NANOESTRUCTURAS V Escuela Nacional de Física de la Materia Condensada

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1 NANOESTRUCTURAS V Escuela Nacional de Física de la Materia Condensada Parte III Sergio E. Ulloa Department of Physics and Astronomy, CMSS, and Nanoscale and Quantum Phenomena Institute Ohio University, Athens, OH Supported by US DOE & NSF NIRT

2 Photons, excitons, spins, energy transfer & entaglement.. all in QDs Gammon/Steel optical control of quantum dot state Imamoglou single photon source from quantum dots Klimov Förster coupling between quantum dots Zrenner coherent control of quantum dot photodiode

3 Gammon/Steel optical control of quantum dot state Bonadeo et al PRL 1998 Naturally Formed GaAs QDs Al mask with apertures 500 Å GaAs cap layer 500 Å Ga 0.3 Al 0.7 As 4 Å GaAs layer 50 Å Ga 0.3 Al 0.7 As 4 Å 40nm STM image showing the island formation and elongation. Gammon et al., Phys. Rev. Lett.76, 3005 (1996) Samples are provided by D.S. Katzer, D. Park, and E. S. Snow, NRL

4 B QD Magneto-excitons * - g factor Photoluminescence of a Single Exciton splitting shift T T T Magnetic Field (Tesla) Weak field limit: H int = g * exµ B B 0 S z + αb 0 g * ex = g * e + g * hh g * hh = 6κ + 7q/ Zeeman splitting 1.90 T.150 T T T T * First reported by S. W. Brown et al., Phys. Rev. B 54, R (1996) Energy (mev)

5 Photoluminescence in SINGLE QD Excitons Excited excitons (s- and p-shell) Biexcitons, X -, X --, etc. laser power Findeis et al, Sol. State Comm, 000

6 Experimental Techniques Linear Spectroscopy: Photoluminescence Indirect probe of exciton resonances Requires spectral diffusion of excited carriers CW Frequency Stabilized Dye Lasers Coherent Nonlinear Spectroscopy: CW differential transmission Resonant excitation Probe coherent interaction in the system E NL (ε) ~ χ (3) (ε) E pump E* pump E probe I signal = Re ( E NL E* probe ) D Steel et al U Michigan RF Electronics Reference Lock-in Amplifier E pump E NL Detector E probe AOM ƒ~100 MHz E probe 5 K Imaging

7 Non-degenerate Nonlinear Spectroscopy: Advantages Probe single excitonic state decay dynamics Measure both T 1 and T * Probe coupling between different excitonic states Probe inter-dot energy transfer and dot-dot coupling Study excited states of excitons Probe multi-exciton correlation effects ; Study the coherent interaction between exciton doublet. * Nicolas H. Bonadeo et al., PRL, 81, 759 (1998)

8 hh Excitonic Level Diagram c v B 0 = 0 B 0 0 σ σ σ- state Scattering states + 1 Two-exciton state E Bound state of multi-excitons σ+ state Ground state: 0-exciton state Non-degenerate experiments can excite both σ+ and σ- excitons by varying the frequency and the polarization of the excitation beams (pump and probe beam).

9 Exciting Two Electrons 3 c v σ- state + 1 Pump σ σ σ+ state σ level diagram in -electron basis + Probe σ+ 3 Ground state Resonant and coherent excitation of two electrons Two contributions: 1. Incoherent: Ground state depletion. Coherent: Zeeman coherence between σ- and σ+ state

10 Optically Entangling Two Systems: the Importance of Coupling coupling H total = H 0 + H H 0 + H Without coupling Product state of the two subsystems. A strong coupling allows one system to see the excitation of the other. Coulomb interaction between charged particles: trapped ions Magnetic dipole interaction: NMR systems Exciton-exciton Coulomb coupling: excitons Mutual coherence between E and E is essential.

11 Coulomb Correlation*: Coulomb interaction between electron-hole pairs within single QD 1 σ- state Two-exciton state E Bound state of multi-excitons + 1 Pump σ Probe σ+ 3 Scattering states σ+ state + 3 Ground state: 0-exciton state Two-exciton state cancels the signal due to the symmetry in the level diagram. σ- σ But Two electrons are involved within a single QD. Coulomb interaction between the two excitons is important. 1 3 * Kner et al Phys. Rev. Lett. 78, 1319 (1997) Ostreich et al Phys. Rev. Lett. 74, 4698 (1995)

12 Turn on the Coulomb Correlation - Pump σ g σ σ+ + Probe σ+ Turn off the Coulomb Correlation - + Pump σ g Probe σ+ Pump: σ Groundstate Depletion Zeeman Coherence γ + = + γ γ = γ = =1 No Signal!! Total Signal Probe ( γ ) Probe ( γ )

13 Experiment : Coulomb Correlation and Zeeman Coherence σ+ σ Pump: σ + γ = γ = + γ = γ=1 Ground state depletion Zeeman Coherence Total Signal Degenerate and Non-degenerate Coherent Nonliear Response Evidence for Zeeman Coherence in Single QDs Degenerate Non-degenerate pump σ σ σ+ 1.3 Tesla 5K probe σ Probe ( γ ) Creation of two-electron entanglement Energy (mev)

