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Witnessing Quantum Coherence
IWQSE 2013, NTU
Oct. 15 (2013)
Yueh-Nan Chen (陳岳男 )
Dep. of Physics, NCKU
National Center for Theoretical Sciences (South)
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Outline
Coherence and entanglement
Cavity QED
The Leggett-Garg Inequalities
Witnessing Quantum Coherence in
Biological Systems
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QuantumInformation
TeleportationTeleportation
Dense coding
Secret sharing
Key distribution
QuantumComputation
Algorithms
coherence and entanglement
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Bit : 0, 1 or +, - or boy, girl…. Any two-level system
1 01 0
timet0
t1 t2
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Q-bit: Any two-level and physical system(Quantum bit)
00
Two-level atom
timet0
t1 t2
11
00
11
0
1 1
0
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Two qbits : two spins
Spin up Spin down
interaction
Schrodinger eq.
Spin up Spin down
--
A B
A B
A B A B
time
t0
t entangledstate
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Entanglement
A+ + a2a2
A
( a1 )B
+ + b2b2B
( b1 )
Impossible to factory
Symbol of connecting to independentsystem
*.*?
BABA 2
1
2
1
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薛丁格的貓: To be or not to be?
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Cavity QED
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The Nobel Prize in Physics 2012
The Nobel Prize in Physics 2012 was awarded jointly to Serge Haroche and David J. Wineland "for ground-breaking experimental methods that enable measuring and manipulation of individual quantum systems"
Serge Haroche David J. Wineland
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Interaction between a two-level atom and the photon reservoir:
In the interaction picture, the state vector :
, where
atomofoperatorcreatingoperatorphotonb
cHebDH
q
xqiq
::
..
q tftft
1;)(0;)()( 0
q1;
0;
: an atom initially in the excited state
: a photon of q in the radiation field
• Spontaneous emission of single two-level atom
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Results :Results :
,)(0ttietf where is the decay rate
represents the Lamb Shift
The radiation intensity distribution :
220
2
2
)()(
qc
Dtf
q
q
, where
0 is the energy spacing
q
q
qc
D
qcD
0
2
0
2),(
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Two-level atom inside a cavityThe interaction between the atom and single-mode cavity:
1;)(0;)()( tftft
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J. M. Raimond, M. Brune, and S. Haroche, Rev. Mod. Phys. 73, 565 (2001).
Vacuum Rabi oscillations
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Vacuum Rabi splitting
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Gate-confined Double Quantum Dots
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Quantum Coherence in Double Quantum Dots
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K. D. Petersson, J. R. Petta, H. Lu, and A. C. Gossard, PRL 105, 246804 (2010)
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Question:
Are they truly quantum?
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The Robotic Bugs
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 200.0
0.2
0.4
0.6
0.8
1.0 機率
機率
t (s)
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Quantum vs ClassicalBell’s Inequality: Locality and Realism
10012
1
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The Bell-CHSH inequality
1,1,,, bBaA
)0,2(),2,0(, aAaA
2,2 baABaA
22 abaBAbAB
2 abaBAbAB
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Predictions of QM for the singlet state
10012
1
AB
BAAB
cos
ˆˆ
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QM violates the Bell-CHSH inequality
abaBAbAB
abaBAbABF
coscoscoscos
QM
2/)(ˆ
2/)(ˆ
ˆ
ˆ
xy
xy
y
x
b
B
a
A
!!!222QM F
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Leggett-Garg Inequality (Bell’s inequality in time)RealismRealism and and non-invasivenon-invasive measurement measurement
Quantum mechanics versus macroscopic realism: Is the flux there when nobody looks?
Leggett and Garg, Phys. Rev. Lett. 54, 857–860 (1985)
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Palacios-Laloy, A. et al. Nature Phys. 6, 442–447 (2010).
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Distinguishing Quantum and Classical Transport through Nanostructures Transport Charge Inequality:
N. Lambert, C. Emary, Y. N. Chen, and F. Nori, Phys. Rev. Lett. 105, 176801 (2010)
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Double Quantum Dot
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Violation of charge inequality for DQD
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Quantum Transport in Organism ?
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The Quantum Dimension Of Photosynthesis
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ReactionCenter
Pigments (BChl)
Leggett-Garg inequality ?
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Witnessing Quantum Coherence in FMO Complex
C. M. Li*, N. Lambert*, Y. N. Chen*, G. Y. Chen and F. Nori, Scientific Reports 2, 885 (2012)
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Avian Magnetoreception: a tale of two spins
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http://www.technologyreview.com/blog/arxiv/27829/
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Summary
1. Coherence and Entanglement
2. Cavity QED
3. The LG Inequalities
4. Quantumness in Biological Systems
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Thank you for your attention!