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)

Outline

Coherence and entanglement

Cavity QED

The Leggett-Garg Inequalities

Witnessing Quantum Coherence in

Biological Systems

QuantumInformation

TeleportationTeleportation

Dense coding

Secret sharing

Key distribution

QuantumComputation

Algorithms

coherence and entanglement

Bit : 0, 1 or +, - or boy, girl…. Any two-level system

1 01 0

timet0

t1 t2

Q-bit: Any two-level and physical system(Quantum bit)

00

Two-level atom

timet0

t1 t2

11

00

11

0

1 1

0

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

Entanglement

A+ + a2a2

A

( a1 )B

+ + b2b2B

( b1 )

Impossible to factory

Symbol of connecting to independentsystem

*.*?

BABA 2

1

2

1

薛丁格的貓： To be or not to be?

Cavity QED

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

Interaction between a two-level atom and the photon reservoir:

In the interaction picture, the state vector :

, where

atomofoperatorcreatingoperatorphotonb

cHebDH

q

xqiq

qq

::

..

qq

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

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

qq

qc

D

qcD

0

2

0

2),(

Two-level atom inside a cavityThe interaction between the atom and single-mode cavity:

1;)(0;)()( tftft

J. M. Raimond, M. Brune, and S. Haroche, Rev. Mod. Phys. 73, 565 (2001).

Vacuum Rabi oscillations

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

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)

Quantum vs ClassicalBell’s Inequality: Locality and Realism

10012

1

The Bell-CHSH inequality

1,1,,, bBaA

)0,2(),2,0(, aAaA

2,2 baABaA

22 abaBAbAB

2 abaBAbAB

Predictions of QM for the singlet state

10012

1

AB

BAAB

cos

ˆˆ

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

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)

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

ReactionCenter

Pigments (BChl)

Leggett-Garg inequality ?

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!