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Nanoantennas for ultrabright single photon sources

R. Filter, K. Słowik , J. Straubel , F. Lederer , and C. Rockstuhl Institute of Condensed Matter Theory and Solid State Optics Abbe Center of Photonics Friedrich-Schiller- Universität Jena, Germany robert.filter@uni-jena.de. Nanoantennas for ultrabright single photon sources.

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Nanoantennas for ultrabright single photon sources

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  1. R. Filter, K. Słowik, J. Straubel, F. Lederer, and C. Rockstuhl Institute of Condensed Matter Theory and Solid State Optics Abbe Center of Photonics Friedrich-Schiller-Universität Jena, Germany robert.filter@uni-jena.de Nanoantennasforultrabrightsinglephotonsources

  2. Feynman’s Dream • „There‘s Plenty of Room at the Bottom“ • Feynman, Caltech 1959 • goal: arrange atoms on the nanoscale • new opportunities for design • laws of quantum mechanics Conclusion: Nanoantennas – a dream becoming reality

  3. Outline • Nonclassical light basics • Nanoantennasforultrabrightsinglephotonsources

  4. Nonclassical Light • light propertiesthatcannotbeexplainedusingclassicaltheories squeezed light singlephotons entanglement Han et al, Appl. Phys. Lett. 92(2008) Ates et al., Phys. Rev. Lett.103 (2009) Oka, Appl. Phys. Lett. 103 (2013) • nonlin. vs. loss time scales • couplingto non-bosonicsystems • enhancedemission • via interactionofquantumsystems

  5. Nanostructures: Single Photon Sources enhancedsingle-photon em. quantumpropertiessurvive Akimov et al., Nature 450(2007) • Goal: Ultra-brightintegrated • single-photon sources • quantumcomputation • quantumCryptography • single-photon interactions • … Claudon et al., Nat. Phot. 4 (2010)

  6. Single-Photon Source Characterization – g²(τ) Usualquantification: second-order correlationfunction Why? Comparepossibleclassicalandquantumvalues. Classically: Order not impartant: at :

  7. Quantum g²(τ) Cannotignoreorderofoperators! assumption: singlemodefield (otherwisesummation)

  8. Quantum g²(τ) - examples Thermal Radiation: (Boltzmann) Boitier et al., Nat. Comm. 2 (2011) Coherent Radiation: (Poisson) Öttl et al., Phys. Rev. Lett95(2005) interpretation: thephotonsarrive in bunches

  9. Quantum g²(τ) - examples n-photon source: all light is in then‘th (Fock) state: n = 1: g²(0) = 0! noclassicalanalogon – antibunching Kimble et al., Phys. Rev. Lett. 39 (1977)

  10. Why Nanoantennas for Single-Photon Sources? Far field ↔ Near field (passive): enhanced interaction NonlinearProcesses (aktive) H. Yagi & S. Uda, 1926 Utikal et al., Phys. Rev. Lett. 106 (2011) Bharadwaj et al, Adv. Opt. Phot. 1 (2009)

  11. Esteban et al., Phys. Rev. Lett. 104 (2010) sub GHz Busson et al., Nat. Comm. 4 (2012) Michler et al., Science 290 (2000) mainaspects: Emission Rate & Nonclassicality

  12. nonclassical light properties: nanoantennaquantizationinevitable

  13. Nanoantenna& Quantum System Interaction • Semiclassical Description • back-action of quantum system negligible Filter et al., Opt. Expr. 21 (2013) & Phys. Rev. B 86 (2012) • Cavity QED description • back-action of quantum system taken into account • nonclassical field dynamics Słowik, Filter et al., Phys. Rev. B 88 (2013) • Time Dependent Density Functional Theory treatment • exhaustive and demanding • internal properties of nanoantenna, “exact” near-field Zuolagaet al., Nano Lett. 9 (2009)

  14. NanoantennacQED • cQED working horse: atom in a cavity • Parameters: • loss rate Γ • couplingconstant ϰ • cavityandatomfrequenciesωc & ωat • Nanoantennas can be treated similar • Loss rate Γ= Γrad+ Γdiss • couplingconstant ϰ • nanoantenna modeandatomfrequenciesωna & ωat • assumption: bosonicexcitation, i.e. harm. oscillator

