From Cavity QED to Quantum Transport

Transcription

1 Dep. of Physics, NTHU Oct. 3 (20) From Cavity QED to Quantum Transport 陳岳男 成功大學物理系 國家理論科學研究中心 ( 南區 )

2 Unified single-photon and single-electron counting statistics: From cavity QED to electron transport Phys. Rev. A 82, (200), N. Lambert, Y. N. Chen*, and F. Nori Distinguishing quantum and classical transport through nanostructures Phys. Rev. Lett. 05, 7680 (200), N. Lambert, C. Emary, Y. N. Chen, and F. Nori. Quantum or not? Mathematical equations resolve nanostructures behavior

3 In collaborations with: Prof. Franco Nori (Riken, Japan) Dr. Clive Emary (TU Berlin, Germany) Dr. Neill Lambert (Riken, Japan) Dr. Guang-Yin Chen (NCKU) Dr. Che-Ming Li (NCKU) 3

4 Outline Coherence and entanglement Quantum Teleportation Cavity QED Time-adjusted Photon Counting Quantum Transport in Organism

5 Quantum Information Teleportation Dense coding Secret sharing Key distribution coherence and entanglement Quantum Computation Algorithms

6 Bit : 0, or +, - or boy, girl. Any two-level system 0 time t 0 t t 2

7 Q-bit: Any two-level and physical system (Quantum bit) Two-level atom 0 0 t 0 t t time

8 Two qbits : two spins time interaction A Spin up B Spin down t 0 A Spin up Schrodinger eq. B Spin down t - A B A B entangled state

9 Entanglement 2 A B 2 A B *.*? Impossible to factory ( a ) A + a2 A ( b ) B + b2 B Symbol of connecting to independent system

10 薛丁格的貓 :To be or not to be?

11 Quantum Teleportation 量子遠傳 ( 隱形傳送 )

12 Teleportation: Science fiction or science? From Prof. Beenakker s web-page

13 Quantum Teleportation In 993 an international group of six scientists, including IBM fellow Charles H. Bennett, confirmed the intuitions of the majority of science fiction writers by showing that perfect teleportation is indeed possible in principle, but only if the original is destroyed.

14 PREPARING FOR QUANTUM TELEPORTATION... Scientific American, April 2000; by Zeilinger QUANTUM TELEPORTATION OF A PERSON (impossible in practice but a good example to aid the imagination) would begin with the person inside a measurement chamber (left) alongside an equal mass of auxiliary material (green).the auxiliary matter has previously been quantum-entangled with its counterpart, which is at the faraway receiving station (right).

15 ... TRANSMISSION OF RANDOM DATA... MEASUREMENT DATA must be sent to the distant receiving station by conventional means.this process is limited by the speed of light, making it impossible to teleport the person faster than the speed of light.

16 ... RECONSTRUCTION OF THE TRAVELER RECEIVER RE-CREATES THE TRAVELER, exact down to the quantum state of every atom and molecule, by adjusting the counterpart matter s state according to the random measurement data sent from the scanning station.

17 Quantum teleportation across the Danube R. Ursin et al. describe the high-fidelity teleportation of photons over a distance of 600 metes across the River Danube in Vienna. Nature 430, 849 (2004)

18 Teleportation with real atoms:. Deterministic quantum teleportation with atoms M. RIEBE et al., Nature 429, 734 (7 June 2004) With calcium ions 2. Deterministic quantum teleportation of atomic qubits M. D. BARRETT et al., Nature 429, 737(7 June 2004) With atomic ( 9 Be + ) ions

19 Proposal for teleportation in solid state system Phys. Rev. Foucs, 6 February 2004 Beam Up an Electron! C. W. J. Beenakker and M. Kindermann, Phys. Rev. Lett. 92, 05680(2004)

20 Local Unitary Operations U NOTATION Qubit is denoted by horizontal line Single-qubit unitary transformation U : H PATICULAR UNITARY OPERATIONS Hadamard transform 2 H Unilateral Pauli rotations 0 0 x 0 0 i i y 0 0 z

21 Collective Unitary Operations controlled-not(xor) transformation a b a a b addition modulo CNOT T C T C CNOT T C T C 0 CNOT

22 Maximally Entanglement Generation H 00 ( 0 ) ( 0 ) 2 0 ( 0 ) 0 2 ( 0 ) 2 ( 00 2 )

23 Quantum Network for Teleportation 0 0 One qbit Quantum channel One bit Classical channel Entanglement Source H H Party I : ALICE Party II : BOB M M M U σ I σ σ x z y U ( ( 2 ( 2 ( 2 ) ) ) ) ( 0 )[ ( 00 )] 2 ( )] 2 [ 2 ( 0 ( ) 0 ) ( 0 ( ) 0 )] Party I : ALICE H [ 00 ( 0 ) ( 0 ) ( 0 ) ( 0 )]

