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Single Photon Generation & Application in Quantum Information Processing • Quantum Dot Single Photon Sources • Optical Properties of Quantum Dots • Cascaded Emission from Quantum Dots • Quantum Cryptography • Indistinguishable Photons • Generation of Entangled Photon Pairs Single Photon Sources Methods to Generate Single Photons on Demand Intens. g2 bunchig 1 time Intens. time g2 1 time time Intens. g2 anti-bunchig 1 time time Quantum Dot Single Photon Sources Quantum Dots Semiconductor quantum dots are small semiconductor crystals that confine the charge carriers (electrons and holes) in all three dimensions. 3 ways to make quantum dots: chemical synthesis etching from 2D nanostructures 3D, 2D, 1D and 0D density of states self organized growth Nanocrystals Quantum dots chemically synthesized from precursors in solution are called nanocrystals. They are nowadays commercially available, but have been used for many years in color glass or in color filters. eigenenergies and eigenfunctions of two dots of different size Notre Dame, rose window 1250-1260 The different colors of the emitted light are determined by the size of the nanocrystals, which varies from 1 to 10 nanometers. Fluorescence from nanocrystals excited by UV light (left) and TEM images of nanocrystals (right) [provided by A. Rogach Univ. Munich] Nanocrystals or colloidal quantum dots: • allow tuning of fluorescence • provide a clean fluorescence spectrum • have a high fluorescence yield • have a high photostability Obstacles: • photobleaching • blinking & spectral jumps • non-uniform size distributions Nanocrystals have been used as optical markers in biochemistry and biophysics, but also in first photonic applications. Blinking in quantum dot fluorescence Spontaneous transition between on- and off states. excitation and fluorescence (on-state) non radiative decay from off-state Intensity [a.u.] PL image 734 732 730 728 726 724 722 720 718 716 714 712 0 5 10 Time [s] 15 20 S. Götzinger et al., J. Opt. B 6, 154 (2004) Self-organized Quantum Dots MBE growth of slightly lattice mismatched materials (Stranski-Krastanow mode) produces very stable quantum dots. The difficult task: Low density QD samples of high quality GaAs InAs wetting layer formation QD growth QD-density: ~1.8 ML substrate ~ 108 cm-2 QD-density Growth parameter • Ratio of As to In: 50:1 • Temperature: 510 °C • Rate: ~ 0.04 ML/s Leonard et al., 1011 Appl. Phys. Lett. 63, 3203 (1993) 108 1.8 ML From wetting layer to quantum dots: 3*3 μm2 1.7 MLs < critical thickness 600nm 1*1 μm2 1.8 MLs ≈ critical thickness 200nm 1*1 μm2 200nm 3 MLs >> critical thickness Control of dot density and size: AFM image of samples grown at 480° (a), 487° (b), 498° (c), and 520° (d) Transmission electron microscope images [110] AFM 10nm [110] 10nm K. Georgsson et al., Appl. Phys. Lett. 67, 2981 (1995) Contains ~10000 atoms InP dots grown on GaInP Self-organized quantum dots are embedded in a semiconductor with a larger bandgap. They represent a heterostructure. Exciton in a QD: exciton GaInP InP GaInP Biexciton: biexciton Biexciton n=2 Energy n=1 Exciton n=1 n=2 Ground state (empty QD) Size: O(10 nm) Photoluminescence of an ensemble of InAs quantum dots Photoluminescence image of a set of InP quantum dots Due to their atomic-like properties quantum dots are sometimes referred to as artificial atoms. Specific advantages of single quantum dots • Stability • Compatible with chip-technology • Wide spectral range • Electrical Pumping • High repetition rate • Strong interactions “available” A. Badolato, et al., Science 20, 1158 (2005) Specific disadvantages of single quantum dots • Low temperature operation • non-uniformity • Device production yield • Decoherence • Efficiency AFM Optical Properties of Quantum Dots Experimental Setup Coincidence counter CCD StopAPD Spectrograph Liquid He Cryostat (4 K) Laser (cw or pulsed) The following picture shows a setup to study the optical properties of single quantum dots: Filter StartAPD Dichroic mirror Sample SPS Michelson interferometer g1 Hanbury Brown-Twiss correlator g2 Experimental Setup Some Details About the Quantum Dot Sample • Emission around 690 nm (@ maximum detection efficiency of Si detectors !) • Lifetime around 2 ns GaInP (400 nm) InP QDs Al mirror (200 nm) Epoxy Si substrate Intensity (a.u.) • Dot density: 108 cm-2 with 2-nm bandpass filter without filtering 670 675 680 Wavelength (nm) The additional mirror increases the photon emission rate by more than a factor of 2!. 