Transcript System-reservoir interactions in quantum optics
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
Teleportation
Quantum
Dense coding
Information
Secret sharing Key distribution
coherence and entanglement Quantum Computation
Algorithms
Bit
: 0, 1 or +, - or boy, girl…. Any two-level system t 0
1 0
t 1 t 2 time
Q-bit
: Any two-level and physical system (Quantum bit) Two-level atom
1
1
1
1
0
0 t 0 t 1
0
0 t 2 time
Two qbits : two spins
time Spin up A interaction t 0 A Spin up B Spin down B Spin down Schrodinger eq.
t A B
-
A B entangled state
Entanglement 1 2
A
B
1 2
A
B
*.*?
Impossible to factory
( a1
A
+ a2
A
)
( b1
B
+ b2
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
q D
q b
q
e i
q
x
H
.
c
.
b
q
:
photon operator
:
creating operator of atom
In the interaction picture, the state vector : (
t
)
f
0 (
t
) ; 0
q f
q
(
t
) ; 1
q
, where ; 0 ; 1
q
: an atom initially in the excited state : a photon of q in the radiation field
Results :
f
0 (
t
)
e i
t
t
, where is the decay rate represents the Lamb Shift The radiation intensity distribution :
f
q
(
t
) 2 ( 0
c
2
q D
q
) 2 2 , where
q D
q
2 ( 0
c
q
),
q
0
D
q
c
2
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 0.8
0.6
0.4
0.2
機率 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 2 01 10
The Bell-CHSH inequality
A
a
,
A
,
a
,
B
,
b
A
a
( 0 , 2 ), ( 2 , 0 )
A
a A
a
2 , 2 2
AB
Ab
aB
ab
2
AB
Ab
aB
ab
2
Predictions of QM for the
singlet
state 1 2 01 10
AB
cos
AB
QM violates the Bell-CHSH inequality
F
QM
AB
Ab
aB
ab
cos
AB
cos
Ab
cos
aB
cos
ab a
ˆ
x
y
(
y
x
) /
b
ˆ (
y
x
) / 2 2
F
QM 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