Stefano Longhi and Giuseppe Della Valle!Dipartimento di Fisica, Politecnico di Milano (Italy)!

Group meeting, December 15, 2011!

Main Research Activities

1.  Photonic structures for classical simulation of quantum phenomena in the matter"

2.  Light propagation and localization in plasmonic nanostructured media and complex PT metamaterials"

3.  Transport of quantum light in waveguide lattices"

Photonic structures for classical simulation of

quantum phenomena in the matter"

Single-particle non-relativistic quantum phenomena in

atoms, molecules and solids" Physics of strongly-correlated particles"

Relativistic quantum phenomena"

Cavity and circuit QED"

Interacting Quantum Field Theories"

Non-Hermitian Quantum Mechanics and Quantum Field

Theories"

What kind of quantum phenomena can we mimic on a photonic chip?

Motivations of quantum-optical analogs study!

Quantum-Optical Analogies: an old story ...!" “ … our classical mechanics is in the

complete analogy of geometrical optics… Then it becomes a question of searching for an undulatory mechanics … by working out …. the Hamiltonian analogy on the lines of undulatory optics....”!

E. Schrodinger, Wave Mechanics (Ann. Phys. (4) 79, 1926)"

1)  Explore extreme dynamical regimes in the matter on a optical tabletop"

2)  Explore "unphysical" models and theories"

3)  Transfer of ideas and methods from quantum physics to optics and viceversa (eg. photonic crystals, transformation optics and metamaterials...)"

“ …From a certain point of view, arts were created because we humans are not happy with reality. Even though this may appear to be a contradiction for a scientist, quantum simulation is our quantum theater. Here, we may create not only existing physics that is difficult to reproduce, but also physics that may not exist in nature, with the only condition that is possible and does not violate the physical laws …“!

(Quantum Simulation Conference, 2011, Feb 28 -- Mar 05, Spain) "

What is Reality?

Optical analogs of non-relativistic quantum physics"

Optical simulations of non-relativistic wave phenomena in waveguides: the main idea!

Paraxial and scalar optical wave equation"

Kramers-Henneberger transformation"

Schrödinger equation for a particle of mass ns in an external driving force field"

x

z y

x

z x0(z)

Optical analogues of solid-state phenomena!!  Bloch oscillations!

!  Dynamic Localization!

!  Bloch-Zener oscillations!

Are such analogies useful?!Yes! For marketing… !!

Optical analog of coherent population transfer!!  Stimulated Raman Adiabatic Passage (STIRAP)

!P"!S"

time

3-Level Quantum System

|1>

|2>

|3> !P(t)" !S(t)"

Ener

gy"

Experiment"

!  Application: a broad-band beam splitter

The Quantum Zeno paradox!!  The Classical Zeno paradoxes state that if everything is motionless

at every instant, and time is entirely composed of instants, then motion is impossible!

!  The Quantum Zeno paradox states that the dynamical evolution (motion) of quantum mechanical system can be decelerated by frequent observation of the system"

The School of Athens (Raffaello, 1509, Vatican Museums)"

PLATON & ARISTOTELE"

PYTHAGORAS"

HERACLITUS"

ZENO"

Achilles and the tortoise"(most famous paradox)"

I'm a crazy fan of Parmenides!

ALL IS ONE

PARMENIDES"

!  Non-exponential decay and quantum Zeno effect E

nerg

y Irreversible decay of an unstable quantum state |#> coupled to a continuum (reservoir)"

dP(t) / dt ! 0 as t ! 0 (at short times P(t) ALWAYS shows a parabolic decay)"

Deceleration (Zeno effect) or Acceleration (anti-Zeno effect)"of the decay by frequent observation of the system "(frequent restart of the decay by erasing continuum memory)"

P(t)

t $ $

EXP law from Gamow’s theory

non-EXP law

One landmark experiment in an unstable macroscopic quantum system: Fischer et al., Phys. Rev. Lett. 2001"

$Z

Control of quantum mechanical decay!