685 Number of coincidences (raw data, a.u.) 150 100 50 cw 0 -40 -20 0 20 Delay time (ns) ZOOM 50 0 -1 40 Measurement of g(2)(τ) under cw and pulsed optical excitation: • Central peak vanishes nearly completely Ö generation of only one photon per pulse • Single photon generation @ 670 nm observed up to 40 K V. Zwiller, et al., Appl. Phys. Lett. 82, 1509 (2003) Number of coincidences (arb. units) Number of coincidences (raw data, a.u.) Intensity Correlation Measurements (g(2)(τ)) 0 1 Delay time (ns) pulsed 0 -40 -20 0 20 Delay time (ns) 40 Fourier Spectroscopy (g(1)(τ)) CCD Measurement of G(1) of several dots simultaneously imaging on a CCD camera V. Zwiller, et al., Phys. Rev B (2004) Intensity (arb. units) InP 3 Visibility of the interference fringes: 2 v = ( Imax - Imin ) / ( Imax + Imin ) 1 Δν = 50 x Δνrad 0 0 2 4 Piezo position (µm) 6 15K 20K 25K 1 30K 0,1 40K 0,01 0 2 4 6 8 Path difference / mm Single photon generation (anticorrelation below 0.5) up to 40 K 200 linewidth increases by a factor of two by increasing temperature from 7 to 40 K Exciton Biexciton 150 100 50 0 20 40 Temperature (K) Coincidences (a.u.) 7K Linewidth (µeV FWHM) Visibility (normalized to 1) Fourier transform of g(1)(τ) gives the linewidth of the emitted light. 7K 0 15K 0 20K 0 25K 0 30K 0 40K 0 -40 -20 0 20 Delay time (ns) 40 Wave and Particle Aspects A single photon source allows to perform an interesting variation of Taylor‘s experiment. StopAPD Coincidence counter Pulse counter (DAC) Taylor-experiment (1906) T. Aichele, et al., AIP proc. Vol. 750, 35 (2005) V. Jacques, et al. Eur. Phys. J. D 35, 561 (2005) J. T. Höffges, et al. Opt. Comm., 133, 170–174 (1997) Number of counts per 10 ms StartAPD 50 25 0 200 250 300 Path lengththe difference Time after starting measurement (s) Cascaded Emission from Quantum Dots Multicolor Sources Exciton in a QD: It is straightforward to create complex quantum states in quantum dots by adding electrons or holes. exciton GaInP InP Biexciton: biexciton GaInP n=2 n=1 n=2 500 5000 Triexciton Correlations / a.u. Intensity / a.u. Biexciton Exciton 250 670 675 680 685 Wavelength / nm Spectra with increasing excitation power Size: O(10 nm) 400 2500 0 1500 1000 500 0 500 n=1 Energy The decay of these states provide: • photon cascades • multicolor photon sources • sources for complex photonic states 690 Triexciton 300 600 400 Biexciton 200 50 25 0 40 Exciton 60 80 t / ns g(2) measurements for individual spectral lines Coincidence counter exc. Coincidences, a.u. StopAPD Cascaded decay can be proven in a modified HBT setup with narrow-band spectral filters in each arm. 1400 1200 triexciton 1000 800 -20 StartAPD biexc. J. Persson et al., Phys. Rev. B 69, 233314 (2004) D. V. Regelmann, et al. Phys. Rev. Lett. 87, 257401(2001) E. Moreau et al., Phys. Rev. Lett. 87, 163601 (2001) A. Kiraz et al. Phys. Rev. B 65, 161303 (2002) -10 0 10 Delay time (ns) 20 biexciton Coincidences (a.u.) Correlation measurements reveal dynamics of multiphoton cascades biexciton 100 exciton 50 0 -40 -20 0 20 Delay time (ns) 40 The photons emitted in a cascade have different wavelengths due to the additional Coulomb binding energy of the biexciton, triexciton, etc.. A cascaded emitter is thus a multi-color single photon source. The photons can be separated with high efficiency using interferometric techniques. setpoint for photon separation Delay= 1/2 Rep.Rate Interference signal 1 0 0 Path difference The peak at τ=0 is due to background counts. → One quantum emitter acts as two independent single photon sources. 