Sabas Abuabara, Luis G.C. Rego and Victor S. Batista

Department of Chemistry, Yale University, New Haven, CT 06520-8107

Creating and Manipulating Electronic Coherences in Functionalized

Semiconductor Nanostructures

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

TiO2-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, 28089 (2003)

Model System – Unit Cell

TiO2-anatase nanostructure functionalized by adsorbed catechol

124 atoms:

32 [TiO2] units = 96catechol [C6H6-202] unit = 1216 capping H atoms = 16

VASP/VAMP simulation packageHartree 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

TiO2 normal modes

262-876 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 HamiltonianH 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 BandBand 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

)0()(ˆ)( tUt

and withq

qq ttBt )()()(

')'(

)(ˆ dttHi

etU , where

i

iqiq tKtCt )()()( , are the instantaneous MO’s

)()()()()( tEtCtStCtH

obtained by solving the extended-Hückel generalized eigenvalue equation:

)()()()( 2))()((

tptqetBtBp

tEtEi

pq

qp

2))()((

)()(

tEtE

i

qq

qp

etBtB

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

)()()()(ˆ 2)(

2 tqetBttUq

tEi

q

q

)()(

)(),(ˆ

2)(

2

tqetB

tttU

tEi

qq

q

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

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

SYS

j

jij

MOL

iiMOL StCtCtP

,

,,,

,

*, )()()(

Propagation Scheme cont’d

LUMO InjectionP

MO

L(t)

Relaxation Dynamics of Hole States Localized on Adsorbate Monolayer

t=15 ps Super-exchange hole transfer

SYS

j

jij

MOL

iiMOL StCtCtP

,

,,,

,

*, )()()(

Compute Hole Population on each adsorbateAfter photoinduced electron-

hole pair separation due toelectron injection

Hole is left behind, off resonant w.r.t.

conduction and valence bands

Dynamics on Adsorbate Monolayer

0 20 40 60 80 1000.0

0.2

0.4

0.6

0.8

1.0

SU

RV

IVA

L P

RO

BA

BIL

ITY

TIME (PS)

Coherent Hole-Tunneling Dynamics

);(/

)(22

2

22

sin ttPjk

jk

jkj

22 )2/()/( jkjkjk

PM

OL(

t)P

MO

L(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,…)TiO2 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

HOMO2 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, 44101 (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)

)0()0()0(

)()0(2)()(

t

ttt= 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

0 20 40 60 80 1000.0

0.2

0.4

0.6

0.8

1.0

S

UR

VIV

AL

PR

OB

AB

ILIT

Y

TIME (PS)

2- pulses (200 fs spacing)

14 fs 60 fs

0 20 40 60 80 1000.0

0.2

0.4

0.6

0.8

1.0

S

UR

VIV

AL

PR

OB

AB

ILIT

Y

TIME (PS)

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#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 !

Acknowledgment