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Quantum Foundations in Mesoscopic Physics

Mesoscopic Physics & Quantum Information  Lab.     . 2008. 1. 9 – 11 @ KIAS-SNU Physics Winter Camp. Quantum Foundations in Mesoscopic Physics. Kicheon Kang ( 강기천 ). Department of Physics Chonnam National University http://meso.chonnam.ac.kr.

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Quantum Foundations in Mesoscopic Physics

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  1. Mesoscopic Physics & Quantum Information  Lab.      2008. 1. 9 – 11 @ KIAS-SNU Physics Winter Camp Quantum Foundations in Mesoscopic Physics Kicheon Kang (강기천) Department of Physics Chonnam National University http://meso.chonnam.ac.kr

  2. Mesoscopic Physics & Quantum Information  Lab.      Outline • 양자역학의 기묘함 - 중첩, 우연, 상보성, 비국소성, 측정문제 • 중시계 물리학 (Mesoscopic Physics) - Quantum transport, interference, and shot noise • 중시계에서 양자역학의 근본문제 공부하기 - Complementarity and nonlocalitytest

  3. Mesoscopic Physics & Quantum Information  Lab.      Outline • 양자역학의 기묘함 - 중첩, 우연, 상보성, 비국소성, 측정문제 • 중시계 물리학 (Mesoscopic Physics) - Quantum transport, interference, and shot noise • 중시계에서 양자역학의 근본문제 공부하기 - Complementarity and nonlocalitytest

  4. Mesoscopic Physics & Quantum Information  Lab.      양자역학의 기묘함 • 중첩 (superposition) • 객관적 우연 (indeterminism) • 상보성 (complementarity) • 비국소성 (nonlocality) ~ quantum entanglement • “측정문제 (measurement problem)” ~ wave function collapse • ……

  5. Mesoscopic Physics & Quantum Information  Lab.      중첩 (Superposition) Charles Addams, The New Yorker Magazine 1940

  6. Mesoscopic Physics & Quantum Information  Lab.      객관적 우연 (Indeterminism) Quantum Coin 우연 = intrinsic absence of information 동전 던지기 우연 = 무지 (주관적) (lack of knowledge) or measurement

  7. “Stop telling God what to do! (신에게 명령하는 것을 중단하시죠!)” “ God does not play dice (신은 주사위 놀이를 하지 않는다) ” Mesoscopic Physics & Quantum Information  Lab.      객관적 우연 (Indeterminism) A. Einstein vs. N. Bohr

  8. “detector”(environment) states Interference term in the distribution at the rc: measure of the indistinguishability • “Wave-particle duality” or “complementarity” (‘detection’) (no ‘detection’) Mesoscopic Physics & Quantum Information  Lab.      상보성 (Complementarity): Behavior of aQuanton Interference fringe or distinguishability rc Screen Electron gun

  9. 비국소성 (Nonlocality) a b Mesoscopic Physics & Quantum Information  Lab.      Einstein, Podolsky, Rosen (1935) The EPR Paradox (Bohm’s version) Cf. Classical correlation There is correlation, but ‘measurement’on a particle does not affect the (probability of) outcome of the other Entangled state (quantum correlation): • Bell’s inequality (1966) : An inequality that any local hidden variable theory should satisfy • Experiment agrees with the prediction of quantum theory (Aspect et al. (1982)etc.) ”Spooky action at a distance” (원거리에서의 ‘유령의’ 작용)

  10. Mesoscopic Physics & Quantum Information  Lab.      측정문제 (Measurement problem) measurement Wave function (before measurement) A measurement cannot be described in terms of Collpase of the wave function - 파동은 갑자기 어디로 갔나? - 그러면 ‘waving’ 하던 것은 무엇인가?

  11. Mesoscopic Physics & Quantum Information  Lab.      양자역학에 대처하는 우리의 자세 • “Shut up and calculate” interpretation- Dirac, etc. • Copenhagen (Orthodox) Interpretation “No elementary phenomenon is a phenomenon until it is observed.”- Niels Bohr - • Search for the hidden variable (deterministic) theory - de Brogile, Einstein, Bohm, etc. • Matter & mind (quantum & classical) - Wigner, etc. • Many-world interpretation - Everett, etc. • …..

  12. Mesoscopic Physics & Quantum Information  Lab.      양자역학의 기묘함 • 중첩 • 객관적 우연 • 상보성 (complementarity) • 비국소성 (nonlocality) ~ quantum entanglement • “측정문제 (measurement problem)” ~ wave function collapse • …… ** Attention! All these properties are the basic resources for quantum communication and computation.

