IWQSE 2013, NTU
Oct. 15 (2013)
Witnessing Quantum Coherence
Yueh-Nan Chen (陳岳男)
Dep. of Physics, NCKU
National Center for Theoretical Sciences (South)
Outline

Coherence and entanglement



Cavity QED
The Leggett-Garg Inequalities
Witnessing Quantum Coherence in
Biological Systems
Quantum
Information
Teleportation
Dense coding
Secret sharing
Key distribution
coherence and entanglement
Quantum
Computation
Algorithms
Bit : 0, 1 or +, - or boy, girl….
Any two-level system
10
time
t0
t1
t2
Q-bit: Any two-level and physical system
(Quantum bit)
Two-level atom
1
1
1
0
1
0
0
0
time
t0
t1
t2
Two qbits : two spins
time
B
A
Spin up
Spin down
interaction
t0
A
B
Spin up
Spin down
Schrodinger
eq.
t
A
B
A
B
entangled
state
Entanglement
1
1
 
 A B 
 A B
2
2
*.*?
( a1
+ a2
A
)
A

Impossible to factory
( b1
+ b2
B
Symbol of connecting to independent
system
)
B
薛丁格的貓：To be or not to be?
Cavity QED
The Nobel Prize in Physics 2012
Serge Haroche
David J. Wineland
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"
• Spontaneous emission of single two-level atom

Interaction between a two-level atom and the photon reservoir:
H    D b  e

q
 
q q

iq  x
 H .c.
bq : photon operator

  : creating operator of
In the interaction picture, the state vector :
(t )  f 0 (t ) ;0   f q (t ) ;1q

q
, where
;0
: an atom initially in the excited state
;1q
: a photon of q in the radiation field
atom
Results :
it t
f 0 (t )  e
,
where


is the decay rate
represents the Lamb Shift
The radiation intensity distribution :
2
f q (t  ) 
Dq
2

( 0  c q   ) 2   2
, where

    Dq  ( 0  c q ),
2

q
   

q
Dq
2

0  c q
0
is the energy spacing
Two-level atom inside a cavity
The interaction between the atom and single-mode cavity:
 (t )  f  (t ) ;0  f  (t ) ;1
Vacuum Rabi oscillations
J. M. Raimond, M. Brune, and S. Haroche, Rev. Mod. Phys. 73, 565 (2001).
Vacuum Rabi splitting
Gate-confined Double Quantum Dots
Quantum Coherence in Double Quantum Dots
K. D. Petersson, J. R. Petta, H. Lu, and A. C. Gossard, PRL 105, 246804 (2010)
Question:
Are they truly quantum?
The Robotic Bugs
1.0
機率
機率
0.8
0.6
0.4
0.2
0.0
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15 16 17 18 19 20
t (s)
Quantum vs Classical
Bell’s Inequality: Locality and Realism
1
 01  10 
 
2
The Bell-CHSH inequality
A, a, B, b  1,1
 A  a, A a(0,2), (2,0)
 A a B   A ab  2,2
 2  AB  Ab aB ab  2
AB  Ab  aB  ab  2
Predictions of QM for the singlet state


1
 01  10 

2

ˆ
ˆ
AB   A  B 

  cos AB
QM violates the Bell-CHSH inequality
FQM  AB  Ab  aB  ab
  cos AB  cos Ab  cos aB  cos ab
Aˆ   x
aˆ   y
Bˆ  ( y   x ) / 2
bˆ  ( y   x ) / 2
FQM  2 2  2!!!
Leggett-Garg Inequality (Bell’s inequality in time)
Realism and non-invasive measurement
Quantum mechanics versus macroscopic realism:
Is the flux there when nobody looks?
Leggett and Garg, Phys. Rev. Lett. 54, 857–860 (1985)
Palacios-Laloy, A. et al.
Nature Phys. 6, 442–447 (2010).
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)
Double Quantum Dot
Violation of charge inequality for DQD
Quantum Transport in Organism ?
The Quantum Dimension Of Photosynthesis
Leggett-Garg inequality ?
Pigments
(BChl)
Reaction
Center
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)
Avian Magnetoreception: a tale of two spins
http://www.technologyreview.com/blog/arxiv/27829/
Summary
1. Coherence and Entanglement
2. Cavity QED
3. The LG Inequalities
4. Quantumness in Biological Systems
Thank you for your attention!