resonance fluorescence from quantum dots

Transcription

1 resonance fluorescence from quantum dots APS Tutorial Quantum Optics of Quantum Dots Nick Vamivakas University of Rochester Institute of Optics vamivakas/index.html Illustration by Fabian Rüdy / andraia.ch

2 what lies ahead resonance fluorescence from quantum dots indistinguishability and coherence properties of quantum dot single photons coherent control of quantum dots for quantum information cavity quantum electrodynamics with quantum dots

3 quantum heterostructures quantum heterostructures are artificial structures in which electrons & holes are confined by engineering material composition z x y Bulk Crystal Quantum Well 1 Quantum Wire Quantum Dots Crystal Electron Wave Function 1 Dingle, Wiegmann, Henry Phys. Rev. Lett. 33, 827 (1974)

4 quantum heterostructures materials what determines if the electron/hole is confined? à potential energy landscape modification must be commensurate with the De Broglie wavelength! De Broglie wavelength of a free electron λ = h p = h 2mE InAs band edge (0.35 ev)λ ~ 2 nm

5 quantum heterostructures materials what determines if the electron/hole is confined? à potential energy landscape modification must be commensurate with the De Broglie wavelength! De Broglie wavelength of a free electron λ = h p = h 2mE InAs band edge (0.35 ev)λ ~ 2 nm De Broglie wavelength of a crystal electron = h p = h p 2m E = 0 r m m Group Material m e */m m hh */m IV III-V Si At T = 300 K 0.98 (0.19) 0.50 GaAs InAs GaN InP II-VI CdSe at band edge in InAs λ InAs ~ 13 nm J. Appl. Phys. 89, 5815 (2001); Yu & Cardona, Fundamentals of Semiconductors, 4th ed. (2010).

6 quantum heterostructures materials confinement has two major consequences: changes the density of states breaks the (discrete translational) symmetry of the crystal. à dramatic impact on the optical and transport properties. Density of states Bulk Quantum Well Quantum Wire quantum confinement of the single particle wavefunctions (E 1/m*R 2 ) Quantum Dots E g Energy

7 quantum heterostructures materials how about metals? à m* ~ m e 1.14 for Au separation of confined electron states CdSe E 2e -E 1e ~ ev Au E 2e -E 1e ~ ev 4 nm

8 artificial atoms a striking manifestation of the confinement and discrete density of states is apparent in the photoluminescence from CdSe QDs joint density of states Cadmium Selenide QDs E g Energy Quantum Dots increasing radius 2-8 nms

9 artificial atom landscape artificial atoms relevant in quantum optics have been: Colloidal Quantum Dots; Optically Active Defects, Epitaxial Quantum Dots Type Material T (K) Emission, ZPL λ X (nm) Colloidal QDs CdSe/ZnSe [1] Optically Active Defects N-V Centers in Diamond [2] D 0 X in GaAs [3] InAs/GaAs [4] Epitaxial QDs InP/InGaP [5] CdSe/Zn(S,Se) [6] In x Ga 1-x N/Al x Ga 1-x N [7] [1] P. Michler et al., Nature 406, 968 (2000). [2] R. Brouri et al., Optics Lett. 25, 1294 (2000), [3] K. Fu et al., Phy. Rev. Lett. 95, (2005). [4] P. Michler et al., Science 290, 2282 (2000); C. Santori et al., Nature 419, 594 (2002). [5] A. Ugur Appl. Phys. Lett. 100, (2012). [6] K. Sebald et al., Appl. Phys. Lett. 81, 2920 (2002). [7] S. Kako et al., Nature Materials 5, 887 (2006); A. F. Jarjour et al., Appl. Phys. Lett. 91, 52101(2007).