  13. Uncertainty & Double-Slit Experiment Screen Electron gun Mesoscopic Physics & Quantum Information  Lab.      R. Feynman (1965) d Disturbance of electron momentum: D p > h/d requiredto get the which-path information (Dx < d) - This “momentum kick” washes out the interference fringe

  14. Uncertainty & Double-Slit Experiment Mesoscopic Physics & Quantum Information  Lab.      R. Feynman (1965) “It is impossible to design an apparatus to determine which hole the electron passes through, that will not at the same time disturb the electrons enough to destroy the interference pattern.” Heisenberg’s uncertainty principle:

  15. ‘Complementarity Beyond Uncertainty’ (?) Mesoscopic Physics & Quantum Information  Lab.      (M. O. Scully et al. (1991)) “No! it is possible to design experiments which provide which-path information via detectors which do not disturb the system in any noticeable way, (i.e. due simply to the establishing of quantum correlations)” Quantum Eraser  Loss of interference may not be irreversible: Which-path information can be erased by a suitable measurement on the detector.

  16. Realization of Quantum Eraser with Entangled Photons Mesoscopic Physics & Quantum Information  Lab.      Which-path information can be erased by a suitable measurement on the detector (i.e., its entangled twin). • A.G. Zajonc et al., Nature 353, 507 (1991). • P.G. Kwiat et al., PRA 45, 7729 (1992). • T.J. Herzog et al., PRL 75, 3034 (1995). • T.-G. Noh & C.K. Hong, JKPS 33, 383 (1998). • Y.-H. Kim et al., PRL 84, 1 (2000). • ……

  17. Realization of Quantum Eraser with Entangled Photons Mesoscopic Physics & Quantum Information  Lab.      T.G. Noh & C.K. Hong, JKPS, JOSA (1998) - No interference in the single photon detection (complete WP information carried by its entangled twin) - WP information is erased by the coincidence count and the hidden coherence reappears!

  18. Realization of Quantum Eraser with Entangled Photons Mesoscopic Physics & Quantum Information  Lab.      Y.H. Kim et al., PRL (2000) LA, LB >> L0: Choice of ‘wave-like’ or ‘particle-like’ behavior can be delayed after the detection of signal photon R01 R02 LA LB L0 D0 Counts R03

  19. Mesoscopic Physics & Quantum Information  Lab.      Outline • 양자역학의 기묘함 - 중첩, 우연, 상보성, 비국소성, 측정문제 • 중시계 물리학 (Mesoscopic Physics) - Quantum transport, interference, and shot noise • 중시계에서 양자역학의 근본문제 공부하기 - Complementarity and nonlocalitytest

  20. Mesoscopic Physics & Quantum Information  Lab.      What is ‘Mesoscopic’ ?

  21. Mesoscopic Physics & Quantum Information  Lab.      Fermi Wavelength (lF) & Dimensionality

  22. gates Mesoscopic Physics & Quantum Information  Lab.      2-Dimensinal Electron Gas (2DEG) The best solid-state system for studying quantum physics! - High mobility/coherence due to the separation of the conduction channel and doped region - Etching/gating required to get lower dimension (wire, dot)

  23. Mesoscopic Physics & Quantum Information  Lab.      Conductance Quantization Van Wees et al. (1988), D.A. Wharam et al. (1988) Conductance (G) vs. transmission amplitude (tn) (Landauer formula) - Ballistic, coherent motion of electrons

  24. Mesoscopic Physics & Quantum Information  Lab.      Quantum Dots Charge and energy quantization : level discreteness : charging energy of single electron, : Coulomb blockade, single electron tunneling : resonant tunneling (phase-coherent)

  25. Mesoscopic Physics & Quantum Information  Lab.      Resonant Tunneling through a Quantum Dot Coherent resonant tunneling through a single QD level (e0) Phase information cannot be extracted in this geometry

  26. Double-Slit Aharonov-Bohm Interferometer Mesoscopic Physics & Quantum Information  Lab.      Schuster et al., Nature (1997) Coulomb blockade oscillation • Double-slit type • AB oscillation: • Very small probability • of multiple reflections

  27. QD QPC : Change in the # of electrons crossing the QPC > Quantum shot noise Mesoscopic Physics & Quantum Information  Lab.      Controlled ‘Dephasing’ via Charge Detection: Heuristic Argument Aleiner et al., PRL (1997) Detection due to change of transmission probability Binomial random distribution : For td << tdwell, the electron will be detected!

