Light Manipulation with Metamaterial Analogies of Quantum Optics Phenomena

Peking Uni. , 12-07-2012

Hong Chen (陈鸿) School of Physics, Tongji University

Shanghai, China

同舟共济

1. Motivation: metamaterials (Meta-m), novel ways of light manipulation our recent studies on Meta-m

2. Rabi splitting in zero-index Meta-m special cavity mode with uniform field position-independent Rabi oscillation

3. Electromagnetically induced transparency in Meta-m Meta-m analogies of multi-level atom property of Meta-m with EIT-like spectrum

4. Summary

outline

Metamaterials (Meta-m) Definition (Pendry 2000):

Metamaterial : artificial material with effectiveelectromagnetic properties not found in constituent materials and not readily observed in nature.

In Chineses: 特异材料、超材料、超构材料、美特材料

1. Motivation

Quantum interference in nature atoms

two-level atom: Rabi splitting, Rabi oscillation multi-level atom: Electromagnetically induced transparency (EIT) Fano resonance Spontaneous emission interference (SEI)

For example: Fano resonance (1961)

discrete path continuum path

A. E. Miroshnichenko et al., Rev. Mod. Phys. (2010)

For example: Spontaneous emission interference (SEI)

M.O.Scully, S.Y.Zhu,Science 281(1998)1973

Advantage: narrow spectral line, very precise manipulating photons Disadvantage: gas medium, difficult for applications of solid state devices, on-chip, controllable (many or single atom) manipulation

nature atom ↔ artificial “atom” gas medium ↔ Meta-m

1. Band-gap structures and defect modes in Meta-m

theory: Tan et al., Phys. Rev. E 2008.(Quansi 1d PC)

Wang et al, Opt. Express 2010 (Self-collimation)

Jiang et al., Phys. Lett. A 2012 (Anderson localization)

Jiang et al., Philos. Mag. 2012 (Non-Bragg band gaps, overview)

experiment: Zhang et al., Opt. Commun. 2008. .(Quansi 1d PC)

Tan et al., Opt. Express 2009 (Necklace-state manipulation)

Wei et al., Opt. Express 2010 (Negative reflection)

Jiang et al., J Appl. Phys. 2011 (Zero-index cavity)

Wu, et al., Phys. Rev. Lett. 2011 (Chiral structure)

Our recent studies on Meta-m:

Polarization manipulation: linear to circular , Broadband!

2. Quantum optics related phenomena in Meta-m

theory: Yang et al, Phys. Rev. Lett. 2008 (Quantum interference)

Yang et al., Phys. Rev. A 2010 (Casimir force)

Yang et al., Phys. Rev. A (R) 2010 (Entangled distant atoms)

Liu et al., PIER Lett. 2011 (Fano resomance)

experiment: Zhang et al, Phys. Rev. E (R) 2008 (Rabi splitting)

Zhang et al, Phys. Rev. E 2011 (Rabi oscillation)

Sun et al., Phys. Rev. B 2011 (EIT , Dynamical study)

Li et al., JOSAB 2011 (EIT , Q-factor enhancement)

Jiang et al., Opt. Express 2012 (Rabi splitting in zero index)

Sun et al., Euro-Phys. Lett. 2012 (multi-level artificial atoms)

Our recent studies on Meta-m:

2. Rabi splitting in zero-index (ZI) Meta-m

Motivation of the study

Rabi Splitting a cavity mode coupled with an (artificial) atom One of basic phenomenon for Quantum Optics

strong coupling ,g>ĸ,γ, Rabi splitting occurs.

In the solid-state case, two-level atoms are replaced by atomic-like quantum dots.

G. Khitrova, et al. Nat. physics (2006).

Alexandre Blais et al., 2004

Coupling strength g: ∼ ( cavity field E) ∼ 1/ ( cavity volume V )

How to realize strong coupling ??

Desired Resonator: With high E , small V

E(x) ∼ sin (x)

Cavity fields: standing waves, inhomogeneous distribution.

Physical Limit in traditional cavity with normal materials:

at peak, strong coupling at node, weak coupling

position-dependent coupling → position-dependent Rabi splitting

inevitable result of inhomogeneous cavity field

so one needs homogeneous field

Positional accuracy: 30 nm

A technical challenge to fabricate a quantum dot right at the cavity field maximum!

How to get uniform cavity field??

