Quantum Optics with Surface Plasmons at CYCU 國家理論科學中心（南區） 成大物理系 陳光胤

Outline Introduction SE of excitons into surface plasmons Coherent single surface plasmon transport Experiment proposal Summary Outlooks

I.Introduction

What is surface plasmon? Classical : Quantum : Surface plasmon modes on the surface of metals Nature 424, 824 (2003)

Lycurgus Cup and Stained Glass normal (reflected light)held up to the light Trustees of The British Museum SP excitation Gothic Window in Notre-Dame de Paris Himmelsfahrskirche, Dresden

Spontaneous Emission (SE) of Quantum Dot (QD) Pulse laser inject QD he Vacuum life time of QD~ ns

II. SE of excitons into nanowire surface plasmons

nanowires sp dots Recent experiment

Model z metal nanowire e h strong interaction Why strong? h

SP fields C. A. Pfeiffer et al., Phys. Rev. B 10, 3038 (1974) Tanscendental Equation

APL, 87, (2005) Indep. of φ wire, n=0 Dispersion relations of SP thin film

Dispersion relations of SP Key feature: nonlinear dispersion with local minimum

approach : Fermi’s golden rules (with dipole approx.) SE rate calculations e h electric dipole moment + -

SE rates into SP R=0.1R=0.5 strongly enhanced SE rates OBTAINED! G.Y Chen, Y. N Chen and D. S. Chuu, Opt. Lett. 33, 2212 (2008).

Band-edge effect 0 ∞ perturbation treatment is inappropriate ! Markovian : weak interactions Non-Markovian : strong interactions

Non-Markovian treatment Schrödinger’s Equation Laplace Transf.

Decay dynamics Y. N. Chen, G. Y. Chen*, D. S. Chuu, and T. Brandes, Phys. Rev. A 79, (2009).

III. Coherent single surface plasmon transport

D. E. Chang, A. S. Sǿrensen, E. A. Demler, and M. D. Lukin, Nature Physics 3, 807 (2007). Single QD coupling strength between QDs and SP

Scattering of nanowire SP Real space H : t r

Scattering of nanowire SP P=20 J. T. Shen, and S. Fan, Opt. Lett. 30, (2005); D. E. Chang, A. S. Sǿrensen, E. A. Demler, and M. D. Lukin, Nature Physics 3, 807 (2007).

Our model d Transmitted Reflected Incident Reflected ｜e1 〉｜e1 〉｜e2 〉｜e2 〉

Method The model Hamiltonian : The stationary state : The probability amplitude of each QD in excited state t r

Results

I. II. maximal entanglement entangled state !

concurrence A property to quantify entanglement For two qubits state ρ: spin-flip state C=1 maximal entanglement W. Wootters, PRL 80, 2245 (1998)

G. Y. Chen, Y. N. Chen, F. Mintert, N. Lambert, D. S. Chuu, and A. Buchleitner, in preparation.

Experimental realizations B. Dayan, A. S. Parkins, T. Aoki, E. P. Ostby, K. J. Vahala, H. J. Kimble, Science 319, 1062 (2008). D. E. Chang, A. S. Sǿrensen, E. A. Demler, and M. D. Lukin, Nature Physics 3, 807 (2007).

Experiment proposal d dielectric waveguide |g 1 > |g 2 > |e 1 > |e 2 > minimize the dissipations

Summary The SE rate of QD exciton can be strongly enhanced by coupling to SP. The decay dynamics around the band edge should be treated with non- Markovian way. Through the scattering of SP, the maximal entanglement between two QDs can be achieved.

Outlook I: surface-plasmonic switch z CdSe QD GaN Ag nm e h An external constant magnetic field B z BzBz The dispersion relations would be variated. Surface-Plasmonic Switch

Outlook II: Quantum Phase Transition of Surface Plasmons Simulation of QPT from a Superfluid to Mott insulator by using utralcold atoms : hoppingOn-site interaction U > t : Insulator t > U : Superfluid L. Buluta and F. Nori, Science 326, 108 (2009).

|g 1 > |g 2 > |g 3 > JJ |e 1 > |e 2 > |e 3 > Simulation by using surface plasmons :

Detection of Mott Transition |g 1 > |g 2 > |g 3 > J J waveguide |e 1 > |e 2 > |e 3 > insulator or superfluid ?

Collaborators : Prof. Dr. Andreas Buchleitner (Uni. Freiburg, Germany) Dr. Florian Mintert (Uni. Freiburg, Germany) Prof. Franco Nori (The Uni. of Michigan, Ann Arbor, USA and RIKEN, Japan ) Dr. Neil Lambert (RIKEN, Japan) Prof. Dr. Tobias Brandes (TU Berlin, Germany) Prof. 陳岳男 成大物理系＆ NCTS （ south ） Prof. 褚德三 交大電子物理系 退休教授