Ultrafast 2D Quantum Switching of p‑Electron Rotations in a Nonplanar Chiral Molecule by Using Linearly Polarized UV Laser Pulses Mineo, Hirobumi (峯尾　浩文) Institute of Atomic and Molecular Sciences, Academia Sinica  (中央研究院原子分子科學研究所) email: mineo@gate.sinica.edu.tw J. Am. Chem. Soc. 134, 14279 (2012) J. Chem. Phys. 138, 074304 (2013) 各位大家好, 我叫峰尾浩文. 我來台灣11年, 但是第一次來中興大學演講, 我想幾乎大家都不認識我, 所以我想先簡單地自我介紹一下. 其實我原本在台灣出生, 因為我母親是台灣人, 後來到日本, 一直待在那裡 長大. 11年前又回來台灣當博士後. 剛回來台灣的時候我作的研究領域是原子核物理的理論計算. 就是把電子和質子scatter之後, 得到質子結構的資訊. 所以跟我現在做的研究有差別. 後來7年前轉到原子分子, 光學方面, 研究對象變成原子分子, 就變大. 用強雷射來引起分子的游離化, 或離子的解離的數值計算. 在今天的演講我所用到的都是獨立的分子, 但是研究的方向還是往更大的scale. 固態的分子nano particle, 大小也是從angstrom到幾十或幾百nm的scale. 我的演講是照這個流程進行. 先介紹背景跟目的. 因為透過演講我要討論aromatic ring, 環狀的分子上的pi electron current的控制. 所以用一個aromatic molecule來解釋引起pi electron current的mechanism. 這個時候同時產生角動量angular momentum. 接下來, 用兩個環狀的分子連結起來做的分子來示範2維的quantum switching. 在任何2維的方向, 產生pi electron current跟angular momentum. swithcing的時間是100fs之內的,超快的短時間. 最後總結演講. Introduction of purpose and background Mechanism of p electron ring current 2D ultrafast quantum switching Numerical simulations Summary and conclusion

Introduction Quantum control of electronic and molecular dynamics? Chemistry Ionization, and electronic states in molecules Dissociations of molecules and ions Selection of chiral molecules Industry, Electronics LCD, Organic electroluminescence display Molecular transistor (potential possibility) HDD (~ ps) = :Laser field L.Y. Hsu, H. Rabitz, PRL 109, 186801 (2012) Possibility of Ultrafast switching (~fs)? Organic molecule is more ecology We will demonstrate 2D Ultrafast switching in a non-planar chiral molecule Applicability depends on development of technology

Quantum control is important in chemistry, electronics, physics and industry (We focus on) Laser control of electron (p-electron) ring current UV laser pulse =angular momentum ~ magnetic field p-electron rotations in a chiral aromatic molecule UV laser pulse 2D switching of p-electron rotations in a non-planar chiral molecule

Important role of p electrons in aromatic molecules High reactivity due to delocalization of p electrons Kekulé structure (1865) and delocalized p electrons in benzene p-orbital=pz-orbital Resonant delocalized Question: p-electrons rotate ? Which direction? Clockwise or anti-clockwise ? How to control rotation by using laser?

Fundamental studies on laser-induced p electron rotations Ex. Simulations electron rotations in aromatic molecules ( I. Barth et al., J. Am. Chem. Soc., 128 , 7043 (2006) Generation of p- electron currents by a circularly polarized laser pulse; The rotational direction is determined by circularly polarized pulse.

Ex. : p electron rotations in Chiral aromatic molecules driven by a linearly polarized (LP) laser pulse S R M. Kanno, et al., Angew. Chem. Int. Ed. 45, 7995 (2006) 2,5-dichloro[n](3,6)pyrazinophane (DCP) (CH2)n Cl N N Cl Cl:氯 N:氮 Planar chirality Molpro 2006.1 structure optimization: MP2 / 6-31G* : CASSCF(10,8) / 6-31G*

Can LP laser pulses rotate p electrons? Because i) LP pulse has no photon angular momentum ii) Chiral aromatic molecule has no angular momentum states. What is the mechanism of p electron rotation? Use a DCP chiral molecule to understand the mechanism and principles Under fixed-nuclei condition, “no” vibrational states

Mechanism of p electron ring current

The principle of p-electron rotations Coherent excitation of a coupled quasi-degenerate electronic states using linearly polarized laser pulses benzene（D6h) Chiral molecule DCP (C2h) S0 G (1Ag) 1E1u L (1Bu) H (1Bu) Symmetry breaking e+ (e-) |𝑐 𝐻 | 2 = |𝑐 𝐿 | 2 UV pulse laser Chirality Generation of an electronic coherent state

 electron rotational direction and laser polarization vectors Approx. angular momentum states Anti-clockwise Clockwise |+ | Electron rotation Resonant excitation of LP pulse in-phase |L |H out-of- phase　|L |H e+ excitation + e excitation Temporal behavior of superposition of 　　　　　　　　　　　 + +

