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Teleportation of Quantum Dot Exciton Qubits via Superradiance

Aug. 5, 2005 Center for Theoretical Sciences NCKU. Teleportation of Quantum Dot Exciton Qubits via Superradiance. Yueh-Nan Chen ( 陳岳男 ) and Che-Ming Li Group leader : Prof. Der-San Chuu Dep. of Electrophysics, NCTU, Taiwan Collaborator : Prof. Tobias Brandes ( Univ. of Manchester ).

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Teleportation of Quantum Dot Exciton Qubits via Superradiance

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  1. Aug. 5, 2005 Center for Theoretical Sciences NCKU Teleportation of Quantum Dot Exciton Qubits via Superradiance Yueh-Nan Chen (陳岳男) and Che-Ming Li Group leader : Prof. Der-San Chuu Dep. of Electrophysics, NCTU, Taiwan Collaborator :Prof. Tobias Brandes (Univ. of Manchester)

  2. 感謝 1. 國科會特約博士後研究計畫： 介觀物理系統在光子晶體中的量子散粒雜訊 NSC 94-2112-M-009-019 計畫主持人：陳岳男 共同主持人：鄭舜仁 2. 國科會奈米計劃： 奈米結構的空腔量子電動力學及量子傳 NSC 94-2120-M-009-002 計畫主持人：褚德三 共同主持人：許世英，林俊源，朱仲夏，趙天生 計畫參與人員：林高進、邱裕煌、李哲明、廖英彥、 簡賸瑞、唐英瓚

  3. Outline • Brief review of quantum teleportation • Brief review of superradiance (collective decay) • Teleportation of charge qubits via superradiance • in purely quantum optic system • 4. Extension to quantum dot systems • 5. Summary

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

  5. Quantum Teleportation In 1993 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.

  6. 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).

  7. ... TRANSMISSION OF RANDOM DATA ... MEASUREMENT DATAmust 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.

  8. ... 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.

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

  10. Teleportation with real atoms: 1. Deterministic quantum teleportation with atoms M.RIEBE et al.,Nature429, 734 (17 June 2004) With calcium ions 2. Deterministic quantum teleportation of atomic qubits M.D.BARRETT et al., Nature429, 737(17 June 2004) With atomic (9Be+) ions

  11. Proposal for teleportation in solid state system Phys. Rev. Foucs, 6February2004 “Beam Up an Electron!” C. W. J. Beenakker and M. Kindermann,Phys. Rev. Lett. 92, 056801(2004)

  12. teleportation Creation of an entangled electron-hole pair. An electron meets a hole.

  13. Local Unitary Operations NOTATION U Single-qubit unitary transformation U : Qubit is denoted by horizontal line PATICULAR UNITARY OPERATIONS Hadamard transform H H Unilateral Pauli rotations

  14. Collective Unitary Operations controlled-NOT(XOR) transformation addition modulo 2

  15. Maximally Entanglement Generation H

  16. Quantum Network for Teleportation One qbit Quantum channel H M One bit Classical channel M U M Entanglement Source PartyI: ALICE H Party II: BOB U PartyI: ALICE H

  17. 2. Brief review of superradiance

  18. Spontaneous emission of a single two-level atom • Interaction between a two-level atom and the photon reservoir: • In the interaction picture, the state vector : , where : an atom initially in the excited state : a photon of q in the radiation field

  19. Results : where  is the decay rate  represents the Lamb Shift , where is the energy spacing

  20. Spontaneous emission from two atoms The interaction : position of the j th atom raising operator of the j th atom One can define the so-called Dicke states :

  21. Decay scheme for two-atom system : Limiting case : << wavelength of the photon   +=2, - =0

  22. Measurements of superradiance in previous works Experiment in real atoms: [R. G. DeVoe and R. G. Brewer, P. R. L. 76, 2049 (1996)]

  23. 3. Teleportation of charge qubits via superradiance • in purely quantum optic system

  24. Teleportation of charge qubit to cavity photon state teleportation  2 +  2 Cavity photon 1 1 2 entangled Collective decay trap leakage detector detector

  25. The scheme: The interaction between the atom and single-mode cavity: With the appropriate preparation of the initial state of atom-1 and the control of its passing time through the cavity, the singlet entangled state is created between atom-1 and the cavity photon.

  26. How to distinguish between super- and sub-radiance? Our proposal: superradiant detector subradiant detector

  27. The advantages: It’s a “one-pass” process! i.e. the Hadamard and CNOT transformations are omitted and the joint measurements are performed naturally by collective decay. The disadvantages: The maximum successful chance is 50%. (can be modified to teleportation with insurance by “redundant encoding”) [S. J. van Enk et al., Phys. Rev. Lett. 78, 4293 (1997)]

  28. 4. Extension to solid-state systems QD excitons

  29. Recent experiment on QD excitons (I) • The QD exciton states are constructed from electron (e) and heavy hole (h) single-particle basis states with spin projections along the QD growth axis (z) of • However, the and eigenstates are often mixed in dots with reduced symmetry, forming two linearly polarized eigenstates separated by the anisotropic e–h exchange splitting of a few times 10 eV.

