Single photons on demand New light for quantum

Single photons on demand: New light for quantum information processing Oliver Benson Humboldt-Universität zu Berlin, Nano Optics Group http: //nano. physik. hu-berlin. de Thanks to: T. Aichele 1, M. Scholz, S. Ramelow, V. Zwiller 2 1 CEA, Grenoble (F); 2 Tech. Univ. Delft (NL) Funding:

SQE 2005, Beijing, Nov. 23 -27 Einstein 1905 (Annalen der Physik): Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt „Es scheint mir nun in der Tat, daß die Beobachtungen über die „schwarze Strahlung“, . . . , und andere die Erzeugung bzw. Verwandlung des Lichtes betreffende Erscheinungsgruppen besser verständlich erscheinen unter der Annahme, daß die Energie des Lichtes diskontinuierlich im Raume verteilt sei. . es besteht dieselbe aus einer endlichen Anzahl von in Raumpunkten lokalisierten Energiequanten, welche sich bewegen, ohne sich zu teilen und nur als Ganze absorbiert und erzeugt werden können. Photoelectric Effect: Ekin=hn-W e-

Outline SQE 2005, Beijing, Nov. 23 -27 • Introduction and Overview • Single Photon Sources based on Quantum Dots • Multi-Photon Sources • Multiplexed Quantum Cryptography • Demonstration of Deutsch-Jozsa Algorithm • Summary & Outlook

Motivation SQE 2005, Beijing, Nov. 23 -27 Quantum information processing relies on the controlled manipulation of qubits. |y> = Prerequisites for Quantum Computing* 1. 2. 3. 4. 5. A scalable physical system with well characterized qubits The ability to initialize the state of the qubits to a simple initial state Long relevant decoherence times, much longer than gate operations A universal set of quantum gates (single and two-qubit gates) A qubit-specific measurement capability *David Di. Vicenzo, Fortschr. Phys. 48, 9 -11, p. 771 (2000)

Motivation SQE 2005, Beijing, Nov. 23 -27 Why photons? • They interact very weakly with the environment (kb. T<<hn in the visible). • They are quick (v = c, “flying qubits”). • They can be easily detected (commercial detectors with >70% efficiency). Any problems? • They interact only very weakly with each other. • They are difficult to store (flying qubits!). For the moment: Photon as tools to transfer quantum information from one place to another (quantum cryptography, teleportation) or among different quantum systems (quantum interfaces) Future: Proposals and first steps towards optical quantum computing [Knill, Laflamme, Milburn, Nature 409, 46 (2001); P. Walther, et al. , Nature 434, 169 (2005); O'Brien, et al. Phys. Rev. Lett. 93, 080502 (2004); Okamoto et al. quant-ph/0506263 ].

Introduction SQE 2005, Beijing, Nov. 23 -27 Single photons from attenuated light? • Attenuted light pulses only mimick real single photon sources. • There is always a finite probability to find more than one photon per pulse 1. 00 Weak pulse with <n> = 0. 25 SPSwith SPS 25% efficiency 100% efficiency 0. 75 Probability • Attenuation of a light pulse does not change the Poissonian photon statistics. 0. 50 0. 25 0. 00 0 1 2 Number of photons 3

Methods to Generate Single Photons on Demand SQE 2005, Beijing, Nov. 23 -27 1. Coherent evolution (STIRAP and cavity QED) Atoms/ions in cavities A. Kuhn et al. , Phys. Rev. Lett. 89, 067901 (2002) A. Kreuter et al. , Phys. Rev. Lett. 92, 203002 (2004) W. Lange et al. , Nature 431, 1075 (2004) C. Maurer et al. , New Journal of Physics 6, 04 (2004) P. Bertet et al. , Phys. Rev. Lett. 88, 143601 (2002) B. Varcoe et al. , Nature 403, 743 (2000)

Methods to Generate Single Photons on Demand SQE 2005, Beijing, Nov. 23 -27 2. Projection (down-conversion and cavity QED) • • parametric down-conversion in a non-linear crystal Rydberg atoms C. K. Hong et al. , Phys. Rev. Lett. 59, 2044 (1987) P. Kwiat et al. , Phys. Rev. Lett. 24, 4337 (1995) G. Weihs et al. , Phys. Rev. Lett. 81, 5039 (1998) B. Varcoe et al. Nature 403, 743 (2000)