  28. Mesoscopic Physics & Quantum Information  Lab.      Controlled Dephasing in a Which-Path Interferometer Buks et al., Nature (1998) Visibility reduced by charge detection Detector sensitivity

  29. : Change in the phase of electrons crossing the QPC > Phase flutuation Mesoscopic Physics & Quantum Information  Lab.      Phase-Sensitive Detection QD Detection due to change of scattering phase (not observed) QPC Phase-sensitive detection

  30. Mesoscopic Physics & Quantum Information  Lab.      Phase-Sensitive Detection: Experiment Sprinzak et al., PRL (2000)

  31. A Mesoscopic Two-path Interferometer Mesoscopic Physics & Quantum Information  Lab.      - Electronic analogue of optical Mach-Zehnder interferometer Optical Mach-Zehnder Interferometer ~100% visibility, sensitive phase measurement Solid-State Mach-Zehnder Interferometer? E B >>0 B Edge state  Electron beam M : Mirror BS : Beam Splitter S : Source D : Detector Quantum Point Contact  Beam splitter

  32. A Mesoscopic Two-path Interferometer Mesoscopic Physics & Quantum Information  Lab.      - Electronic analogue of optical Mach-Zehnder interferometer Y. Ji et al., Nature (2003) Optical Mach-Zehnder interferometer quantum Hall edge state  Electronic beam quantum point contact (QPC) Beam splitter

  33. Mesoscopic Physics & Quantum Information  Lab.      Outline • 양자역학의 기묘함 - 중첩, 우연, 상보성, 비국소성, 측정문제 • 중시계 물리학 (Mesoscopic Physics) - Quantum transport, interference, and shot noise • 중시계에서 양자역학의 근본문제 공부하기 - Complementarity and nonlocalitytest

  34. Complementarity Test in a Two-Path Interferometer I Single particle interference: Fringe visibility is proportional to |n | Two particle interference: (for a symmetric BS-1, BS-2) : visibility independent of |n| : WP information erased by the projective measurement in the detector Measure of the indistinguishability Mesoscopic Physics & Quantum Information  Lab.      KK, PRB (2007) Coulomb interactions  modified trajectories  Entanglement Two particle state at this stage: For symmetric BS-1 & BS-3 with Df=p ‘Bell state’

  35. Complementarity Test in a Two-Path Interferometer I Mesoscopic Physics & Quantum Information  Lab.      KK, PRB (2007) • In summary: • Interferometer-detector entanglement through the elastic Coulomb interaction • The entanglement and the WP information encoded in the relative phase Df • Single particle interference suppressed by the WP information • The WP information encoded in the phase is erased by the coincidence count, because the electron count in the detector deletes the phase information • The interference reappears

  36. Complementarity Test in a Two-Path Interferometer I Mesoscopic Physics & Quantum Information  Lab.      KK, PRB (2007) In solid-state circuit: “Entangled many-body transport state”: (two input electrodes are biased with voltage V) Current (Ia) and cross correlation (Sag) Single-pariticle detection & joint-detection probability can be obtained from the current and cross correlation measurement

  37. Experimental Realization! Mesoscopic Physics & Quantum Information  Lab.      I. Neder et al., PRL (2007) detector input interferometer input Interferometer & detector output • Two edge states of filling factor 2: outer channel - interferometer • inner channel - detector • Coulomb interaction between the two channels  phase shift  entanglement • Total current fluctuations (shot noise) in D2: Cross correlation

  38. Experimental Realization! Mesoscopic Physics & Quantum Information  Lab.      Low detector voltage High detector voltage current Almost perfect WP detection • Single particle interference is suppressed by the WP information • Interference is recovered by the cross correlation shot noise

  39. Complementarity Test in a Two-Path Interferometer II Mesoscopic Physics & Quantum Information  Lab.      KK, PRB (2007) Two particle interference: + Two coupled Mach-Zehnder interferometers Output currents at lead a, b are not affected by the presence of another beam splitter ‘Particle-like’ or ‘wave-like’ behavior can be chosen by controlling the detector

  40. Complementarity Test in a Two-Path Interferometer II A duality relation: V: visibility of interference D: distinguishability Mesoscopic Physics & Quantum Information  Lab.      KK, PRB (2007) For upper path For lower path Output current at g

  41. Nonlocality Test: Bell’s Inequality BS-1,BS-2,BS-3: Symmetric beam splitters BS-4: Phase of MZI-d fixed at some value depending on Bell’s inequality: [CHSH inequality](Clauser et al. PRL (1969)) where In our case we find: Bell’s inequality is violated for any nonzero Mesoscopic Physics & Quantum Information  Lab.      KK & K.H. Lee, arXiv:0707.1170(2007)

  42. Mesoscopic Physics & Quantum Information  Lab.      요 약 (Summary) • 양자역학의 기묘함 - 중첩, 우연, 상보성, 비국소성, 측정문제 • 중시계 물리학 - Quantum transport, interference, and shot noise • 중시계에서 양자역학의 근본문제 공부하기 - Complementarity and nonlocalitytest

  43. Mesoscopic Physics & Quantum Information  Lab.      결론 (Conclusion) ? “If quantum mechanics hasn’t profoundly shocked you, you haven’t understood it yet.” - Niels Bohr “Although quantum mechanics has profoundly shocked me, I haven’t understood it yet.” - KK

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