Quantum Optics in Wavelength Scale Structures

Transcription

1 Quantum Optics in Wavelength Scale Structures SFB Summer School Blaubeuren July 2012 J. G. Rarity University of Bristol

2 Confining light: periodic dielectric structures Photonic crystals From; Photonic Crystals: Moulding the Flow of Light, Joannopoulos et al, 2008, Princeton University Press

3 Quantum optics in wavelength scale structures Motivation More efficient single photon sources gates, Hybrid QIP. Content 2-level system in a cavity Charged quantum dots in cavity Spin-photon interface Quantum repeater Progress towards experiment

4 True single photon sources Particle like Wave-like during propagation Particle like V+ Single atom or ion (in a trap) Single dye molecule Single colour centre (diamond NV) Single quantum dot (eg InAs in GaAs) Key problem: how to get single photons from source efficiently coupled into single spatial mode

5 Single photons from NV - centres in diamond

6 Solid immersion lens fabricated on diamond using focussed ion beam FDTD simulation ~5% collection into 0.9NA lens from flat surface ~30% collection into SIL + 0.9NA lens

7 Serendipitous discovery of single NV centres under SILs on Polycrystalline diamond (E6) J.P. Haddon et al APL 97,

8 QUANTUM DOTS IN MICRO CAVITIES: SINGLE PHOTON SOURCES

9 Pillar microcavities for enhanced outcoupling of photons from single quantum dots FIB etching ICP/RIE etching

10 Cavity Quantum Electrodynamics (CQED) Weak coupling QD dipole decay rate Cavity decay rate Weak cavity coupling Efficiency η γ ω κ + κ = = 1 s Q τ ~ g << κ + κ, γ s κ κ + κ s ( ) Purcell Factor 3Q λ n P ~ 1 + 4π 2 V eff 3

11 Ex Field Intensity (a.u.) Efficiency (%) Time(ps) FDTD simulations: 0.50μm radius micropillar microcavity: Plane wave resonance=1001 nm 15 mirror pairs on top and 30 bottom Efficiency Q-factor Number of top mirror pairs (N t ) Q-factor

12 Experimental Setup Time Interval Analyser Hanbury-Brown Twiss measurement g (2) ( τ ) = < n( t) n( t < n > + τ ) 2 > ~ p( t : t + τ ) p( t)

13 PL Intensity (arb. units) 3µm 3µm FIB Single QD emission and temperature tuning 50K 48K 46K 44K 42K 40K 38K 36K 34K 32K 30K 28K 26K 24K 22K 20K 15K 10K 7K 4.3K Wavelength (nm) Energy (mev) QD1 QD Temperature (K) Cavity mode Single QD emission can be observed in smaller pillar at low excitation power QD emission line shifts faster than cavity mode

14 Single photon generation in circular pillars With increasing excitation power QD emission saturates Cavity mode intensity develops

15 Single photon generation in circular pillars g (2) (0)=0.05 indicates multiphoton emission is 20 times suppressed. g (2) (0) increases with pump power due to the cavity mode (2) g b ρ = ( τ ) I signal ( (2) g ( ) 1) = ρ τ + I I signal cavity + I background (2) g b 2 ( 0) = 1 ρ

16 Progress outside Bristol Single-photon sources Optically driven with multiphoton emission <2% 1.3µm single photons: Quantum Key Distribution demonstrated over 35km Electrically driven single-photon sources Single photon LED HoM Interference demonstrated between separate photons from the same QD (75% visibility) Bennett et al, Optics Exp 13, 7778 (2005) Journal of Optics B 7, (2005). Entangled photon pairs from Biexciton Exciton cascaded emission Nature 439, , PRL 102, (2009), Douce et al., Nature 466, 217 (2010) 15nm bright m=±1 dark m=±2 Large dot Biexciton State Ground State Exciton States

17 On-chip generation and transmission of single-photons In-plane emission of single photons from a semiconductor QD. X peak - Pulsed mode X Counts per second g (2) (0) Intensity (counts/s) XX Coincidences Excitation power (µw) Photon energy (ev) Time (ns) More details: Appl. Phys. Lett. 99, (2011)

18 Hybrid QIP

19 The PROBLEM: many qubits quantum processor N η s η N N g, F N η d U Single Qubit source Single 2-level ~ 2-10% Heralded from pair ~ 80% Throughput~ Unitary transform Linear gates η<0.5 F>0.99 Non-linear optics? η~1 F>0.9? N N N ηs ηd ηg. f ( F). R Detectors Si nm ~70% (100%?) InGaAs um ~30% Superconducting~10-88%

20 Spin photon interface using charged quantum dots in microcavities C.Y. Hu, A. Young, J. L. O Brien, W.J. Munro, J. G. Rarity, Phys. Rev. B 78, (08) C.Y. Hu, W.J. Munro, J. G. Rarity, Phys. Rev. B 78, (08) C.Y. Hu, W.J. Munro, J. L. O Brien, J. G. Rarity, Arxiv: (09) C.Y. Hu, J. G. Rarity, Arxiv: , PRB XX, XXX (2011)