14 Ultimate Goal Combine: Optical control of individual QDs Long spin lifetimes QD nanostructure engineering To produce: Qubit register of QD spins Coherence of a single QD can be controlled Gammon et al have demonstrated this for excitons [Stievator et al., PRL (001)] Next: QNOT and other quantum gates Spins have long coherence times: dephasing times T* = 5ns-300ns [Dzhioev et al., PRL (00)] Next: explore in single QDs; optical read-out and initialization schemes

15 Science 001

16 Imamoglou single photon source from QDs Michler et al., Science 90, 8 (000) It is difficult to isolate a single photon, or fix the number of photons in a pulse Fluctuations in photon number mask the quantum features of light A stable train of laser pulses have Poissonian (photon number) statistics It is desirable to have single photon sources: single photon turnstile Complete regulation of photon generation

17 Single Photon Sources Quantum Cryptography: Quantum Computation: Available sources: Highly attenuated laser pulse Parametric down conversion secure key distribution by single photon pulses single photons + linear optical elements E. Knill, R. Laflamme, and G.J. Milburn, Nature 409, 46 (001) Poisson fluctuations Random generation of single photons Possible solution: Deterministic (triggered) single photon emission: Single Photon Turnstile Device A. Imamoglu, Y. Yamamoto, Phys. Rev. Lett. 7, 10 (1994) Experiments: Coulomb blockade of electron/hole tunneling in a mesoscopic pn-junction: J. Kim et al. Nature 397, 500 (1999) Single Molecule at room temperature: B. Lounis and W.E. Moerner, Nature 407, 491 (000) Single InAs Quantum Dot in a microcavity: P. Michler et al., Science 90, 8 (000)

18 Signature of a triggered single-photon source Intensity (photon) correlation function: g () ( τ ) = : I ( t) I ( t + τ ) : I ( t) Single quantum emitter (I.e. an atom) driven by a cw laser field exhibits photon antibunching. g () (τ) 1 0 τ Triggered single photon source: absence of a peak at τ=0 indicates that none of the pulses contain more than 1 photon. g () (τ) 0 τ

19 Photon antibunching Intensity correlation (g () (τ)) of light generated by a single two-level (anharmonic) emitter. Assume that at τ=0 a photon is detected: - We know that the system is necessarily in the ground state g> - Emission of another photon at τ=0+ε is impossible. Photon antibunching: g () (0) = 0. pump (nonclassical light) photon at ω p g () (τ) recovers its steady-state value in a timescale given by the spontaneous emission time. If three are two or more -level emitters, detection of a photon at τ=0 can not ensure that the system is in the ground state (g () (0) >0.5).

20 Single InAs Quantum Dots InAs/GaAs Single QD P (W/cm ) s-shell 650 p-shell T=4K Intensity (a.u.) X 1X 17 x5 in intensity Energy (ev) x in intensity Two main wavelengths emitted from each shell (For s-shell) X recombination while there is already an e-h pair in the s-shell (biexciton) 1X recombination while there is no other e-h pair in the s-shell (exciton) Due to carrier-carrier interaction Typically hν 1X = hν X + -3meV Unique wavelengths for 1X and X transitions

21 Exciton linewidth measured by a scanning Fabry-Perot Under non-resonant pulsed excitation Free Spectral Range: 6 µev 50 Intensity (a.u.) X X1 Intensity (a.u.) Energy (ev) Bins linewidth: 5.6 µev

22 Photon antibunching from a Single Quantum Dot (c) W/cm g (0)=0.1 τ = 750 ps PL spectrum Correlation Function g () (τ) (b) Coincidence Counts n(τ) 55 W/cm g (0)=0.0 τ = 1.4 ns Intensity (a.u.) P=55W/cm T=4K X 1X (a) W/cm g (0)=0.0 τ = 3.6 ns Energy (ev) Delay Time τ (ns) proof of atom-like behavior

23 A single quantum dot excited with a short-pulse laser can provide single-photon pulses on demand BUT How about embedding quantum dots in a microcavity to increase collection efficiency and fast emission?