10 artificial atoms for solid-state quantum optics Type Material T (K) Emission, ZPL λ X (nm) γ (s -1 ) γ ZPL (s -1 ) Homogeneous Linewidth Nanofabrication and integration with cavities Epitaxial QDs InAs/GaAs γ (1 1000) γ high Optically Active Defects N-V Center in Diamond γ (1 1000) γ Low D 0 X in GaAs > 1 γ 1 GHz Low several types of artificial atoms can be sources of non-classical light, show coherent population trapping 1 and entanglement of emitted photons 2, that is, basic building blocks for quantum optical experiments. however, very few artificial atoms exhibit the pristine optical properties of InAs/GaAs which makes them suitable for quantum optics 1 D. Bruner et al. 2009; K. Fu et al., Phy. Rev. Lett. 95, (2005). 2 Akopian et al., 2006; Stevenson et al., 2006

11 growth of InAs/GaAs quantum dots molecular beam epitaxy (MBE) of InAs/GaAs quantum dots Growth chamber semiconductor substrates ("wafers") are baked in a multi stage load lock system before being transferred into the growth chamber.

12 growth of InAs/GaAs quantum dots QDs form from hetero-epitaxy of lattice mismatched crystals layers a substrate < a epilayer ε ε a (InAs) = 6.06 Å Epilayer wetting layer QDs a (GaAs) = 5.65 Å Substrate substrate substrate after certain thickness energetically preferable for InAs islands à island formation is a balance between surface and strain energy coherent mechanism of elastic relaxation à pristine optical properties

13 growth of InAs/GaAs quantum dots random distribution of QDs in plane & nonuniform size distribution wetting layer QDs dislocations QD density (µm -2 ) InAs coverage (ML) AFM topographies 1x1µm 2 ~ diffraction limited spot size

14 quantum confined energy levels in InAs QDs from bulk to quantum dots à quantum confinement bulk energy band diagram (InAs & GaAs) MBE grown self-assembled QD ~ 10 5 InAs = 1 QD! 2-5 nm cap growth direction z

15 quantum confined energy levels in InAs QDs from bulk to quantum dots à quantum confinement spatial confinement d p c-band minimum MBE grown self-assembled QD ~ 10 5 InAs = 1 QD! E g (GaAs)= 1.42 ev E g (InAs) = 0.35 ev s s p d E pp - E ss ~ 40 mev (30 nm) HH LH ~ 30 mev 3 2, ± , ± 1 2 v-band minimum 2-5 nm cap growth direction z quantization of the electron/hole energies bulk symmetry breaking degeneracy lifting of heavy & light holes giant oscillator strength of ~ 10 (0.6 nm dipole, ~ 30 debye)

16 quantum dot s-shell excitons four optically active s-shell exciton complexes à most resonant optical studies are with these states notation for charge & spin: ( ) electron = +1/2 (-1/2) ( ) hole = +3/2 (-3/2) = (+1/2,-1/2,+3/2)

17 quantum dot s-shell excitons four optically active s-shell exciton complexes à most resonant optical studies are with these states notation for charge & spin: ( ) electron = +1/2 (-1/2) ( ) hole = +3/2 (-3/2) = (+1/2,-1/2,+3/2) X 0 exciton dark excited states dark single particle states s-shell c-band s-shell v-band σ + multiparticle states σ + 0 σ - ΔE X ground state σ +/- Polarization (RHCP/LHCP) spontaneous emission rate ~ 1GHz (1-ns)

18 quantum dot s-shell excitons four optically active s-shell exciton complexes à most resonant optical studies are with these states notation for charge & spin: ( ) electron = +1/2 (-1/2) ( ) hole = +3/2 (-3/2) = (+1/2,-1/2,+3/2) XX biexciton excited states single particle states s-shell c-band s-shell v-band σ + multiparticle states σ + σ - ΔE XX X 0 excited state σ +/- Polarization (RHCP/LHCP) spontaneous emission rate ~ 1GHz (1-ns)

19 quantum dot s-shell excitons four optically active s-shell exciton complexes à most resonant optical studies are with these states notation for charge & spin: ( ) electron = +1/2 (-1/2) ( ) hole = +3/2 (-3/2) = (+1/2,-1/2,+3/2) X 1- trion excited states single particle states s-shell c-band s-shell v-band σ + multiparticle states σ + σ - ΔE X- ground state σ +/- Polarization (RHCP/LHCP) spontaneous emission rate ~ 1GHz (1-ns)