100 Coincidences (a.u.) Autocorrelation of the exciton transition. 80 60 40 20 0 -40 → Generation of photons beyond the maximum rate limited by the natural transition lifetime 40 Coincidences (a. u.) Autocorrelation after delaying and recombining the exciton and biexciton line Delaying the two photons by half the excitation repetition time doubles the photon rate. 13.2 ns -20 0 20 Delay Time (ns) 40 6.6 ns 30 20 10 0 -40 -20 0 20 Delay time (ns) 40 Quantum Cryptography The BB84 Protocol Eve Eve cannot copy the photon (no cloning theorem) Bob Alice 1 1 0 0 Quantum channel Classical public channel: Bennett, Brassard, Proc. IEEE Int. Conf. on Computers, Systems & Signal Processing (1984), First realization with QDs: Waks et al., Nature 420, 762 (2002) • Alice sends randomly polarized photons (0, 45, 90 or 135°) to Bob. • Bob randomly measures in the straight or diagonal base. • Bob keeps his results secret. • Bob publically tells his measurement bases (not the results!). Alice publically tells him if he chose the right base. • Alice and Bob keep only the results with the common bases. • They both have now a common and random key: 1 1 0 0 1 ... Quantum Channel w1 From Single Photon Source EOM Michelson Michelson w2 EOM ALICE Michelson MUX DEMUX 1 w n e iF lS g o S rP m tn o h u e rc E ro m u tn o h P e rc M U X Delay ic M e h a yl n o ls e h ic M l e n a h C m tu n a l e n a A Detection BOB O E n o ls r e z ly a n n o ls e h c M i E M e O tD O B B X U M E D M A r e z ly a n M O E tc e D O B B Quantum Channel w1 Analyzer Michelson w2 h C m tu n a Q M O e D 1 w 2 w EOM D M te O E M c n o ls e h i C LI A E E Q M O ch i lso M e n 2 w F n e li g o S C LI A E From Single Photon Source Analyzer Detection EOM ALICE Michelson EOM EOM Detection BOB From single photon source Polarizer Analyzer EOM EOM Alice Alice´s original data APD Bob Encoded image Bob´s decoded image Transmission to Bob: 30 successfull counts/s at a laser modulation of 20 kHz Similarity between Alice´s and Bob´s keys: 95% T. Aichele, G. Reinaudi, O. Benson, Phys. Rev. B, 70, 235329 (2004) Indistiguishable Photons The KLM Proposal Knill, Laflamme, and Milburn [Knill, Laflamme, Milburn, Nature 409, 46 (2001)] suggested a probilistic two-qubit gate implemented with single photons and linear optical elements. The gate requires photon number resolving counters and additional so-called ancilla states represented by photons which have to be indistinguishable. It relies on two-photon quantum interference, e.g. at a beam splitter: classical particles bosons fermions The quantum interference of bosons at a beam splitter was first measured by Hong, Ou, and Mandel [Phys. Rev. Lett. 59, 2044 (1987)] and is known as Hong-Ou-Mandel dip: The depth of the HOM dip gives the „degree of indistinguishability“ of two photons. With the help of HOM interference a fundamental two qubit gate, the CZ or controlledphase gate, can be realized. A CZ gate can be constructed with the help of the controlled phase shift gate NS-1: NS-1 gate construction of a CZ gate with two NS-1 gates How to make an NS-1 gate? The original KLM gate uses ancilla states. These are measured after passing the gate. The operation of the gate is accepted only if a specific outcome is measured. Otherwise the operation has to be started again. Thus the gate is probabilistic with success probabilty 1/4 It acts on arbitrary initial states |ψ>. x = -1 if φ1=φ2=φ3=0, φ4=π θ1=-θ3=π/8, θ2=3π/8 Sources for Ancilla States: On-demand Photons From a Single Quantum Dot In an important experiment the Yamamoto group at Stanford was able to demonstrate the indistinguishability of subsequent photons from a quantum dot. Realization of indistinguishable photons and entangled photon pairs in the experiment by Yamamoto [Santori, et al., Nature 419, 594 (2002)]: A next breakthrough would be to demonstrate the generation of indistinguishable