1. 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: Single photons on demand: New light for quantum information processing

2. 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: E kin =h -W e-e-

3. 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 Outline

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

5. SQE 2005, Beijing, Nov. 23-27 Motivation Why photons? They interact very weakly with the environment (k b T<<h 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 ].

6. SQE 2005, Beijing, Nov. 23-27 SPS with 100% efficiency SPS with 25% efficiency Introduction Single photons from attenuated light? Attenuation of a light pulse does not change the Poissonian photon statistics. Attenuted light pulses only mimick real single photon sources. There is always a finite probability to find more than one photon per pulse 0123 0.00 0.25 0.50 0.75 1.00 Probability Number of photons Weak pulse with = 0.25

7. SQE 2005, Beijing, Nov. 23-27 1.Coherent evolution (STIRAP and cavity QED) Atoms/ions in cavities Methods to Generate Single Photons on Demand 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)

8. SQE 2005, Beijing, Nov. 23-27 Methods to Generate Single Photons on Demand 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)

9. SQE 2005, Beijing, Nov. 23-27 Methods to Generate Single Photons on Demand 3.Spontaneous emission (single emitters) atoms, molecules, quantum dots, defect centers optical, electrical and STIRAP excitation 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) DC: Kurtsiefer et al., PRL 85, 290 (2000) Beveratos et al., PRA 64, 061802(R) (2001) M: Brunel et al., PRL 83, 2722 (1999) Lounis & Moerner, Nature 407, 491 (2000)

10. 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 Outline

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

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

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

14. SQE 2005, Beijing, Nov. 23-27 Experimental Setup S p e c t r o g r a p h Coincidence counter L a s e r ( c w o r p u l s e d ) Filter Start- APD S t o p - A P D C C D Michelson interferometer Dichroic mirror Hanbury Brown-Twiss correlator Liquid He Cryostat (4 K) Sample g1g2SPS

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

16. SQE 2005, Beijing, Nov. 23-27 InP Quantum Dots in GaInP Emission around 690 nm (@ maximum detection efficiency of Si detectors) Lifetime around 2 ns Dot density: 10 8 cm -2 through 2 nm bandpass filter Linewidth around 100 µeV

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

18. SQE 2005, Beijing, Nov. 23-27 Coincidence counter Wave and Particle Aspects Start- APD S t o p - A P D Pulse counter (DAC) Taylor-experiment (1906) Path length difference T. Aichele, et al., AIP proc. Vol. 750, 35 (2005) V. Jacques, et al. Eur. Phys. J. D 35, 561 (2005)

19. 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 Outline

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

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

22. SQE 2005, Beijing, Nov. 23-27 Cascaded Emission biexciton triexciton exciton 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)

23. SQE 2005, Beijing, Nov. 23-27 Single Photon Multiplexing 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.

24. 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 Outline

25. SQE 2005, Beijing, Nov. 23-27 Quantum Cryptography: the BB84 Protocol Alice Bob Quantum channel Classical public channel: 10 10 Eve Eve cannot copy the photon (no cloning theorem) Bennett, Brassard, Proc. IEEE Int. Conf. on Computers, Systems & Signal Processing (1984), First realization with QDs: Waks et al., Nature 420, 762 (2002)

26. SQE 2005, Beijing, Nov. 23-27 BB84 Protocol 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...

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

28. SQE 2005, Beijing, Nov. 23-27 Multiplexed Quantum Cryptography BB84 Protocol Alice´s original data 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)

29. 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 Outline

30. SQE 2005, Beijing, Nov. 23-27 Deutsch-Jozsa-Problem 0101 0101 1010 0000 1111 f 01 f 10 f 00 f 11 Counterfeighter problem Mathematical problem: constant or balanced function?

31. SQE 2005, Beijing, Nov. 23-27 Quantum circuit:Four possible functions f(x): f 00 f 11 f 01 f 10 f(0)0101 f(1)0110 constantbalanced | | 2 0011 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)! Deutsch-Jozsa-Algorithm

32. SQE 2005, Beijing, Nov. 23-27 qubit |x>: spatial modes of the photon qubit |y>: polarization of the photon photon state behind polarizer |y>=( |0> - |1> )/2 1/2 = Hadamard gate for |y> BS1 and BS2 represent Hadamard gates for |x> Implementation of U f by /2 plates flipped in the beam. f 00 f 11 f 01 f 10 /2 at {|x>= |0>} outinoutIn /2 at {|x>= |1>} outinInout Realization with Linear Optics Polarizer 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) Single photon

33. 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) Deutsch-Jozsa-Algorithm: Experimental Results

34. SQE 2005, Beijing, Nov. 23-27 from source BS PBS phase noise BS H b -V b H a -V a H b -V a H a -V b H b -V b H a -V a /2 Demonstration of Algorithms and Influence of Decoherence Scholz, et al., submitted M. Mohseni, et al., PRL 91, 187903 (2003) M. Bourennane, et al. PRL 92, 107901(2004) 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. E.g.: Encoding of qubits in states that are insensitive to a certain class of (phase) noise

35. 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 Outline

36. SQE 2005, Beijing, Nov. 23-27 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) ]: Quantum Computing with Single Photons

37. 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 Summary and Outlook