20 quantum dot s-shell excitons four optically active s-shell exciton complexes X 0 exciton XX biexciton multiparticle states σ + σ - ΔE X multiparticle states σ + σ - ΔE XX 0 X 0 X 1- trion X 1+ trion multiparticle states σ + σ - ΔE X- multiparticle states σ - σ + ΔE X+

21 quantum dot s-shell excitons these 4 exciton complexes basis of a number of applications à on-demand generation of single photons X 0 σ + σ - 0

22 quantum dot s-shell excitons these 4 exciton complexes basis of a number of applications à on-demand generation of single photons à on-demand generation of entangled photon s (XX-X 0 cascade) XX σ - σ + X 0 σ + σ - 0

23 quantum dot s-shell excitons these 4 exciton complexes basis of a number of applications à on-demand generation of single photons à on-demand generation of entangled photon s (XX-X 0 cascade) XX σ - σ + electron-hole exchange interaction * ; Δ eh H XX V XX X 0 need to work a bit to generate entanglement X H H Δ eh X V X 0 σ + σ - V 0 0 * Byer et al PRB 65, (2002)

24 quantum dot s-shell excitons these 4 exciton complexes basis of a number of applications à on-demand generation of single photons à on-demand generation of entangled photon s (XX-X 0 cascade) à charges/spins as qubits, all-optical quantum computing 11 XX H V 01 Δ eh 10 H V X Li et al Science (2003).

25 quantum dot s-shell excitons these 4 exciton complexes basis of a number of applications à on-demand generation of single photons à on-demand generation of entangled photon s (XX-X 0 cascade) à charges/spins as qubits, all-optical quantum computing excited state for optical control 11 XX H V σ + 1 = 0 = B z 01 Δ eh 10 H V X 0 ground state spin qubits Imamoglu et al PRL 83, 4204 (1999). and the next speaker 0 0 Li et al Science (2003).

26 quantum dot s-shell excitons these 4 exciton complexes basis of a number of applications à on-demand generation of single photons à on-demand generation of entangled photon s (XX-X 0 cascade) à charges/spins as qubits, all-optical quantum computing à study many-body physics excited state for optical control 11 XX H V σ + 1 = 0 = B z 01 Δ eh H V 10 X 0 ground state spin qubits Imamoglu et al PRL 83, 4204 (1999). and the next speaker 0 0 Li et al Science (2003).

27 quantum dot optics: μphotoluminescence (μpl) simplest optics characterization à nonresonant optical charging - photon in ħw 1

28 quantum dot optics: μphotoluminescence (μpl) simplest optics characterization à nonresonant optical charging - photon in ħw 1 a starry night.imaging single quantum dots with a CCD ~ 50 x 50 μm 2 defocus excitation laser limit our detection to one of those regions à confocal detection à aperture array on surface

29 quantum dot optics: μphotoluminescence (μpl) simplest optics characterization à nonresonant optical charging - photon in - + ħw 1 + above band-gap excitation non-radiative relaxation optical recombination - photon in ħw 2 + photon energy/polarization fixed by recombining exciton complex

30 quantum dot optics: μphotoluminescence (μpl) identification of few level systems 1 st step towards quantum optics temperature 4.2K - electron - hole

31 quantum dot optics: μphotoluminescence (μpl) identification of few level systems 1 st step towards quantum optics à Coulomb Interactions give spectral diversity to exciton complexes temperature 4.2K - electron - hole transition energies ΔE X =E e +E h -V eh ΔE X- =E e +E h +V ee -2V eh ΔE X+ =E e +E h +V hh -2V eh hole more localized à V ee <V eh <V hh X 1+ (X 1- ) higher (lower)energy than X 0 ΔE XX =E e +E h +V hh +V ee -3V eh XX lower energy than X 0 V eh = e 2 4πε o ψ e ψ h 1 r ψ hψ e

32 quantum dot optics: μphotoluminescence (μpl) identification of few level systems 1 st step towards quantum optics à Coulomb Interactions give spectral diversity to exciton complexes à sure it is 1? confirm single photon emission to check temperature 4.2K - electron - hole photon antibunching 1 challenge: charge control to ensure specific ground state Michler et al Science 290, 2282 (2000). Santori et al Nature 419, 594 (2002).