24 Q=13500 Q>17000 Microdisk Cavities No roughness on the sidewall up to 1nm! Q>18000 for 4.5µm diameter microdisk Q=9000 for µm diameter microdisk Michler et al., Appl. Phys. Lett. 77, 184 (000) Fundamental whispering gallery modes cover a ring with width ~ λ/n on the microdisk

25 A single quantum dot in a microdisk Larger width of the peaks due to larger lifetime of the quantum dot Intensity (a.u.) P=0W/cm T=4K X WGM 1X Q = 6500 Pump power well above saturation level Energy (ev)

26 Tuning the quantum dot into resonance with a Cavity Mode Energy (mev) 133 WGM 1X 13 Cavity coupling can provide better collection T=44K WGM Intensity (a.u.) Temperature (K) WGM E 0.0 1X -E 0.5 (mev) 1.0 Small peak appears at τ=0: Purcell effect: reduction of emission time

27 Klimov Förster coupling between QDs Crooker et al PRL 00 Non-Radiative Energy Transfer Mechanism D * + A D + A * Coulomb-driven interaction Dipole-dipole interaction (Förster 1946) Higher multipoles interaction (Förster Dexter) Exchange-driven interaction (Dexter)

28 trioctylphosphine oxide (TOPO) ~11A A acceptor: larger dot D donor: smaller dot NQDs have better characteristics than biological light harvesting compounds, eg LH

29 (a) PL decays from a dense film of monodisperse R=1.4A/9A CdSe/ZnS NQDs at the energies specified in the inset. Inset: cw PL spectra from film (solid) and original solution (dashed). (b) Dynamic redshift of the peak emission. Inset: PL spectra at the specified times. Crooker et al PRL 00

30 (a) Schematic of NQD energy-gradient bilayer for light harvesting 13 A dots on 0.5 A dots. (b) Instantaneous PL spectra at 500 ps intervals (from 0 to 5 ns), showing rapid collapse of emission from 13 A dots.

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32 Our Goal Study the excitation energy transfer in quantum-dot arrays using an appropriate model Hamiltonian N N ( ) N N H = T c c T d d Uc c d d U c c d d e i j + i j + h i i i i + NN i i j j + Vc s i d i djcj ij, i ij, = NN i j

33 Probability of each basis state as a function of time Period of small oscillation ~ 1.3 ~ 1 T V e c Period of large oscillation ~ 15 ~ 1 V f V c > 1001> 0110> 0011> total probability of exciton state Calculations V c for two t/(π) V c dots t/(π ) Probability of each basis as a function Probability of each basis as a function of time without Förster Probability of each basis as a function of time T e /V c =-0.8 V f =0 V cnn /V c = > 1001> 0110> 0011> of time without tunneling T e /V c =0 V f /V c =-0.04 V cnn /V c = > 1001> 0110> 0011> V c /(π) V t/(π)

34 3.0 V c =10 mev 1 Psec V c =100 mev Oscillator strength T e /V c = V c,nn /V c =0.1 V f /V c =0.04 T h = V c t/π Time evolution of the oscillator strength of an exciton initially localized at dot 1 in a 4 dot chain G. W. Bryant, Physica B 314, 15 (00).

35 The movie of the 4 dots exciton probability at each dot (1) (11) (14) (10) (15) (9) (16) (8) (17) (7) (18) (6) (19) (5) (0) (4) (1) (3) () () (3) (1) (4) V c t/π

36 1.0 probability of exciton state in each dot exciton probability at each dot From graph/calculation Förster rate for polymer h π V c π t = = 3.1 n n + 1 8U 8U V c V c c /(π) V c t/π 3 π t. V c efficient interdot transfer rate 4

37 Zrenner coherent control of quantum dot photodiodes Zrenner et al Nature 00 Laser focus Shadow mask Top contact: 5nm Ti (semitransparent) QDs InGaAs Back contact Possibles measurements Photolumenescence (PL) spectrum (for τ rad < τ tunnel ) Photocurrent (PC) spectrum (for τ rad > τ tunnel )

38 Rabi Oscillation in a two level system ω 0 For ω = ω 0 and using RWA H ω0 Ω() t = σ z + cos( ω t ) σ x Ω () t = µ ε () t P = 0 X sin Θ Exciton Population τ Θ= Ω() tdt π π Pulsed Area (Θ) 3π 4π

39 rad Time scales for the device τ 1 ns τ tunnel 3 ps Tuned by Vb Photoluminescence τ rad < τ tunnel τ rad < τ tunnel τ rad > τ tunnel NeHe laser Photocurrent τ rad > τ tunnel Ti:sapphire laser τ pulse 1 ps f pulse 8 MHz F. Findeis et al. Appl. Phys. Lett. 78, 958 (001)

40 Artificial ion (charged exciton) τ rad < τ tunnel F. Findeis et al. Phys. Rev. B 63, (001)

41 How does the Zrenner device work? τ rad > τ tunnel A. Zrenner et al. Nature 418, 61 (00)

42 How does the Zrenner device work? τ pulse 1 ps f pulse 8 MHz I = eρ f XX pulse ρ XX Θ = sin

43 Mesoscopic optical spectrum analyser QCSE

44 Rabi Oscillation in the photocurrent I = eρ f XX pulse

45 What we are doing... Villas Boas, Govorov, SU Estimating the tunneling time Which one tunnels first, electron or hole? And, after one tunnels, how long before the other tunnels? What is the effect of Coulomb interaction? π W = ψα VDot ψ0 δ( Eα E0 ) α 1 τ tunnel = W Luyken et al. Appl. Phys. Lett. 74, 486 (1999) Modeling in terms of density matrix with tunneling How much was population inverted? Can this be controlled by gates? Detuning?