Optical Zeno Effect!

semi-array"alternating semi-array"

Quantum Bouncing Ball!Non-classical dynamics of a quantum bouncing ball (revival and collapse due to quantum interference)"

STOM" Simulation"

STOM" Simulation"

STOM" Simulation"

CLASSICAL STATE"

COLLAPSED STATE"

FRACTIONAL REVIVAL"

Optical Bouncing BallPhotonic analog: "light bouncing by total internal reflection in a circular slab waveguide"

STOM" Simulation"

Optical analogs of Dirac equation and relativistic quantum physics"

The Dirac particle!! Free motion of a Dirac particle: energy states!

Energy-momentum dispersion curves"

"Dirac sea"!

The Zitterbewegung! trambling motion of the freely-

moving relativistic electron"

2mc"2"

!  Light propagation in 2D photonic crystals under appropriate conditions is described by a Dirac-type (spinor) wave equation!

Dirac physics in condensed-matter, atom optics and photonic systems!

! Photonic crystals provide accessible classical simulators of Dirac (spinor-like) wave dynamics!

! Dirac-type equation for electronic or matter wave transport in crystals (e.g. graphene)!

Fisrt esperimental observation of an analogue of ZItterbewegung!

Photonic Zitterbewegung in waveguide arrays!

Continuous-limit!

Miniband dispersion curves!

Binary Waveguide Array! Coupled-mode equations!

Experimental demonstration of optical Zitterbewegung!

Klein Tunneling in waveguide arrays!

Binary Waveguide Array!

Experimental observation of photonic Klein Tunneling !

! (F. Dreisow et al., EPL, in press)!

Relativistic quantum harmonic oscillator (Dirac oscillator)!

Dirac form of coupled-mode equations!

non-minimal coupling!

! Space-energy diagram!

!Transmisssion

spectrum!

Dirac oscillator!

QED e+e- pair production by strong fields!!  Dirac sea picture of vacuum instability and pair production !

Tunneling !

!ac fields!

Mechanism !of pair production!

Vacuum !Rabi !

oscillations!

! Multiphoton !transition!

dc fields!(Schwinger!

effect)!

Visualization of pair production in curved waveguide arrays !

!  A negative-energy electron in the Dirac sea is represented by a Gaussian wave packet. When the pulsed field is switched on, e+e- pair production is visualized as a droplet!

C!

!  Two-level model description of pair-production in spatially-homogeneous time-dependent fields:!

A!

B!

Optical simulation of Relativistic non-Hermitian Quantum Mechanics!

!  Wave propagation in DFB structures with gain/loss regions "(z)

!  PT non-invariant structure

(laser/coherent perfect absorber) !  PT-invariant structure

(laser threshold corresponds to PT symmetry breaking)

Classical simulations of "many-body physics"

Hubbard models! Simplified models describing interacting particles on a

lattice (in second-quantization framework)

! FERMIONS (HUBBARD MODEL)

! BOSONS (BOSE-HUBBARD MODEL)

Mmh! Always formulas!?

Many-body coherent destruction of tunneling!

Optical simulation of other condensed-matter many-body models!

Fermi-Hubbard model"

Hubbard-Holstein "model"

Bloch oscillations of correlated particles"

(experiment in preparation with Roberto)"

Tunneling control of correlated particles"

Optical simulations of cavity QED "and quantum-field theories"

Optical simulation of the quantum Rabi model!

The quantum Rabi model"

Experimental demonstration of the quantum Rabi model in the

deep strong coupling regime!

Experiment done by Andrea & Roberto in fs-laser-written waveguides"

A. Crespi et al., PRL (submitted)"

Optical simulations of strong interacting quantum field theories!

Optical simulation of Yukawa coupling in the strong regime "(2 fermions and 1 boson interacting fields)"

S. Longhi and G. Della Valle, PRL (submitted)"

Optical simulations of PT-symmetric quantum field theories!

Optical simulation of the QFT Lee model in the “ghost” regime"

S. Longhi and G. Della Valle, PRA (submitted)"

GHOST BUSTING !

Light propagation and localization in plasmonic nanostructured media

and complex PT "meta-materials"

#R!

µ!

Introduction!

The regimes of physical optics"

#I!