21 Cavity Quantum Electrodynamics (CQED) QD-cavity interaction g = h 2 0 πe 2 4πε ε mv QD dipole decay rate γ r f eff f=oscillator strength m= electron effective mass V= cavity volume Cavity decay rate Strong coupling κ g > + κ s = κ + κ 4 h s ω Q To optimise g/κ Maximise Q/V 1/2

22 Giant optical Faraday rotation C.Y. Hu, Rarity et al, Phys. Rev. B 78, (08) C.Y. Hu, Rarity et al, Phys. Rev. B 78, (08) Single-sided cavity Reflection coefficient Cold Cavity g = 0 r ( ω ) = 1 Hot cavity g >> κ, γ Phase shift gate Uˆ ( ϕ ) = r ( ω ~ ω ) = 1 e c i ϕ ϕ ( ω ) = 0 ± π + 2 tan 1 ( ω ω ) ( L L + R R ) 2 κ c

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24 Giant optical Faraday rotation Electron spin, L-light feels a hot cavity and R-light feels a cold cavity Electron spin, R-light feels a hot cavity and L-light feels a cold cavity By suitable detuning can arrange orthogonal, Giant Faraday rotation angle ϕ0 ϕ 0 π θ F = = θf = 45 ϕ > 2 2 g > 0.1 κ ~ 1 ( + ) κ Low efficiency κ κs s Achievable with g > 1.5 κ >> 1 High efficiency ( κ + κ ) κs s

25 Quantum non-demolition detection of a single electron spin Input light H = ( R + L ) 1 2 Spin up H Spin down H U& ( π / 2) U& ( π / 2) Spin superposition state α H + β { } 0 0 α ( α + β ) β 2 A photon spin entangler! C.Y. Hu, et al, Phys. Rev. B 78, (08)

26 Photon-spin quantum interface (a) State transfer from photon to spin (b) State transfer from spin to photon Deterministic High fidelity Two sided cavity makes an entangling beamsplitter (Phys Rev B 80, , 2009)

27 Quantum Repeater: arxiv

28 Quantum Repeater: arxiv

29 Experiments Strong coupling seen in resonant reflection experiment Phase shift between resonant and nonresonant case ~0.2 radians Young, Rarity et al arxiv , PRB 2011

30 Reflection spectroscopy Conditional phase shift interferometer D V A H = sin φ ( ω )

31 Empty cavity r(ω) κ s =0 κ s =κ/5 κ s =3κ φ (rad) κ s =0 κ s =κ/5 κ s =3κ Detuning (mev) Detuning (mev)

32 Resonant reflection spectra of an empty 4µ pillar (Q~84000) Reflected intensity Lorentzian fit Intensity (counts) Phase Phase Radians Wavelength(nm)

33 Strongly coupled cavity on resonance φ (rad) r(ω) g=5k κ s =κ/5 g=5k κ g=5k κ s =κ/5 s =3κ g=k κ g=5k κ s =3κ s =κ/5 g=k κ g=k κ s =κ/5 s =3κ g=k κ s =3κ Detuning (mev) (mev)

34 Resonant reflection spectra of a 2.5µ pillar containing a single dot: temperature tuning to resonance (Q~54000)

35 Comparing PL and resonant spectroscopy

36 Conditional phase seen between a dot on and off-resonance with cavity g~9.4uev κ+κs ~ 26ueV γ~5uev g> (κ+κs +γ)/4 φ~0.05 rad (0.12rad) 21K 21K 22K 22K

37 Attojoule switch Input a few photons Input enough photons (1 in principle) to saturate the dot and return to weak coupling. Change phase of reflection, modulate D and A All optical switch (1 photon ~0.1 attojoule)

38 Future: Improve coupling and reduce losses to achieve phase shift > pi/2 Establish strong coupling with charged dots. modulation doped electrically charged Investigate dynamics of spin via Faraday rotation We cool the spin by measurement Creating spin superposition states (hard) Rotating spin around equator for spin echo (easy=u(φ)) Spin coherence times (of microseconds?) Nuclear calming to extend coherence times

39 Approaches to 3D cavities With Daniel Ho

40 1D Photonic Defect in 3D Inverted Structure FCC array of spherical holes in Silicon Top view Y Z X Y Z X Y Top view of central 2D Photonic Defect Layer Z X

41 The finite difference time domain method FDTD

42 λres= nm, Eymode (c) Z Y X E+02

43 Preliminary calculations of cavity volume and Q- factor: inverse FCC in n=3.5 material silicon. V ~ eff 9e-5µm 3 =0.19(λ/2n) 3 Q = Q/V = 2.84E8 Q/(V) 0.5 = 4.8E6 For NV centres κ/2π ~ 6 GHz γ/2π ~ 3-10 MHz (ZPL) g/2π ~ 20 GHz

44 3D Two-photon Lithography 100µm 10µm 200 nm 5µm 100 nm 2µm 100µm 67µm 6µm

45 Summary and Outlook Interaction between light and matter in wavelength scale optical structures Quantum dots in nanocavities, 1D systems such as pillar microcavities Diamond based microstructures Solid immersion lenses suspended waveguide photonic crystal cavities Strong coupling leading to gates Attojoule classical switches Spin photon interface Quantum repeater Modelling 3D systems capable of showing strong coupling 45