classical states of light: generation and applications

Transcription

1 Hybrid entanglement between quantum and classical states of light: generation and applications 12 December, APCWQIS 2014, Tainan, Taiwan Hyunseok Jeong Center for Macroscopic Quantum Control Department of Physics and Astronomy Seoul National University The Brussels Journal (29 October 2007)

2 SNU Quantum Group

3 SNU Quantum Group HJ (Group leader) Seung-Woo Lee Chae-Yeun Park Jinwoo Park (PhD) (Research Faculty) (PhD) Hoyong Kim (PhD) Youngrong Lim (PhD) Minsu Kang (PhD) Seung Lee Bae (PhD) Seung Ho Yang (PhD) Hyukjoon Kwon (PhD)

4 Collaborators Florence Group Alessandro Zavatta Luca S. Costanzo Samuele Grandi Marco Bellini SNU Group Hyunseok Jeong Minsu Kang Seung-Woo Lee Uni of QLD Timothy C. Ralph

5 Collaborators Florence Group Alessandro Zavatta Luca S. Costanzo Samuele Grandi Marco Bellini Myungshik Kim (Imperial) Jinhyoung Lee (HYU) SNU Group Hyunseok Jeong Minsu Kang Seung-Woo Lee Chang-Woo Lee (now at KIAS) Hyukjoon Kwon Hoyong Kim Jonas S. Neergaard-Nielsen (now at TUD) Yujiro Eto Masahide Sasaki (NICT) Uni of QLD Timothy C. Ralph

6 Contents Hybrid entanglement as a Schrödinger cat state All-optical quantum information processing using hybrid entanglement Generation scheme and experimental results entangling quantum and classical states

7 E. Schrödinger, Naturwissenschaftern. 23 (1935) Alive 1 2 e g Dead The Brussels Journal (29 October 2007) 1 1 ( e g ) Alive 2 2 e Alive g Dead Entanglement between quantum and classical systems

8 n 2 Ch Coherent state: tt /2 e n Classical n0 n! Coherent states are most classical among all pure states - semi-classical descriptions available - most robust against decoherence ( pointer states ) The two coherent states > and - > are classically (or macroscopically) distinguishable for >>1, i.e., they can be well discriminated by a homodyne measurement (HD) with limited efficiency. (For 70% of HD efficiency: D99.7% for =1.6 and D>99.9% for =2.0.) Single photon: 1 Non-classical Discrete light quantum containing the minimum quantized amount of energy available at a given frequency. Negative values in well-known quasi-probability distributions such as the Wigner function.

9 1 2 H V 1 2 e Alive g Dead

10 What is the correct measure of Schrödinger s-cattiness? Ideally, one would like a quantitative measure which corresponds to our intuitive sense; I shall attempt one below, but would emphasize that the choice between this and a number of similar and perhaps equally plausible definitions is, with one important exception (see below), very much a matter of personal taste, and that I very much doubt that 50 years from now anything of importance will be seen to have hung on it. (A. J. Leggett, J. Phys.: Condens. Matter 14 (2002) R415 R451)

11 References taken from H. Jeong, M. Kang and H. Kwon, Characterizations and quantifications of macroscopic quantumness and its implementations using optical fields (Review article) Special Issue on Macroscopic Quantumness, Optics Communications 337, (2015)

12 C.-W. Lee and H. Jeong, Phys. Rev. Ltt106 Lett. 106, (2011) It can be applied to any harmonic oscillator systems such as light fields. Independent of the decomposition of the component states. For an arbitrary state, t it simultaneously l quantifies (1) how far-separate the component states of the superposition are and (2) the degree of genuine quantum coherence between the component states against their classical mixture.

13 Schrödinger cat states of light: i cat N e >>1 Xˆ Pˆ aˆ aˆ i( aˆ aˆ ) Wigner function A. Ourjoumtsev, H. Jeong, R. Tualle-Brouri and Ph. Grangier, Nature 448, 784 (2007) Evidence of fquantum interference

14 I Wigner function

15 Wigner function I

16 1 2 H V 2 I - maximum value 1 n 0 0 n H N V N

17 Micro-macro entanglement or macro-macro entanglement as analogies of Schrödinger s thought experiment

18 N. Bruno et al., Nature Physics 9, 545 (2013); A. I. Lvovsky et al. Nature Physics 9, 541 (2013) D ( ) = D ( ) = D ( ) D ( ) D ( ) D ( )

19 N. Bruno et al., Nature Physics 9, 545 (2013); A. I. Lvovsky et al. Nature Physics 9, 541 (2013) D ( ) = D1 ( ) D D( ) 0 1 ( ) 0 1 H. Jeong, M. Kang and H. Kwon, Optics Communications 337, (2015) (2014)

20 1 2 H V H K d H J "Vi l ti f H. Kwon and H. Jeong, "Violation of the Bell-Clauser-Horne-Shimony-Holt inequality using imperfect photodetectors with optical hybrid states," Phys. Rev. A 88, (2013).