33 quantum dot charge control charge control to enable transition selective excitation à coherent interfacing of a single photon and qd transition ~200nm InAs ~30nm embed the QDs in a Schottky diode heterostructure Coulomb blockade ensures fixed number of electrons trapped in a quantum dot Exciton (1e, 1h) Trion (2e, 1h) X 1- X2- X3- gate voltage produces an electric field on the quantum dots Stark shift. X 0 T = 4.2K Warburton et al Nature 405 (2000)

34 quantum dot resonant light scattering how does a 2-level system interact with a near resonant cw-laser? incoming laser (E 0 ~Ω) scattered field e s scattered field intensity E 0 +e s E 0 QD E 0 +e s saturation power e g ~200 nm e s = e si + e sc On a detector we measure P M ~ E e si 2 + e sc 2 + 2Re{E * 0 e sc } + 2Im{E* 0 e sc } s = 2 Ω2 2 character, ie coherence, depends on laser Rabi frequency (power) Loudon, The Quantum Theory of Light, 3rd ed. Cohen-Tannoudji et al, Atom-Photon Interactions

35 quantum dot resonant light scattering how does a 2-level system interact with a near resonant cw-laser? an optical transition (of a quantum system) has two components: 1) coherently scattered part (resonant Rayleigh scattering) - first-order coherence properties follows the excitation laser. - second-order correlation function shows antibunching. 2) incoherent part (resonance fluorescence) - first-order coherence properties depend solely on the transition. - second-order correlation function shows antibunching.

36 quantum dot resonant light scattering how does a 2-level system interact with a near resonant cw-laser? an optical transition (of a quantum system) has two components: 1) coherently scattered part (resonant Rayleigh scattering) - first-order coherence properties follows the excitation laser. - second-order correlation function shows antibunching. only discuss recent cw experiments (what I have done!) QD light generated by the transition being driven (no Raman photons) à Include refs at end to other work mix of laser spectroscopy, solid-state quantum optics and QIS 2) incoherent part (resonance fluorescence) - first-order coherence properties depend solely on the transition. - second-order correlation function shows antibunching.

37 qd resonant light scattering: coherent part I In the beginning (2004) à homodyne the laser with the scattered qd field ω L laser ω QD transition incoming laser (E 0 ~Ω,Δ) scattered field e s power detector -P M Forward Direction e g ω L ω QD E 0 QD E 0 +e s Δ e s = e si + e sc vary detuning, Δ,between the laser and the transition P M ~ E e si 2 + e sc 2 + 2Re{E * 0 e sc } + 2Im{E* 0 e sc } dip due to destructive interference; optical thm or phase-shifts Alen et al APL (2003)

38 qd resonant light scattering: coherent part I measure the fine structure of X 0 transition selective excitation via polarization; same for Trion! 1 dip due to destructive interference; optical thm or phase-shifts X V X H X H Δ eh X V X 0 Δ eh H+V tune laser frequency H a.u. V 0 Δ eh needs to be suppressed to generate entangle photons 1 Hogele et al PRL (2004)

39 qd resonant light scattering: coherent part I spin-state preparation à nuclear spins mediate spin-flip in plateau center at B z 0 Faraday configuration B = 0T B = 350mT σ + γ r ~10-3 Bz nuclear spin mediated e - spin flip cotunneling spin pumping time ~ 1-μs 1 also Voigt (B in-plane) à spin pumping time ~ ns s 2 1 Atatüre et al. Science 312 (2006); 2 Xu et PRL 99, (2007).

