quantum foundations in mesoscopic physics

Quantum Foundations in Mesoscopic PhysicsQuantum 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 Camp2008. 1. 9 – 11 @ KIAS-SNU Physics Winter Camp

Mesoscopic Physics & Quantum Information Lab.

OutlineOutline

• 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


• 중첩 (superposition)

• 객관적 우연 (indeterminism)

• 상보성 (complementarity)

• 비국소성 (nonlocality) ~ quantum entanglement

• “ 측정문제 (measurement problem)” ~ wave function collapse

• ……


양자역학의 기묘함


Charles Addams, The New Yorker Magazine 1940

중첩 (Superposition)

동동동동동

우연 = 무지 (주관적 )

(lack of knowledge)

Quantum Coin

동동 intrinsic absence of information


객관적 우연 (Indeterminism)

or

measurement

“God does not playdice (신은 주사위 놀이를 하지 않는다 )

”


A. Einstein vs. N. Bohr

“Stop telling Godwhat to do!( 신에게 명령하는 것을 중단하시죠 !)”

객관적 우연 (Indeterminism)

상보성 (Complementarity): Behavior of a Quanton


Screen

Electrongun

Interference fringe or distinguishability

rc

“detector”(environment) states

“Wave-particle duality” or “complementarity”

Interference term in the distribution at the rc:

measure of the indistinguishability

(no ‘detection’)(‘detection’)


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.)

a b

There is correlation, but ‘measurement’on a particle does not affect the (probabilityof) outcome of the other

비국소성 (Nonlocality)


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 bedescribed in terms of

양자역학에 대처하는 우리의 자세양자역학에 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.

• …..


• 중첩 • 객관적 우연• 상보성 (complementarity)

• 비국소성 (nonlocality) ~ quantum entanglement

• “ 측정문제 (measurement problem)” ~ wave function collapse

• ……


양자역학의 기묘함

** Attention! All these properties are the basic resources for quantum communication and computation.


Screen

Electrongun

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 ExperimentR. Feynman (1965)


Uncertainty & Double-Slit ExperimentR. 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:


‘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))


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).



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!



Y.H. Kim et al., PRL (2000)

LA

LB

LA, LB >> L0: Choice of ‘wave-like’ or ‘particle-like’behavior can be delayed after the detection of signal photon

L0

R01 R02

R03

D0 Counts

OutlineOutline









What is ‘Mesoscopic’ ?


Fermi Wavelength (F) & Dimensionality


- 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!


Conductance Quantization

Conductance (G) vs. transmission amplitude (tn) (Landauer formula)

- Ballistic, coherent motion of electrons

Van Wees et al. (1988), D.A. Wharam et al. (1988)


Charge and energy quantization

: charging energy of single electron, : level discreteness

: Coulomb blockade, single electron tunneling

: resonant tunneling (phase-coherent)

Quantum Dots


Resonant Tunneling through a Quantum Dot

Coherent resonant tunneling through a single QD level (0)

Phase information cannot be extracted in this geometry

Coulomb blockadeoscillation


Double-Slit Aharonov-Bohm Interferometer Schuster et al., Nature (1997)

Double-slit typeAB oscillation: -Very small probability of multiple reflections

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 td << tdwell , the electron will be detected!

QPC

QD


Aleiner et al., PRL (1997)

Controlled Dephasing in a Which-Path Interferometer

Detectorsensitivity

Visibility reducedby charge detection

Buks et al., Nature (1998)



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


Sprinzak et al., PRL (2000)Phase-Sensitive Detection: Experiment


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 SplitterS : Source D : Detector

Solid-State Mach-Zehnder Interferometer?

E

B >>0

Edge state Electron beam

B

Quantum Point Contact Beam splitter

Optical Mach-Zehnder interferometer


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

OutlineOutline









KK, PRB (2007)

Coulomb interactions modified trajectories Entanglement

Two particle stateat this stage:

Two particle interference:(for a symmetric BS-1, BS-2)

: visibility independent of |동 |: 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


In summary:

1. Interferometer-detector entanglement through the elastic Coulomb interaction

2. The entanglement and the WP information encoded in the relative phase 동동

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)



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 correlationmeasurement

KK, PRB (2007)



Experimental Realization!

detectorinput

interferometerinput

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)


Experimental Realization!

Almost perfect WP detection

Low detector voltage High detector voltage

curr

ent

shot

noi

se

• Single particle interference is suppressed by the WP information• Interference is recovered by the cross correlation


Two coupled Mach-Zehnder interferometers

Output currents at lead 동동동동 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


A duality relation:

V: visibility of interferenceD: distinguishability

KK, PRB (2007)

Complementarity Test in a Two-Path Interferometer II

Out

put c

urre

nt a

t For upper pathFor lower path


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 splittersBS-4:

Phase of MZI-d fixed at some valuedepending on

Bell’s inequality is violated for anynonzero

In our case we find:

요 약 (Summary)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


“If quantum mechanics hasn’t profoundly shocked you, you haven’t understood it yet.” - Niels Bohr


결론 (Conclusion) ?결론 (Conclusion) ?

“Although quantum mechanics has profoundly shocked me, I haven’t understood it yet.” - KK

quantum foundations in mesoscopic physics

Documents