PT-symmetric media! !("!r ) = !*(!r )

Plus Nonlinearity

Motivations (I)!1) Beat The Fundamental Limit of Diffraction

Nano-guiding" Nano-focusing "

towards Nano-Circuitry

towards Nano-Sensing

The Plasmonic Route

Motivations (II)!

2) Functionalize Parity-Time symmetry in Optics Ex. Non-reciprocal scattering"( Optics without multiple scattering ? )!

Ex. Anti-laser device"( A perfect absorber regardless the limited absorption of the media ! )!

(transparency)

(transparency)

(scattered amplified wave)

Sub-wavelength localization of light in plasmonic waveguides

and nano-resonators"

Non-linear optics in metallic nano-structures"

PT-symmetric photonic structures and complex media"

...What's in the menu? !

Sub-wavelength localization of light in plasmonic waveguides and

nano-resonators"

Localization and diffraction-management in curved plasmonic structures (I)!

%2 (metal)"

%1 (dielectric)"

x z

y

%2 (metal)"

%1 (dielectric)"

x z

y

x

y

z

%2 (metal)"

%1 (dielectric)"Htran"

Elong"

!SPP

y

TM wave!

- - - + + + - - - + + + - - - + + + - - - + + + "

generalized !cylindrical!interface! (! ,", z)

Solve for full vectorial Maxwell's equations in local curvilinear coordinates"under TM-TE decomposition "to z-direction of propagation."

Localization and diffraction-management in curved plasmonic structures (II)!

1D optical!Schrödinger quation!

(paraxial wave equation)! !i! "F

"z= ! !

2

2ne(0)

"2F"# 2 + Vgeo (# ) F = H F

Vgeo (! ) = !ne

(0)

2R(! )" 1#1 + #2

Geometric!Potential!

MODE 1"

MODE 2"

FEM Simulations!Analytical Model!

H Fi = !"ni Fi

ne, i = ne(0) + !ni

Localization and diffraction-managementin curved plasmonic structures (III)!

Eigenvalue equation!for plasmonic Modes!

FEM Simulations!

Analytical Model!(...Floquet Theory...) "

Self Imaging!

Straight Array"

Curved Array (SI condition)"

!R0

= 2" z0

a#e

, J0 (z0 ) = 0

cn (!) = cn (0) "n

Localization and diffraction-managementin curved plasmonic structures (IV)!

generalized !cylindrical!

multiple!interface!

x"

y"

z"

A Planar !Plasmonic Waveguide"

y"x=x'!

z"

2D (xy)"plasmonic"waveguide"

1D (y-confined)"PLASMONIC"waveguide"

1D (x-confined)"OPTICAL"

waveguide"

neff = ?!

y"

x"

ne (x)!

neff !

x"

y"

z"

x'!

analytical"1D PROBLEM 1"

semi-analytical"1D PROBLEM 2"

complicated"2D PROBLEM "

Graded-Index Plasmonic Devices (I)!

Graded-Index Plasmonic Devices (II)!

Gold!

Air!L!

x"

Modes are spaced by "Spatial!Period"

"  Self-imaging after $ propagation distance "  Spatial Inversion after $/2 propagation distance "  Focalization after $/4 propagation distance [M. S. Sodha and A. K. Ghatak, Inhomogeneous Optical Waveguides, Plenum, 1977]

Properties:!

Norm

aliz

ed !

Inte

nsity!

Insertion Loss 4.4 dB"

Propagation Loss 4 dB"

Graded-Index Plasmonic Devices (III)!A 4x4 cross-connect for plasmonic waveguides"

Graded-Index Plasmonic Devices (IV)!A fiber-coupled launcher for Slow-plasmons"

G. Della Valle and S. Longhi, Opt. Express (submitted)!

Plasmonic Nano-resonators (I)!Wave-retarder nano-plates (a single-layer plasmonic metamaterial)"The meta-atom model (detuned nano-resonators) Experimental results (polarization analysis)

& y - &

x!

|'y / E

x| !

Plasmonic Nano-resonators (II)!Plasmonic Split-Cylinder-Resonators for nano-sensing"

G. Della Valle at al., Invited review paper in Annalen Der Physik (to be published)!(Some theoretical and experimental papers in collaboration with Bozhevolnyi's group in DK ) "

Non-linear optics in"metallic nano-structures"

General Aspects!

