Generation of entangled quantum states in nonlinear ...qcn.physics.uoc.gr/qmm2016/sites/files/qmm2016/titles/QMM 2016... · states in nonlinear plasmonic structures and metamaterials
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23/06/2016
1
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
23/06/2016
2
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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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
23/06/2016
12
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)
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