photons from two different quantum dots. Hong-Ou-Mandel dip for three different quantum dots [Santori, et al., Nature 419, 594 (2002)] A next breakthrough would be the demonstration of indistinguishable photons from two different quantum dots. Figure of merit for linear optical quantum computation (LOQC) with single photons: ηSηD > 2/3 detector efficiency source efficiency [Varnava et al., PRL 100, 060502 (2008) Indistinguishable Photons From a Single Quantum Dot LED In a more recent experiment the group by Andrew Shields demonstrated emission of indistinguishable photons from a light emitting diode (LED). [Bennett et al., APL 86, 181102 (2005)] Left: Schematic of the device structure. A single QD within a cavity (formed by a Bragg mirror and the top interface) is isolated with an aperture in the metallic contact. The cavity enhances the collection efficiency of photons. Under pulsed electrical excitation antibunching is observed both from the exciton (k) and from the biexciton (l). The lines are filtered out with a monochromator. Single photons are sent in an unbalanced (Fiber-)Mach-Zehnder interferometer. When the repetition period of the exciting AC voltage matches the time difference between of the two arms, photons meet at the second beamsplitter. Distinguishability can be enforced with a λ/2 plate. [Bennett et al., APL 86, 181102 (2005)] Schematic of the setup A clear Hong-Ou-Mandel dip is observed when the two photons have the same polarization, i.e. when they are (nearly) indistinguishable. In Situ Tuning of Single Quantum Dots In striking contrast to atoms artificial atoms (quantum dots) are not identical. An additinal „tuning knob“ is required, e.g. by applying external fields. Rastelli et al. [APL 90, 073120 (2007)] developed the method of in situ laser processing: A focussed laser causes heating to above 1000 K and thus intermixing of In and Ga atoms in the quantum dots producing a blueshift. Left: heating of quantum dots in a microdisc Right: tuning three quantum dots to the same emission wavelength Generation of Entangled Photon Pairs Exciton in a QD: exciton GaInP InP Biexciton: biexciton GaInP biexciton Energy n=2 n=1 n=1 n=2 σ+ σ- σ− σ+ exciton ground state (empty QD) Size: O(10 nm) In a symmetric quantum dot there are two possible decay paths to conserve angular momentum: 1) First a right, then a left circularly pol. photon: 2) First a left, then a right circularly pol. photon: If both paths are indistinguishable quantum mechanics requires to add probability amplitudes: The state is an entangled state! Benson & Yamamoto, PRL 84, 2513 (2000) Unfortunately, a quantum dots state is usually not symmetric. There are: asymmetric dot shape, crystal anisotropy, piezoelectric fields, anisotropic strain, etc. The asymmetry is „tested“ by the electron-hole exchange interaction and leads to a splitting of the exciton state. The decay produces two classically correlated linearly polarized photons. biexciton σ+ σ- exciton σ− σ+ exciton level splitting ground state (empty QD) Recent work was successful in reducing the splitting below the natural linewidth. Young et al., PRB 72, 113305 (2005) A result on the generation of entangled photon pairs. The excition splitting was reduced by (a) annealing & selection of appropriate dots, (b) by an in-plane magnetic field [Stevenson et al, Nature 439, 179 (2006); Hafenbrak et al., NJP 9, 315 (2008)] Another result on the generation of entangled photon pairs. Here, a subset of indistinguishable photons was selected by spectral filtering. [Akopian et al, PRL 96, 130501 (2006)] Yet another proposal to create entangled photon pairs relies on erasing the distinguishability between pairs of biexciton (XX) to exciton (x) decays. If both the difference in energy and in emission time is absent, entangled photons are emitted. [Avron, et al., PRL 100, 120501 (2008)] Left: creating degeneracy of the XX-X and X-0 transitions [Reimer, arXiv: 0706.1075v1] Bottom: Apparatus to erase timeing information