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

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

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

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

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

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

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

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

9. Mesoscopic Physics & Quantum Information Lab. Einstein, Podolsky, Rosen (1935) The EPR Paradox (Bohm’s version) Entangled state (quantum correlation): ”Spooky action at a distance” ( 원거리에서의 ‘ 유령의 ’ 작용 ) Cf. Classical 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.) ab There is correlation, but ‘measurement’on a particle does not affect the (probability of) outcome of the other 비국소성 (Nonlocality)

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

11. 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. ….. Mesoscopic Physics & Quantum Information Lab.

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

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

14. Mesoscopic Physics & Quantum Information Lab. Uncertainty & Double-Slit Experiment 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. Mesoscopic Physics & Quantum Information Lab. ‘Complementarity Beyond Uncertainty’ (?) “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. (M. O. Scully et al. (1991))

16. Mesoscopic Physics & Quantum Information Lab. Realization of Quantum Eraser with Entangled Photons 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). …… Which-path information can be erased by a suitable measurement on the detector (i.e., its entangled twin).

17. Mesoscopic Physics & Quantum Information Lab. Realization of Quantum Eraser with Entangled Photons 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. Mesoscopic Physics & Quantum Information Lab. Realization of Quantum Eraser with Entangled Photons Y.H. Kim et al., PRL (2000) LALA LBLB L A, L B >> L 0 : Choice of ‘wave-like’ or ‘particle-like’ behavior can be delayed after the detection of signal photon L0L0 R 01 R 02 R 03 D 0 Counts

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

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

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

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

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

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

25. Mesoscopic Physics & Quantum Information Lab. Resonant Tunneling through a Quantum Dot Coherent resonant tunneling through a single QD level (  0 ) Phase information cannot be extracted in this geometry

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

27. Controlled ‘Dephasing’ via Charge Detection: Heuristic Argument Detection due to change of transmission probability : Change in the # of electrons crossing the QPC > Quantum shot noise Binomial random distribution : For t d << t dwell, the electron will be detected! QPC QD Mesoscopic Physics & Quantum Information Lab. Aleiner et al., PRL (1997)

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

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

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

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

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

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

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

35. Mesoscopic Physics & Quantum Information Lab. In summary: 1.Interferometer-detector entanglement through the elastic Coulomb interaction 2.The entanglement and the WP information encoded in the relative phase Df 3.Single particle interference suppressed by the WP information 4.The WP information encoded in the phase is erased by the coincidence count, because the electron count in the detector deletes the phase information 5.The interference reappears KK, PRB (2007) Complementarity Test in a Two-Path Interferometer I

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

37. Mesoscopic Physics & Quantum Information Lab. Experimental Realization! 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 I. Neder et al., PRL (2007)

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

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

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

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

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

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