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Generation of entangled quantum

states in nonlinear plasmonic

structures and metamaterials

Alexander N. Poddubny1,2,3, Ivan V. Iorsh2,

and Andrey A. Sukhorukov1

1 Nonlinear Physics Centre, Research School of Physics and

Engineering, Australian National University, Canberra, Australia

2 ITMO University, St. Petersburg, Russia

3 Ioffee Institute, St. Petersburg, Russia

Outline

• Introduction: photon

entanglement

• Photon-pair and photon-

plasmon generation in nonlinear

metamaterials

• Hyperbolic metamaterial:

broadband enhancement

• Quantum-classical

correspondence

• Nonlinear dielectric

nanoresonators and

metasurfaces

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Entanglement

The entanglement is essential in quantum computation,

cryptography, metrology, teleportation, information processing.

|1

|2

A

|1

|2

B

Quantum entanglement occurs when pairs or groups of

particles are generated or interact such that the quantum

state of each particle cannot be described independently

1

2(|1 𝐴⨂|2 𝐵 + 𝑒−𝑖𝜃𝐴𝐵|2 𝐴⨂|1 𝐵)

Integrated Quantum Photonics

IBM’s Integrated

Nanophotonics Chip

(classical regime)

Bristol Uni integrated

quantum chip

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Nonlinear generation of photon pairs

Spontaneous parametric

downconversion

(SPDC)

Spontaneous four-wave

mixing

(SFWM)

Quantum optics with dielectric waveguide circuits

Quantum state control Shadbolt et al. Nat. Photon. 6, 45 (2012)

On-chip SPDC photon sources –

higher efficiency and greater flexibility

compared to bulk crystals Leng et al., Nature Comm. 2, 429 (2011)

Integrated photonic structures – interferometrically stable,

suitable for path-encoding qubit and higher-dimensional qudits

Fast photon manipulation with electro-

optic effect in LiNbO3 Bonneau et al., Phys. Rev. Lett. 108, 053601 (2012)

Efficient generation & separation of

signal and idler photons [Zhang et al., Opt. Exp., 15, 10288 (2007)]

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Towards quantum plasmonics

• Plasmon quantum interference survives the losses

• Single photon/plasmon regime

Integrated quantum state generation

• Compact and stable, No decoherence, No In-coupling losses

• Demonstrated in nonlinear dielectric circuits

• Metamaterials with strong nonlinear interactions:

potential for on-chip generation of entangled plasmons

Silverstone et al., Nat. Phot. 8, 104 (2014)

Jin et al., PRL 113, 103601 (2014)

Kruse et al, PRA 92, 053841 (2015)

Setzpfandt et al, LPR 10, 131 (2016)

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Treatment of losses

Electric Field Quantization

Vogel & Welsh “Quantum Optics” (2006), Crosse & Scheel, PRA 83, 023815 (2011)

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Detection of photons

Result: quantum two-photon amplitude

A. Poddubny, I. Iorsh, A. A. Sukhorukov, arXiv 1601.08093 (2016)

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Metal on nonlinear dielectric substrate

Oblique pump incidence

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Single photon detection probability

Heralding efficiency

• Efficiency of signal heralding

by far field idler photons

• Reaches 70%

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Nondegenerate SFWM in Hyperbolic Metamaterial

Two-photon correlations above the

surface (z = -100 nm) in

k-space for signal energy 3.46 eV

(358 nm wavelength)

Metal (silver, 7.5nm) and nonlinear dielectric ( = 2, 15 nm) layers

Topological broadband enhancement

Phase matching map vs.

the signal energy and in-

plane wave vector

Black lines - boundaries

between topologically

different dispersion of

signal and idler photons

Photon pair spectrum in the

TM polarization for signal

and idler, inside the signal

light cone

Broadband topological

enhancement when the

signal is in the elliptic

regime and the idler is in

the hyperbolic regime

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Quantum-classical correspondence: SPDC-DFG

M. Liscidini and J. E. Sipe,

Stimulated Emission Tomography,

PRL 111, 193602 (2013)

Correspondence between SPDC

and DFG:

1) Measure classical DFG, using

the same pump and specially

chosen idler

2) Directly predict the two-photon

wavefunction generated by SPDC

? Limitation: no losses (material or

scattering)

Spontaneous parametric down-conversion (SPDC)

Difference frequency generation (DFG)

Quantum-classical correspondence: SPDC-SFG

L. G. Helt and M. J. Steel,

OL 40, 1460 (2015)

Correspondence between SPDC

and SFG:

1) Measure classical SFG, using

the signal and idler at chosen

frequencies

2) Predict the two-photon SPDC

wavefunction at the corresponding

wavenumbers

+ Valid in presence of losses

? Limitation: established only for a

homogeneous waveguide

Spontaneous

parametric down-

conversion

(SPDC)

Quadratic waveguide

pump Signal & idler

photon pair

Sum frequency generation (SFG)

Quadratic waveguide

pump

Signal & idler

classical inputs

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General correspondence: SDPC & reversed SFG

Our prediction for any quadratic nonlinear structures:

• Counter-directional classical sum-frequency generation

emulates two-photon wavefunction produced through

spontaneous parametric down-conversion

Quadratically

nonlinear

structure

pump Signal & idler

photon pair

SPDC

SFG

Quadratically

nonlinear

structure

pump Signal & idler

classical inputs

A. Poddubny, I. Iorsh, A. A. Sukhorukov, arXiv 1601.08093 (2016)

Experimental validation: SPDC-SFG correspondence

Measurements with asymmetrically poled coupled 2 cm long waveguides in Lithium Niobate [ANU, Griffith, RMIT (Australia), ITMO (Russia) collaboration. Lenzini, Titchener, Fisher, Boes, Poddubny, Kasture, Haylock, Villa, Mitchell, Solntsev, Sukhorukov, Lobino, CLEO 2016]

Quantum SPDC

Classical direction-reversed SFG

Signal & idler

photon pair

correlations

SFG for

different

signal & idler

inputs

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Nonlinear dielectric nanoresonators: theory

Optimize SFG for 10-5

forward efficiency in

AlGaAs nano-resonator:

diameter 450 nm,

height 400 nm

Predict angular quantum

correlations for photon

pairs generated through

SPDC

Experiments feasible,

fabrication established [Carletti et al, Opt. Exp. 23,

26544 (2015)]

Summary

• Theory of entangled photon

generation in nonlinear

nanostructures with arbitrary

dispersion and losses

• General solution via the classical

electromagnetic Green function

• Prospects for photon-plasmon

generation in nonlinear

metasurfaces and metamaterials

• Quantum-classical

correspondence of SPDC with

direction-reversed SFG

• Experimental confirmation in

waveguides

A. Poddubny, I. Iorsh,

A. A. Sukhorukov,

arXiv 1601.08093 (2016)