Free Carriers" Carrier-Carrier "Relaxation !

Environment"

Pump"(pulse)"

Carrier-Phonon "Relaxation !

Heat dissipation"

Phonons"

The Two-Temperature Model" Our main aims:!

1) Apply the TTM to non-conventional metallic media"(in collaboration with IIT)"

2) Extend the TTM to extend the theory of non-linear optics in metals"(in collaboration with UniBS)"

3) Modelling and Design of innovative nanosystems for ultra-fast optical switching "( i n c o l l a b o r a t i o n w i t h experimental group of Prof. G. Cerullo)"

Plasmon Dynamics in Degenerete Semiconductor Nanocrystals (II)!

Ab-initio Derivation of the %(3) of nano-gold!

In the visible, peak value is ~10-15 m2/V2!

i.e. 6 order of magnitudes larger than in SiO2!

Extended Two-Temperature Model!for electron-phonon dynamics !

M. Conforti and G. Della Valle, PRL (submitted) !

gold!

Ultra-fast dynamics in nano-gold!

D. Brida et al. in preparation for submission to PRL!

Ultra-fast dynamics in a single gold nanorod!

D. Polli et al. !to be presented at Photonics West !(January 2012)!

Simulations!

5nm rounding" TTM "+ "

3D FEM"

Simulation!

Experiment!

Tran

sient

Sca

tterin

g"Tr

ansie

nt R

eflec

tion"

Time delay (ps)"0" 12"4" 8"

& pump = 800 nm"& probe = 1045 nm"

PT-symmetric "photonic structures "and complex media"

Non-Hermitian Quantum Mechanics!! Non-Hermitian quantum mechanics !

! Optical realizations of PT-symmetric non-Hermtian Hamiltonians!

PT optical crystals!! Paraxial light propagation in optical crystals!

! Even-symmetric profile of the real part of n!! Odd-symmetric profile of the imaginary part of n!PT crystal!

! PT-invariance condition [H,PT] = 0

! PT-symmetry breaking

Example: !

Real energies !(unbroken PT symmetry)!

Complex energies also! !(broken PT symmetry)!

one has !

Bragg scattering in PT crystals!Complex potential!

(i.e. at the PT symmetry-breaking point)!

! Gapless Crystals (dispersion as of a free particle)

! Non-reciprocal scattering!

A photonic world"without multiple"

reflection?!"

! Giant Goos-Hanchen Shift

= −"

Transport in PT crystals!

! Non-reciprocal Bloch oscillations!

! Dynamic localization and wave-packet ramification!

F0FC

0.5"

1.0"

1.5"

3.0"

F < 0 F > 0

Time-reversal of a laser (“anti-laser”)!I'm skeptic!"Hah! Hah!"

!2E(x)!2x

+ " 2

c02 #n + i ##n[ ]E(x) = 0

!2E*(x)!2x

+ " 2

c02 #n $ i ##n[ ]E*(x) = 0

c.c.!

gain!

loss!

PT-symmetric laser-absorber!

Time-reversal of nonlinear optical processes!

This device can simultaneously generate laser rad ia t ion and perfectly aborbs certain incoming radiations at the PT-symmetry break!"

Transport of Quantum Light in Waveguide

Lattices"

Bloch oscillations and Zener tunneling of non-classical light"

Quantum interferometry based on Bloch oscillations"

Transport and localization of highly-entangled states (NOON

states) in waveguide lattices"

Quantum light in waveguide lattices ?!

Bloch oscillations and Zener tunneling of non-classical light!

Two-Photon Excitation"

Two-Photon coincidence"

Bloch oscillations of photon pairs in binary waveguide lattices"

Path-entangled"" cats !"

Quantum Mach-Zehneder interferometry based on multiband Bloch Oscillations!

Single Photon Excitation"Two-band BO dynamics"

!  de Broglie wavelength of a ʻbiphoton ̓state: with two-photon excitation the period of interfence fringes is halved "

Localization and quantum interference of NOON states in waveguide lattices!

!  Lattice excitation with two path-entangled NOON beams"