40 qd resonant light scattering: suppress the laser Is it possible to only measure the scattered QD field? à yes! but need to reject the excitation laser incoming laser (E 0 ~Ω) scattered field e s scattered field intensity E 0 +e s E 0 QD E 0 +e s e g ~200 nm e s = e si + e sc On a detector we measure P M ~ E e si 2 + e sc 2 + 2Re{E * 0 e sc } + 2Im{E* 0 e sc } s = 2 Ω2 2 character, ie coherence, depends on laser Rabi frequency (power)

41 qd resonant light scattering: suppress the laser how we do it in the lab side excitation (atomic physics approach) polarization suppression first time seen with QD à Muller et al PRL (2007)

42 qd resonant light scattering: suppress the laser how we do it in the lab side excitation (atomic physics approach) polarization suppression first time seen with QD à Muller et al PRL (2007) Citron et al PRA 16 (1977).

43 qd resonant light scattering: suppress the laser how we do it in the lab side excitation (atomic physics approach) polarization suppression how it works Ω pol H ~ σ + +σ -, σ + excite: H ~ σ + +σ - emit: σ + ~ H+V measure: V H first time seen with QD à Muller et al PRL (2007) Citron et al PRA 16 (1977).

44 qd resonant light scattering: suppress the laser a typical resonance fluorescence data set QD X 1- Na: D 2 line at saturation 12 MHz M.L. Citron et al PRA 16 (1977).

45 qd resonant light scattering: coherent part II low power limit of resonant light scattering scattered field intensity saturation power e g s = 2 Ω2 2

46 qd resonant light scattering: coherent part II low power limit of resonant light scattering Ω ~ à as a function of laser detuning à coherent scatter on an incoherent background incoherent coherent coherent incoherent

47 qd resonant light scattering: coherent part II low power limit of resonant light scattering; only the coherent

48 qd resonant light scattering: coherent part II single photon generation à ultracoherent subnatural linewidth single photons (Heitler regime) à single photons inherent laser coherence >> Γ -1 r ; τ coh ~ 22 ns laser incoherent pumping coherent QD à optical charging/incoherent excitation reduces photon coherence

49 qd resonant light scattering: coherent part II high power limit of resonant light scattering scattered field intensity saturation power e g s = 2 Ω2 2

50 qd resonant light scattering: incoherent part large Rabi frequency resonance fluorescence: the Mollow triplet à strong laser dresses the QD optical transitions X 1- trion Jaynes-Cummings ladder Ω Ω à n+1 pol H bottom of the ladder is vacuum Rabi splitting à cqed peak height 1:3:1

51 qd resonant light scattering: incoherent part large Rabi frequency resonance fluorescence: the Mollow triplet à strong laser dresses the QD optical transitions Ω

52 qd resonant light scattering: incoherent part large Rabi frequency resonance fluorescence: the Mollow triplet à strong laser dresses the QD optical transitions Ω from Carlos Stroud, Na D2 F Schuda et al 1974 J. Phys. B: At. Mol. Phys. 7 L198 Wu et al Phys. Rev. Lett. 35, 1426 (1975)

53 qd resonant light scattering: incoherent part the Mollow triplet as a function of laser frequency à laser tunable single photon generation, no laser leakage

54 qd resonant light scattering: incoherent part photon coherence properties à power induced phonon dephasing (also in sideband linewidth 1 ) à example 1 of not-so-atom like behaviour 1x 650x 4000x saturation 0.5x saturation saturation decay Decay ps ps 20-π rotations 1 S. M. Ulrich et al., Phys. Rev. Lett. 106, (2011).

55 qd resonant light scattering: incoherent part spin-dependent sideband frequencies à Mollow quintuplet à different effective Rabi frequencies à Zeeman splitting, laser detuning, selection rules H B z 50 mt

56 qd resonant light scattering: incoherent part spin-dependent sideband frequencies à Mollow quintuplet à different effective Rabi frequencies à Zeeman splitting, laser detuning, selection rules à leverage to measure spin orientation (need more cnts!) H B z

57 qd resonant light scattering: incoherent part spin-dependent sideband frequencies à Mollow quintuplet à different effective Rabi frequencies à Zeeman splitting, laser detuning, selection rules à full spectral overlap of photons with anti-correlated polarization H B z

58 qd resonant light scattering: incoherent part resonance fluorescence to monitor Bohr spin quantum jumps à qd molecule; spin-to-transition energy mapping à QIS: direct single shot spin measurement spin quantum jumps