Methods to Generate Single Photons on Demand SQE 2005, Beijing, Nov. 23 -27 3. Spontaneous emission (single emitters) • • atoms, molecules, quantum dots, defect centers optical, electrical and STIRAP excitation pulsed, (non-resonant) excitation relaxation decay M: Brunel et al. , PRL 83, 2722 (1999) Lounis & Moerner, Nature 407, 491 (2000) DC: Kurtsiefer et al. , PRL 85, 290 (2000) Beveratos et al. , PRA 64, 061802(R) (2001) spontaneous single photon emission QD: Kim et al. , Nature 397, 500 (1999) Michler et al. , Science 290, 2282 (2000) Santori et al. , PRL 86, 1502 (2001) Yuan et al. , Science 295, 102 (2002)

Outline SQE 2005, Beijing, Nov. 23 -27 • Introduction and Overview • Single Photon Sources based on Quantum Dots • Multi-Photon Sources • Multiplexed Quantum Cryptography • Demonstration of Deutsch-Jozsa Algorithm • Summary & Outlook

Quantum Dots SQE 2005, Beijing, Nov. 23 -27 Transmission electron microscope images [110] Atomic force microscope image AFM 10 nm [110] 10 nm K. Georgsson et al. , Appl. Phys. Lett. 67, 2981 (1995) Contains ~10000 atoms In. P dots grown on Ga. In. P

Quantum Dots SQE 2005, Beijing, Nov. 23 -27 exciton biexciton Biexciton Exciton Ground state (empty QD) Photoluminescence of an ensemble of In. As quantum dots Photoluminescence image of a set of In. P quantum dots

Quantum Dots SQE 2005, Beijing, Nov. 23 -27 Specific advantages of single quantum dots • Stability • Compatible with chip-technology • Wide spectral range • Electrical Pumping • High repetition rate • Strong interactions “available” AFM Specific disadvantages of single quantum dots • Low temperature operation • Device production yield • Decoherence • Efficiency TEM

Experimental Setup Coincidence counter CCD Stop. APD Spectrograph Liquid He Cryostat (4 K) Laser (cw or pulsed) SQE 2005, Beijing, Nov. 23 -27 Filter Start. APD Dichroic mirror Sample SPS Michelson interferometer g 1 Hanbury Brown-Twiss correlator g 2

Experimental Setup SQE 2005, Beijing, Nov. 23 -27

In. P Quantum Dots in Ga. In. P SQE 2005, Beijing, Nov. 23 -27 • Emission around 690 nm (@ maximum detection efficiency of Si detectors) • Lifetime around 2 ns • Dot density: 108 cm-2 through 2 nm bandpass filter • Linewidth around 100 µe. V

Intensity Correlation Measurements SQE 2005, Beijing, Nov. 23 -27 ZOOM cw pulsed • Central peak vanishes nearly completely generation of only one photon per pulse • Single photon generation observed up to 40 K V. Zwiller, et al. , Appl. Phys. Lett. 82, 1509 (2003)

Wave and Particle Aspects Stop. APD SQE 2005, Beijing, Nov. 23 -27 Coincidence counter Start. APD 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) Path length difference

Outline SQE 2005, Beijing, Nov. 23 -27 • Introduction and Overview • Single Photon Sources based on Quantum Dots • Multi-Photon Sources • Multiplexed Quantum Cryptography • Demonstration of Deutsch-Jozsa Algorithm • Summary & Outlook

Cascaded Emission SQE 2005, Beijing, Nov. 23 -27 exciton biexciton s+ s. Young et al. , PRB 72, 113305 (2005) exciton s- ground state (empty QD) s+ Benson & Yamamoto, PRL 84, 2513 (2000)

Cascaded Emission SQE 2005, Beijing, Nov. 23 -27 Spectra and anti-bunching in photon cascades:

Cascaded Emission SQE 2005, Beijing, Nov. 23 -27 triexciton biexciton Correlation measurements reveal dynamics of multiphoton cascades 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) exciton

Single Photon Multiplexing SQE 2005, Beijing, Nov. 23 -27 Separating spectral lines using a Michelson interferometer One quantum emitter acts as two independent single photon sources. Delaying the two photons by half the excitation repetition time doubles the photon rate.

Outline SQE 2005, Beijing, Nov. 23 -27 • Introduction and Overview • Single Photon Sources based on Quantum Dots • Multi-Photon Sources • Multiplexed Quantum Cryptography • Demonstration of Deutsch-Jozsa Algorithm • Summary & Outlook

Quantum Cryptography: the BB 84 Protocol SQE 2005, Beijing, Nov. 23 -27 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)

BB 84 Protocol SQE 2005, Beijing, Nov. 23 -27 • Alice sends randomly polarized photons (0, 45, 90 or 135°) to Bob. • Bob randomily 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. . .