Time evolution of p-electron driven polarization vector e+ :one cycle of electronic transition Time T/4 T/2 3T/4 State |L + |H |L - i |H |L - |H |L + i |H +i −i +1 +i −i +1 +i −i +1 Phase Factor +i −i +1 −1 Rotational direction of electron (no rotation) (Clockwise rot.) (no rotation) (Anti-clockwise rot.) The initial rotational direction is determined by the direction of polarization vector: e+: clockwise rotation; e− : Anti-clockwise rotation

Results of p-electron dynamics in the fixed-nuclei approximation E(t) T/2 |0> |-> |+> |-> |+> 1.0 clockwise rotation counterclockwise rotation Oscillations between clockwise and counterclockwise rotations -1.0 10 20 30 40 50 fs 9-cycle clockwise Rotation of electron

Summary of first half p-electron rotation in Chiral molecule is induced by LP laser Initially, direction of rotation Angular momentum e+ in phase clockwise negative e- out of phase Anti-clockwise positive Design of multi-dimensional ultrafast switching devices? <- Non-planar Chiral molecule Later alternatively oscillate by a period

2D ultrafast quantum switching

Ultrafast 2D quantum switching of p-electron rotations in a Non-planar chiral molecule (P)-2,2’- biphenol C2 point group OH A, B OH X Geometry optimization: DFT 6-31+g(d,p) Excitation states: TDDFT 6-31+g(d,p)

b1 b2 a b1 C: clockwise A: anti-clockwise p-Electron rotation Angular momentum

pump-dump laser pulse Coherent control Fix directions of p-electron rotations Angular momentum 6.84 eV b2(B) b1(B) 6.78 eV 6.67 eV a (A) dump dump pump pump 0 eV 17 g

Theory, formalism Density matrix method Liouville equation: diagonal: population, off-diagonal: coherence :interaction with laser field : the transition dipole moment operator : angular frequency difference between states a and b 18

:single electron operator Expectation value :single electron operator Excited states: 19

is a unit vector which is perpendicular to a ring K Angular momentum is a unit vector which is perpendicular to a ring K Current S is a surface perpendicular to a current

m: electronic excited states i: atomic cite m: electronic excited states a: a a’ b: b b’ = or H. Mineo et al., J. Chem. Phys. 138, 074304 (2013) 21

Numerical simulations

(a) H. Mineo et al., J. Am. Chem. Soc. 134, 14279 (2012) 0.1 0.0 -0.1 300 0.1 200 0.0 -0.1 100 t/fs (b) 100 200 300 0.0 -0.5 -1.0 0.5 1.0 (b) E(t)/GVm-1 t/fs 0.2 0.0 EX(t) -0.2

Maximum values of magnetic field and current b1b2 excitation case: H. Mineo et al., JCP 138, 074304 (2013) Intensity of laser field used for pump: Comparative! Mg-porphyrin Ex., Benzene CP laser I. Barth et al., JACS,128, 7043 (2006)

Summary and conclusion We proposed a method for control of a 2D ultrafast switching of p-electron rotations for nonplanar chiral aromatic molecule, (P)-2,2’-biphenol by using LP laser pulses. Direction of p-electron rotations is determined by polarization direction and central wavelength We designed a sequence of overlapped pump-dump laser pulse The key point for 2D rotations is to select a set of three quasi-degenerate excited states involving both A and B irreducible representations in the C2 point group. Angular momentum Excited states pump-dump Component of A B B B wc, (pump pulse)

Application Ultrafast multi-dimenstional quantum switching device 2-qubit quantum computer Perspective In this work we only treat isolated molecule (gas phase) to demonstrate 2D ultrafast switching NOT enough treatment Extend to more complicated system, Solid state

Appendix

a R I: ring current m0 =4px10-7 H/m=(Wb/A/m) :magnetic permeability If Use If , the laser field induced magnetic field is Magnetic flux:

ii) Photocurrent induced magnetic flux for a selective control of single spin Current I and magnetic flux density B

iii) New method for identification of molecular chirality R- enantiomer or S-enantiomer can be identified by observing photo-current induced magnetic moments.

Relations of p-electrons rotation and direction of angular momentum ab1 excitation b1b2 excitation Ex. polarization Ex. polarization Y Z x X L R Y Z x X L R X Z Rotations in the same direction Rotations in the opposite direction Z X

The UV spectrum of the optically-allowed p-electronic excited states with transition energies. The excited state 27 has A symmetry, and the other excited states 28, 32 have B symmetry, which are defined to be called as a, b1, b2 respectively. The excited energies are given as follows, a (Ea=6.67 eV), b1 (Eb1=6.78 eV), b2 (Eb2=6.84 eV)

Porphyrin Scaffold (chirality) Electrode (Au)

S1 R1

S1 R1 Average asymmetry factor =−0.005±0.001 S1 , 0.004±0.002 (R1)