  30. Optically programmable electron spin memory using semiconductor quantum dots Miro Kroutvar et al., Nature, 432, 81 (2004). To enable optical selection of pure spin states, magnetic field (B=4T) is applied to the QDs, such that Zeeman splitting > anisotropic e–h exchange splitting

  31. Teleportation of QD exciton qubit to photonic qubit

  32. Recent experiment on QD excitons (II) It is now possible to generate single-photon electrically! [Z. Yuan et al., Science 295, 102 (2002).]

  33. Energy-band diagram of the p-i-n junction: Typical InAs QD exciton decay time: 1.3ns.

  34. Current detection of superradiance 1. Current through dot-1. 2. Superradiance between dot-1 and dot-2 excitons. D (U): coupling constant between D (U) state and hole (electron) reservoir are the super-radiant and sub-radiant decay rate

  35. Double-dot embedded inside a rectangular microcavity with length   

  36. Expectation value of the entangled state <nT> and <nS> in a rectangular microcavity Solid line Dashed line [Y. N. Chen, D. S. Chuu, and T. Brandes, Phys. Rev. Lett. 90, 166802 (2003)]

  37. Teleportation with semiconductor QD excitons metal contact Vg3 Vg1 n-GaAs insulator insulator 1 2 InAs QDs 3 entangled p-GaAs collective decay Steps: • Subradiance-induced singlet entangled state is generated between QD 1 and 2. • The bandgap of the exciton in QD 3 (1) is tuned to be (non)-resonant with that in QD 2. • A joint measurement is done naturally by collective decay of QD 2 and3. • [Y. N. Chen et al., cond-mat/0502412]

  38. Some remarks about the fidelity of the entangled state: When one starts to tune the energy band gap of QD 1, the excitons in QD 1 and 2 will no longer decay collectively but are described by the following interactions, The fidelity of the singlet entangled state after the tuning time t is ( The initial condition is )

  39. Existing experimental parameters: • The lifetime of QD excitons in a microcavity is shown to be greatly inhibited (≥10ns) by tuning the level-spacing 4 meV away from the resonant mode. • [M. Bayer et al., Phys. Rev. Lett. 86, 3168 (2001)] • 2. The tuning pulse from the gate voltage is a step-like function with raising time 40ps. • [Y. Nakamura et al., Nature 398, 786 (1999)] The fidelity of the entangled state can be as high as 0.98.

  40. Detection scheme in QDs: Angle resolved measurement. (x) • Time resolved measurement is required! • But, it’s a statistical average, there must be errors! • The steps: • Setting the border line of time to distinguish between • super- and subradiance. • 2. Estimating the success probability P. • - For the ration (super/sub) of (1+0.7)/(1-0.7), • P is about 0.47.

  41. Another proposal for QD excitons (II) Experimental setup for entanglement generation Vi V Au ZnTe n+-ZnSe GaAs 45° 45° CdTe quantum dots

  42. Summary • We have proposed a teleportation • scheme based on superradiance. • 2. This scheme can be applied to both • purely quantum optic and solid state • QD systems. Y. N. Chen et al. cond-mat/0502412 (2005). To appear in “New Journal of Physics” (2004 impact factor: 3.1)

  43. superradiant detector subradiant detector

  44. Current detection of superradiance 1. Current through dot-1. 2. Superradiance between dot-1 and dot-2 excitons. D (U): coupling constant between D (U) state and hole (electron) reservoir are the super-radiant and sub-radiant decay rate

  45. Some remarks about the fidelity of the entangled state: When one starts to tune the energy band gap of QD 1, the excitons in QD 1 and 2 will no longer decay collectively but are described by the following interactions, The fidelity of the singlet entangled state after the tuning time t is ( The initial condition is )

  46. You were searching for : (taiwan <IN> aff)You found 13 out of 3319 (13 returned) What about the other countries? China : 284 Japan : 232 Brazil : 57 Korea: 49 Singapore : 47 Hong Kong : 43 Taiwan : 13 Turkey : 8

  47. Existing experimental parameters: • The lifetime of QD excitons in a microcavity is shown to be greatly inhibited (≥10ns) by tuning the level-spacing 4 meV away from the resonant mode. • [M. Bayer et al., Phys. Rev. Lett. 86, 3168 (2001)] • 2. The tuning pulse from the gate voltage is a step-like function with raising time 40ps. • [Y. Nakamura et al., Nature 398, 786 (1999)] The fidelity can be as high as 0.98.

  48. Current through the double-dot In plotting the figure we have assumed : D =1 ,U =0.2 , and  =1/(1.3[ns]) (in free space). , where  is the decay rate of the quantum dot exciton • As the inter-dot distance is close enough, the current is inhibited. • The current shows oscillatory behavior as a function of inter-dot distance — superradiant effect!

  49. Decay rate 1/1.3(ns) Constant speed 1/10(ns) t t

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