  15. CavityQuantization also forNanoantennas? • cQEDapproachappealingvsinvolvedGreen‘sfunctionquantization • open cavity: losses! • Mode usagejustified? Yes, quasinormal modes • Basics: Ching et al., Rev. Mod. Phys. 70 (1998), plasmonicscalculations: de Lasson et al., JOSA B 30(2013) • quantization not trivial • approximate determination: • eigenmodefrequencyωn via scatteringanalysis • normalize scattered near fields to energy ħωn En(r) & Bn(r) • calculatelossratesvia Poynting‘stheorem e.g. dipoleinteraction: Słowik, Filter et al., Phys. Rev. B 88 (2013)

  16. Single-Photon Sources– Real Quantum Approach Isitpossibletobuild a miniaturizedultra-brightsinglephotonsourcewithnicenonclassicalproperties? Answer so far: ofcourse, just a matter of high Purcell factor! But: Things arenot that easy… Need fullyquantumapproach! Quantum dotcoupledtonanoantenna in cQEDformalism, Jaynes-Cummings Heisenberg picturewithincoherent pump of QD andlossofnanoantenna: Filter et al., Opt. Lett. 39 (2014)

  17. Quantum Single Photon Source – Emission rate coldreservoirsolution: withnanoantennaefficiency Purcell factorconnection: • Twolimitingcasesof R vs. : • weak pump: • strong pump: But usuallyfaraway from strong pump! Emission Rate: Purcell & pumping rate Filter et al., Opt. Lett. 39 (2014)

  18. Nanoantenna Design • two-ellipsoid nanoantennas, varyingconformalratios a/d • parameterdetermination • trade-off: efficiency vs. couplingstrength Filter et al., Opt. Lett. 39 (2014)

  19. Quantum Calculations • densitymatrixformulation • includelosses All quantum observables canbecalculated! Filter et al., Opt. Lett. 39 (2014)

  20. Emission Rate Theory Check vs. fullyquantumcomputation Filter et al., Opt. Lett. 39 (2014)

  21. Check fornonclassicality – quantumsimulations trade-off: Purcell factorvs. g²(0) Filter et al., Opt. Lett. 39 (2014)

  22. Conclusion • Plasmonics: • Electricalengineering – nanoantenna design • Nanofabrication – physical, chemical • Nanophotonics – theoreticaldescription • Quantum optics • nanoantennacQED: • parametersfromclassicalsimulations • truequantumphenomena

  23. Appendix

  24. CavityQuantization in a Nutshell I Single-mode cavity, Volume Hamilton functionfromenergydensityandwith Hamilton eqs:

  25. CavityQuantization in a Nutshell II Canonicalcommutationrelation → annihilation & creationoperators → Hamilton & interactions : fullyquantumfields:

  26. Squeezed Light - Heisenberg Heisenberg: withstd.deviation example: Possibility: improveonestandarddeviationatcostoftheother - ex.: definedstatewithrespecttoposition, but high uncertainty in momentum Squeezedstates: amplitude vs. phasedeviation trade-off

  27. Squeezed Light - Operators Quadrature Operators: Connection toamplitudeandphase: Squeezed State:

  28. Squeezed State Generation - Theory Squeeze Operator: Squeezedvacuumstate Variancesofquadratureoperators, squeezingstrength ~ r: i.e. amplitudesqueezingfor

  29. Squeezed State Generation - Physics • Two different nonlineareffectsareusedtogeneratesqueezedstates: • degenerateparametric down conversion • degeneratefour-wavemixing • Connection tosqueezedstates: • assumecoherent (classical) state in pump b, withamplitudeβ • defineand • interactioncanbewrittenas • Unitary time evolution:squeezedstates

  30. Squeezedstates – Opportunities?! cavitypolaritons – strong nonlinearity Nanoantennas? Nonlinearities vs. lossesverysmall negligiblesqueezing Karr et al, Phys. Rev. A 69 (2004)

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