Download Quantum Foundations in Mesoscopic Physics

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
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 nonlocality test
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 nonlocality test
Mesoscopic Physics & Quantum Information Lab.
양자역학의 기묘함
•
•
•
•
•
•
중첩 (superposition)
객관적 우연 (indeterminism)
상보성 (complementarity)
비국소성 (nonlocality) ~ quantum entanglement
“측정문제 (measurement problem)” ~ wave function collapse
……
Mesoscopic Physics & Quantum Information Lab.
중첩 (Superposition)
Charles Addams, The New Yorker Magazine 1940
Mesoscopic Physics & Quantum Information Lab.
객관적 우연 (Indeterminism)
동전 던지기
Quantum Coin
or
measurement
우연 = 무지 (주관적)
(lack of knowledge)
우연 = intrinsic absence
of information
Mesoscopic Physics & Quantum Information Lab.
객관적 우연 (Indeterminism)
A. Einstein vs. N. Bohr
“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.
상보성 (Complementarity):
Behavior of a Quanton
Interference fringe or distinguishability
“detector”(environment) states
rc
Screen
Interference term in the distribution at the rc:
measure of the indistinguishability
Electron
gun
“Wave-particle duality”
or “complementarity”
(‘detection’)
(no ‘detection’)
Mesoscopic Physics & Quantum Information Lab.
비국소성 (Nonlocality)
Einstein, Podolsky, Rosen (1935)
The EPR Paradox (Bohm’s version)
a
Cf. Classical correlation
b
There is correlation, but ‘measurement’on
a particle does not affect the (probability
Entangled state (quantum correlation): of) outcome of the other
Bell’s inequality (1966) :
An inequality that any local hidden
variable theory should satisfy
”Spooky action at a distance”
(원거리에서의 ‘유령의’ 작용)
Experiment agrees with the prediction of
quantum theory (Aspect et al. (1982) etc.)
Mesoscopic Physics & Quantum Information Lab.
측정문제 (Measurement problem)
Wave function
measurement
(before measurement)
Collpase of the wave function
A measurement cannot be
described in terms of
- 파동은 갑자기 어디로 갔나?
- 그러면 ‘waving’ 하던 것은 무엇인가?
Mesoscopic Physics & Quantum Information Lab.
양자역학에 대처하는 우리의 자세
•
“Shut up and calculate” interpretation
•
Copenhagen (Orthodox) Interpretation
- Dirac, etc.
“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.
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.
Mesoscopic Physics & Quantum Information Lab.
Uncertainty & Double-Slit Experiment
R. Feynman (1965)
Electron
gun
Screen
d
Disturbance of electron momentum:
D p > h/d
required to get the which-path information (Dx < d)
- This “momentum kick” washes out the interference fringe
Mesoscopic Physics & Quantum Information Lab.
Uncertainty & Double-Slit Experiment
R. Feynman (1965)
Heisenberg’s uncertainty principle:
“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.”
Mesoscopic Physics & Quantum Information Lab.
‘Complementarity Beyond Uncertainty’ (?)
(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.
Mesoscopic Physics & Quantum Information Lab.
Realization of Quantum Eraser
with Entangled Photons
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).
• ……
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!
Mesoscopic Physics & Quantum Information Lab.
Realization of Quantum Eraser
with Entangled Photons
LA, LB >> L0: Choice of
‘wave-like’ or ‘particle-like’
behavior can be delayed after
the detection of signal photon
LA
LB
Y.H. Kim et al., PRL (2000)
R01
R02
L0
D0 Counts
R03
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 nonlocality test
Mesoscopic Physics & Quantum Information Lab.
What is ‘Mesoscopic’ ?
Mesoscopic Physics & Quantum Information Lab.
Fermi Wavelength (lF) & Dimensionality
Mesoscopic Physics & Quantum Information Lab.
2-Dimensinal Electron Gas (2DEG)
gates
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)
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
Mesoscopic Physics & Quantum Information Lab.
Quantum Dots
Charge and energy quantization
: charging energy of single electron,
: level discreteness
: Coulomb blockade, single electron tunneling
: resonant tunneling (phase-coherent)
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
Mesoscopic Physics & Quantum Information Lab.
Double-Slit Aharonov-Bohm Interferometer
Schuster et al., Nature (1997)
Coulomb blockade
oscillation
Double-slit type
AB oscillation:
-Very small probability
of multiple reflections
Mesoscopic Physics & Quantum Information Lab.
Controlled ‘Dephasing’ via Charge Detection:
Heuristic Argument
QD
Aleiner et al., PRL (1997)
Detection due to change of
transmission probability
QPC
: Change in the # of electrons crossing the QPC > Quantum shot noise
Binomial random distribution
: For td << tdwell , the electron
will be detected!
Mesoscopic Physics & Quantum Information Lab.
Controlled Dephasing in a Which-Path
Interferometer Buks et al., Nature (1998)
Visibility reduced
by charge detection
Detector
sensitivity
Mesoscopic Physics & Quantum Information Lab.
Phase-Sensitive Detection
QD
Detection due to change of
scattering phase (not observed)
QPC
: Change in the phase of electrons
crossing the QPC
>
Phase flutuation
Phase-sensitive detection
Mesoscopic Physics & Quantum Information Lab.
Phase-Sensitive Detection: Experiment
Sprinzak et al., PRL (2000)
Mesoscopic Physics & Quantum Information Lab.
A Mesoscopic Two-path Interferometer
- Electronic analogue of optical Mach-Zehnder interferometer
Optical Mach-Zehnder Interferometer
Solid-State Mach-Zehnder Interferometer?
E
B >>0
B
Edge state  Electron beam
M : Mirror
BS : Beam Splitter
S : Source
D : Detector
~100% visibility, sensitive phase measurement
Quantum Point Contact
 Beam splitter
Mesoscopic Physics & Quantum Information Lab.
A Mesoscopic Two-path Interferometer
- 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
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 nonlocality test
Mesoscopic Physics & Quantum Information Lab.
Complementarity Test in a Two-Path
Interferometer I
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’
Single particle interference:
Two particle interference:
(for a symmetric BS-1, BS-2)
Fringe visibility is proportional to |n |
Measure of the
indistinguishability
: visibility independent of |n |
: WP information erased by the projective
measurement in the detector
Mesoscopic Physics & Quantum Information Lab.
Complementarity Test in a Two-Path
Interferometer I
KK, PRB (2007)
In summary:
1.
2.
3.
4.
5.
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
Mesoscopic Physics & Quantum Information Lab.
Complementarity Test in a Two-Path
Interferometer I
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
Mesoscopic Physics & Quantum Information Lab.
Experimental Realization!
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
Mesoscopic Physics & Quantum Information Lab.
Experimental Realization!
current
Low detector voltage
Almost perfect WP detection
Single particle interference is suppressed by the WP information
Interference is recovered by the cross correlation
shot noise
•
•
High detector voltage
Mesoscopic Physics & Quantum Information Lab.
Complementarity Test in a Two-Path
Interferometer II
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
Mesoscopic Physics & Quantum Information Lab.
Complementarity Test in a Two-Path
Interferometer II
Output current at g
KK, PRB (2007)
For upper path
For lower path
A duality relation:
V: visibility of interference
D: distinguishability
Mesoscopic Physics & Quantum Information Lab.
Nonlocality Test: Bell’s Inequality
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: [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.
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.
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
Mesoscopic Physics & Quantum Information Lab.