Possible way: cavity filed with zero-index meta-m

uniform field distribution from:

Applications:

Directive Emission S. Enoch et al., PRL 2002

Light Squeezing M. Silveirinha and N. Engheta PRL 2006 R. P. Liu et al., PRL 2008 B. Edwards et al., PRL 2008

Reflection Manipulation V. C. Nguyen et al., PRL 2010

PRL 2006

R. P. Liu et al., PRL 2008

B. Edwards et al., PRL 2008

B. Edwards et al., JAP 2008

Theoretical study: D=1 J Appl. Phys. 2011

Aand B denote SiO2 and Ta2O5

zero index at ωp

smaller threshold (40%) for bistability than normal cavity

Theoretical study: D=2 Opt. Express 2012

rods (n=2) are embedded in air The rod radius is 150 nm and the lattice constant is 500 nm.

2

1 ,( )

p

iω

ε µω ω

= = −+ Γ

Silicon rods (n=3.48) are embedded in the polymer (n=1.45). The rod radius is 114.6 nm and the lattice constant is 430 nm.

Without zero-index medium

Oscillator: mimics a quantum dot

With zero-index medium

zero-index Meta-m

The effect of the loss in the zero-index medium on the mode splitting.

Realizing metamaterials by transmission line Proposed by Eleftheriade et al., 2002; and by Itol et al., 2002

Circuit model for metamaterials: Electric coupling

LdCeff 20

1ω

ε −≈

CdLeff 20

1ω

µ −≈

choosing different circuit parameters one gets DNG, ENG, MEG materials

Experimental study

(Wang et al., J. Appl. Phy. 2006)

(Zhang et al., Microwave J..2005) lefthanded.avi righthanded.avi

Experimental study: D=1 cavity with zero-index Meta-m

Uniform Cavity Field J Appl. Phys. 2011

Position-Independent Rabi-like Splitting

Opt. Express 2012

Extended to infrared and visible light??

PNAS 2012

3. Electromagnetically induced transparency (EIT) in Meta-m

bright state

dark state

interference between I3) and I2)

narrow transparent window (Harris 1989 PRL )

one of most important quantum optics phenomena applications: nonlinear optics, quantum information

uncoupled Strong coupled

Dark element

Bright element

Meta-m with EIT-like Spectrum in Planar Configuration Zhang et al., PRL 2008; Papasimakis et al., PRL 2008; Tassin et al., 2009; Liu et al., Nature Mater. 2009

Our Study Meta-m with EIT-like Spectrum in Waveguide Configuration (WG)

why waveguide configuration?

waveguide: basic element for on-chip light manipulation

Boshevolnyi et al., Nature (2006) Wallraff et al., Nature (2004)

quantum circuit plasmonics circuit

Our Study Meta-m with EIT-like Spectrum in Waveguide Configuration (WG)

(1) Meta-m analogies of quantum optical phenomena in multi-level atoms Sun et al., EPL 2012

A : two- level artificial atom

B : three- level artificial atom

nature atom artificial atom

C : four- level artificial atom

nature atom artificial atom

PRB 2011

(2) Influence of loss and dynamic effect

Dark element

Bright element

Delayed ∼ 3.2 ns 20 times longer than That without EIT

influences of intrinsic loss

Loss channel： 1. Radiative loss (Reflectance) 2. Intrinsic loss (Absorption) EIT suppress both loss channels !!

influences of intrinsic loss on group delay

Transmission NOT

Group delay NOT

Bandwidth YES

Then:

Transmission-delay product

(TDP for nonlinear optics)

NOT

Delay-bandwidth product

(DBP for communication)

YES

Dynamical evolution from "bright" to "dark"

Rising edge 4 ns

Transition time tc : Atom: 10-1 ∼ 10-2 ns

Here: 10 ns

tc b = 0.2 mm tc = 24.7 ns vc = 38 mv b = 0.8 mm tc = 36.3 ns vc = 96 mv

Coupling stronger Excitation transfer

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4. Summary

Metamaterial as a platform to mimic quantum optics phenomena with controllable parameters.

Potential applications of metamaterial analogies of quantum optics phenomena, in plasmonic circuit and quantum circuit.

Collaborators: Yong Sun,, Haitao Jiang, Yunhui Li, Yewen Zhang, Hongqiang Li.

Financial Supports: NSFC, 973 Program of MOST

Thank You