21 Contents Hybrid entanglement as a Schrödinger cat state All-optical quantum information processing using hybrid entanglement Generation scheme and experimental results

22 Schemes for all-optical quantum computation Single photon qubits H 0, V 1 L L qubit ah bv Coherent state qubits 0, 1 L qubit a b L CSQC ploqc The best compromise for medium scale quantum computing (100s of logical l operations) appear to be the CSQC scheme and the Parity State scheme. T. C. Ralph and G. J. Pryde, Progress in Optics, Ed. E.Wolf, 54, 209 (2009)

23 Teleportation and quantum gates using coherent state qubits (Jeong et al., PRA 2001, Jeong and Kim, PRA 2002, Ralph et al., Proc. SPIE 2002, Ralph et al., PRA 2003) Nearly deterministic Bell measurement Alice Bob U cat B: Bell measurement Input state cat From Jeong et al., PRA 64, (2001) N ( ) B00 N ( ) From Ralph et al., PRA 68, (2003) Single qubit rotation (Z-rotation) cannot be realized deterministically. Sensitive to photon losses Optimized value ~1.6 [Lund et al. PRL 2008]

24 S.-W. Lee and H. Jeong, "Near-deterministic quantum teleportation and resource-efficient quantum computation using linear optics and hybrid qubits," Phys. Rev. A 87, (2013). a H b V Single-photon mode Coherent-state mode

25 Abi Arbitrary Z rotations Single-qubit rotation a H bv a H be i i V Pauli X (bit flip) Photon-qubit flip -phase shifter H V a H bv a V b H

26 S.-W. Lee and H. Jeong, Phys. Rev. A 87, (2013) Failure probability P f e 2 2 / 2 P P f f ~06%for ~0.6% ~ 0.02% for 2 Universal gate operations can be performed using gate teleportation in a nearly deterministic manner.

27 Ralph-Pryde diagram

28 Ralph-Pryde diagram S.-W. Lee and H. Jeong, Phys. Rev. A 87, (2013)

29 1 2 H V

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31 Cross-Kerr nonlinearity

32 Cross-Kerr nonlinearity Highly nontrivial and demanding

33 Contents Hybrid entanglement as a Schrödinger cat state All-optical quantum information processing using hybrid entanglement Generation scheme and experimental results

34 1 2g F g F 0.998

35 ∠0 p x 0 p x

36 Single photon addition Downconverter Pump stop click [Zavatta et al., Science, 2004 ]

37 Generation of hybrid entanglement r:t Pump stop click silent Pump Downconverter

38 Generation of hybrid entanglement r:t Pump stop click silent Pump Downconverter

39 Generation of hybrid entanglement r:t Pump stop click silent Pump Downconverter

40 Generation of hybrid entanglement r:t Pump stop click silent Pump Downconverter

41 Generation of hybrid entanglement r:t Pump stop click silent Pump Downconverter

42 Generation of hybrid entanglement r:t Pump stop click silent Pump Downconverter

43 Classical information Alice Long distance Noisy environment Schrodinger cat state Bob Reconstructed state Input state J S N d Ni l Y Et C W L H J d J. S. Neergaard-Nielsen, Y. Eto, C.-W. Lee, H. Jeong and M. Sasaki, Nature Photonics (2013)

44 ImprovedFidelity Success Probability bili H. Jeong, A. Zavatta, M. Kang, S.-W. Lee, L.S. Costanzo, S. Grandi, T.C. Ralph & M. Bellini, Nature Photonics 8, 564 (2014).

45 Entangling quantum and classical states of light Hyunseok Jeong, Alessandro Zavatta, Minsu Kang, Seung-Woo Lee, Luca S. Costanzo, Samuele Grandi, Timothy C. Ralph & Marco Bellini, Nature Photonics 8, 564 (2014).

46 H. Jeong, A. Zavatta, M. Kang, S.-W. Lee, L.S. Costanzo, S. Grandi, T.C. Ralph & M. Bellini, Nature Photonics 8, 564 (2014).

47 State Saetomography ogap yand dentanglement ge e Photon added coherent state Coherent state H. Jeong et al. Nature Photonics 8, 564 (2014) f 1 i F 0.76 NPT 0.45

48 State Saetomography ogap yand dentanglement ge e Photon added coherent state Coherent state H. Jeong et al. Nature Photonics 8, 564 (2014) f f 1 i F 0.76 NPT 0.45 Next challenge

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50 We have studied hybrid entanglement of light: Interesting an analogy of Schrödinger s cat Useful for optical quantum information processing We ve made it (in a small scale).

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