Multiplexed Quantum Cryptography SQE 2005, Beijing, Nov. 23 -27

Multiplexed Quantum Cryptography BB 84 Protocol SQE 2005, Beijing, Nov. 23 -27 Alice´s original data Encoded image Bob´s decoded image Transmission to Bob: 30 successfull counts/s at a laser modulation of 20 k. Hz Similarity between Alice´s and Bob´s keys: 95% T. Aichele, G. Reinaudi, O. Benson, Phys. Rev. B, 70, 235329 (2004)

Outline SQE 2005, Beijing, Nov. 23 -27 • Introduction and Overview • Single Photon Sources based on Quantum Dots • Multi-Photon Sources • Multiplexed Quantum Cryptography • Demonstration of Deutsch-Jozsa Algorithm • Summary & Outlook

Deutsch-Jozsa-Problem SQE 2005, Beijing, Nov. 23 -27 Counterfeighter problem Mathematical problem: constant or balanced function? f 01 f 10 f 00 f 11 0 0 1 1 1 0 0 1

Deutsch-Jozsa-Algorithm SQE 2005, Beijing, Nov. 23 -27 Quantum circuit: Four possible functions f(x): f 00 f 11 f 01 f 10 f(0) 0 1 f(1) 0 1 1 0 constant |<1|x>|2 • possibility to decide, if f(x) is balanced or constant using only one evaluation of f(x)! • any classical apparatus would need at least two evaluations of f(x)! 0 0 balanced 1 1

Realization with Linear Optics SQE 2005, Beijing, Nov. 23 -27 qubit |x>: spatial modes of the photon Single photon qubit |y>: polarization of the photon Polarizer • photon state behind polarizer |y>=( |0> - |1> )/21/2 = Hadamard gate for |y> • Implementation of Uf by /2 plates flipped in the beam. E. Brainis et al. , Phys. Rev. Lett. 90, 157902 (2003) M. Michler et al. , Phys. Rev. Lett. 84, 5457 (2000) S. Takeuchi, Phys. Rev. A 62 , 032301 (2000) N. J. Cerf et al. , Phys. Rev. A 57, 1477 (1998) BS 1 and BS 2 represent Hadamard gates for |x> f 00 f 11 f 01 f 10 /2 at {|x>= |0>} out in out In /2 at {|x>= |1>} out in In out

Deutsch-Jozsa-Algorithm: Experimental Results SQE 2005, Beijing, Nov. 23 -27 • distinguishability of balanced from constant function in a single quantum computation with a probability of 85% M. Scholz, S. Ramelow, T. Aichele, O. Benson, submitted • • well controllable single photonic qubit feasibility of upscaling and use in LOQC D. Fattal, E. Diamanti, K. Inoue, Y. Yamamoto, PRL 92, 037904 (2004)

Demonstration of Algorithms and Influence of Decoherence SQE 2005, Beijing, Nov. 23 -27 Single photon sources based on single quantum dots can be used to demonstrate and test influence of noise and decoherence on qubits in quantum algorithms. Hb -Vb E. g. : Encoding of qubits in states that are insensitive to a certain class of (phase) noise • • • BS l/2 Ha -Vb Scholz, et al. , submitted M. Mohseni, et al. , PRL 91, 187903 (2003) M. Bourennane, et al. PRL 92, 107901(2004) PBS phase noise Hb -Vb PBS BS from source Ha -Va Hb -Va

Outline SQE 2005, Beijing, Nov. 23 -27 • Introduction and Overview • Single Photon Sources based on Quantum Dots • Multi-Photon Sources • Multiplexed Quantum Cryptography • Demonstration of Deutsch-Jozsa Algorithm • Summary & Outlook

SQE 2005, Beijing, Nov. 23 -27 Quantum Computing with Single Photons Optical quantum computing based on single photons and linear optics requires triggered indistinguishable photons [Knill, Laflamme, Milburn, Nature 409, 46 (2001)]. Realization of indistinguishable photons and entangled photon pairs in recent experiments by Yamamoto [Santori, et al. , Nature 419, 594 (2002)]:

Summary and Outlook SQE 2005, Beijing, Nov. 23 -27 Demonstration of multiplexed quantum cryptography and realization of a quantum computing algorithm Single photon sources based on quantum dots are a reliable tool for quantum information processing Efficient LOQC based on qdot sources according to KLM [E. Knill, R. Laflamme, and G. J. Milburn, Nature 409, 46 (2000)] can be envisioned Realization of indistinguishable photons (ancillas) Entangled photon pairs on demand Implementations in controlled experiment Next steps Reliable sources of multiple ancilla states Formation of entanglement using cascaded emission Storage of single photons from single quantum dots