59 qd resonant light scattering: incoherent part resonance fluorescence to monitor Bohr spin quantum jumps à qd molecule; spin-to-transition energy mapping à QIS: direct single shot spin measurement à exploit partner QD to control spin spin quantum jumps write- in 0 ( )

60 quantum dots à not so artificial atoms! nuclear spins, like phonons, interact with optical transitions à laser spectroscopy under finite magnetic field à dragging also visible in the RF spectrum à spectroscopic tool

61 quantum dots à not so artificial atoms! nuclear spins, like phonons, interact with optical transitions à nuclear spins can mitigate fluctuations; improve coherence NanoPID (100 Hz)

62 thanks for the attention QD Collaborators Mete Atature, Yong Zhao, Chao-yang Lu, Clemens Matthiesen University of Cambridge Antonio Badolato, University of Rochester Atac Imamoglu, Stefan Falt, Alex Hogele, ETH-Zurich group members Questions?

63 reference list H. Haug and S.W. Koch, Quantum Theory of the Optical and Electronic Properties of Semiconductors, 3rd ed., World Scientific, Singapore, 2001, pp R. Loudon, The Quantum Theory of Light, 3rd ed., Oxford University Press, Oxford, V.V. Mitrin, V.A. Kochelap, and M.A. Stroscio, Quantum Heterostructures: Microelectronics and Optoe- lectronics, Cambridge University Press, Cambridge, S. Mukamel, Principles of Nonlinear Optical Spectro- scopy, Oxford University Press, New York, U. Woggon, Optical Properties of Semiconductor Quantum Dots, Springer, Berlin, L. Jacak, P. Hawrylak, and A. Wojs, Quantum Dots, Springer, Berlin, D. Bimberg, M. Grundmann, N.N. Ledentsov, Quantum Dot Heterostructures, Wiley, Chichester, UK, D.D. Awschalom, D. Loss, and N. Samarth, Semi- conductor Spintronics and Quantum Computation, Springer, Berlin, P.M. Petroff, A. Lorke, and A. Imamoglu, Epitaxially self-assembled quantum dots, Phys. Today 54 (2001), pp D. Gammon and D.G. Steel, Optical studies of single quantum dots, Phys. Today 55 (2002), pp M. Bayer, G. Ortner, O. Stern, A. Kuther, A.A. Gorbunov, A. Forchel, P. Hawrylak, S. Fafard, K. Hinzer, T.L. Reinecke, S.N. Walck, J.P. Reithmaier, F. Klopf,andF.Scha fer,finestructureofneutraland charged excitons in self-assembled In(Ga)As/(Al)GaAs quantum dots, Phys. Rev. B 65 (2002), :1 23.

64 reference list Spin Proposal: Imamoglu, et al, Quantum information processing using quantum dot spins and cavity QED, Phys. Rev. Lett. 83, 4204 (1999). Many of Sophia Economou s papers Single Photons: P. Michler, et al, A Quantum Dot Single-Photon Turnstile Device, Science 290, 2282 (2000). C. Santori, D. Fattal, J. Vuckovic, G.S. Solomon, and Y. Yamamoto, "Indistinguishable photons from a single-photon device", Nature 419, 594 (2002). Q. Cryptography: E. Waks, K. Inoue, C. Santori, D. Fattal, J. Vuckovic, G. S. Solomon, and Y. Yamamoto, "Secure Communication: Quantum cryptography with a photon turnstile," Nature 420, 762 (2002). Entangled Photons: R. M. Stevenson, et al., A semiconductor source of triggered entangled photon pairs, Nature (London) 439, 179 (2006) Electron Spin Rotation: D. Press, T. D. Ladd, B. Zhang, and Y. Yamamoto, Complete quantum control of a single quantum dot spin using ultrafast optical pulses, Nature 456, 218 (2008). J. Berezovsky, M. H. Mikkelsen, N. G. Stoltz, L. A. Coldren, and D. D. Awschalom, Picosecond Coherent Optical Manipulation of a Single Electron Spin in a Quantum Dot, Science 320, 349 (2008).