrasoft Vanderbilt pseudopotentials

Phonon Spectral Density O-H stretch, 3700 cm -1 (H capping atoms) C-H stretch 3100 cm -1 TiO 2 normal modes cm -1 C-C,C=C stretch 1000 cm -1,1200 cm -1

[010] 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). Simulations of Electronic Relaxation Three unit cells extending the system in [-101] direction [-101]

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?

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

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

Which in  0 limit we approximate as Propagation Scheme

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

Injection from LUMO TiO 2 system extended in [-101] direction with PBC in [010] direction Grey ‘Balloons’ are isosurface of electronic density Allow visualization of mechanism

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 Propagation Scheme cont’d

LUMO Injection P MOL (t)

Relaxation Dynamics of Hole States Localized on Adsorbate Monolayer t=15 ps Super-exchange hole transfer Compute Hole Population on each adsorbate 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

Coherent Hole-Tunneling Dynamics P MOL (t) (1) (2) (3)

Measure of Decoherence and Localization

Survival of Electronic Coherences

Inhibiting Hole Super-Exchange by multiple 2  pulses CB VB C L   superexchange Adsorbate molecules (C, L,…) TiO 2 semiconductor 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) HOMO-1 LUMO HOMO 2  pulses hole

Inhibiting Hole Super-Exchange by multiple 2  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. A 63, (2001) L. Viola and S. Lloyd Phys. Rev. A 58, 2733 (1998), L. Viola, E. Knill and S. Lloyd Phys. Rev. Lett. 82, 2417 (1999) D. Vitali and P. Tombesi Phys. Rev. A 59, 4178 (1999) W.M. Itano, D.J. Heinzen, J.J. Bollinger and D.J. Wineland Phys. Rev. A 41, 2295 (1990)

t= k*   = 200 fs,   Inhibiting Hole Super-Exchange by multiple 2  pulses, cont’d 2-  pulses (200 fs spacing) Apply pulsed radiation tuned to frequency  21

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

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

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 2  -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. Conclusions

NSF Nanoscale Exploratory Research (NER) Award ECS# NSF Career Award CHE# 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 ! Acknowledgment