24 Teleportation of Nonclassical Wave Packets of Light N. Lee et al., Science 332, 330 (20) Quantum Teleportation Between Distant Matter Qubits S. Olmschenk et al., Science 323, 486 (2009) Quantum teleportation between light and matter J. F. Sherson et al., Nature 443, 557 (2006)

25 Cavity QED

26 Spontaneous emission of single two-level atom Interaction between a two-level atom and the photon reservoir: H b q In the interaction picture, the state vector :, where q Db e q q iqx : photon operator H. c. ( t) f0( t) ;0 f q t : creating operator of atom q ( ) ; q ;0 ; q : an atom initially in the excited state : a photon of q in the radiation field

27 Results :, ) 0 ( t t i e t f where is the decay rate represents the Lamb Shift The radiation intensity distribution : ) ( ) ( c q D t f q q, where 0 is the energy spacing q q q q c q D c q D ), (

28 Two-level atom inside a cavity The interaction between the atom and single-mode cavity: ( t) f ( t) ;0 f ( t) ;

29 Vacuum Rabi oscillations J. M. Raimond, M. Brune, and S. Haroche, Rev. Mod. Phys. 73, 565 (200).

30 Vacuum Rabi splitting

31 Self-Assembled QDs

32 Colloidal QDs

33 Gate-confined Double Quantum Dots

34 Quantum Coherence in Double Quantum Dots

35 K. D. Petersson, J. R. Petta, H. Lu, and A. C. Gossard, PRL 05, (200)

36 Question: Are they truly quantum?

37 Quantum vs Classical Bell s Inequality: Locality and Realism 2 0 0

38 The Bell-CHSH inequality A, a, B, b, A a, Aa(0, 2),( 2,0) AaB Aab 2,2 2 AB Ab ab ab 2 AB Ab ab ab 2

39 Predictions of QM for the singlet state AB Aˆ Bˆ cos AB

40 QM violates the Bell-CHSH inequality ab ab Ab AB ab ab Ab AB F cos cos cos cos QM 2 ) / ( ˆ 2 ) / ( ˆ ˆ ˆ x y x y y x b B a A 2!!! 2 2 QM F

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42 Leggett-Garg Inequality (Bell s inequality in time) Realism and non-invasive measurement Quantum mechanics versus macroscopic realism: Is the flux there when nobody looks? Leggett and Garg, Phys. Rev. Lett. 54, (985)

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44 Palacios-Laloy, A. et al. Nature Phys. 6, (200).

45 Distinguishing Quantum and Classical Transport through Nanostructures Transport Charge Inequality: N. Lambert, C. Emary, Y. N. Chen, and F. Nori, Phys. Rev. Lett. 05, 7680 (200)

46 Double Quantum Dot

47 Violation of charge inequality for DQD

48 DQD current inequality

49 Violation of DQD current inequality

50 Comparison between DQD and CQED systems

51 Time-adjusted photon counting

52 Comparison between the properties of the cavity-qed system a double quantum dot N. Lambert, Y. N. Chen*, and F. Nori, Phys. Rev. A 82, (200)

53 Violation of the extended LG inequality for typical parameters in singlephoton cavity-qed experiments

54 What else? Cavity QED without Cavity

55 Dicke s superradiance for two atoms The interaction : H x c j j : : j,2 q D b q q c j e iqx position of the j th atom j H. c. raising operator of the j th atom One can define the so-called Dicke states : T T S T

56 Decay scheme for two-atom system Limiting case : << wavelength of the photon +=2, - =0

57 Measurements of superradiance Experiment in real atoms: [R. G. DeVoe and R. G. Brewer, P. R. L. 76, 2049 (996)]

58 Cavity QED without cavity M. O. Scully, A. A. Svidzinsky, Science 325, 50 (2009)

59 Quantum Signatures in a Macroscopic Dipole Moment

60 Violation of the effective photon-current inequality G. Y. Chen, N. Lambert, C. M. Li, Y. N. Chen*, and F. Nori, in preparation (20)

61 Quantum Transport in Organism?

62 The Quantum Dimension Of Photosynthesis

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67 Pigments (BChl) Leggett-Garg inequality? Reaction Center

68 Summary. Coherence and Entanglement 2. Teleportation 3. Extended LG inequalities 4. Time-adjusted photon counting 5. Quantumness in Biological Systems

69 Thank you for your attention! To boldly go where no man has gone before!