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Danish Quantum Optics Center University of Aarhus. QuanTOp. Niels Bohr Institute Copenhagen University. Light-Matter Quantum Interface. Eugene Polzik LECTURE 4. IHP Quantum Information Trimester. Quantum memory for light: criteria. Memory must be able to store independently prepared

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slide1

Danish Quantum Optics Center University of Aarhus

QuanTOp

Niels Bohr Institute

Copenhagen University

Light-Matter Quantum Interface

Eugene Polzik LECTURE 4

IHP Quantum Information Trimester

slide2

Quantum memory for light:

criteria

  • Memory must be able to store independently prepared
  • states of light
  • The state of light must be mapped onto the memory with
  • the fidelity higher than the fidelity of the best
  • classical recording
  • The memory must be readable

B. Julsgaard, J. Sherson, J. Fiurášek , I. Cirac, and E. S. Polzik

Nature, 432, 482(2004); quant-ph/0410072.

slide3

Mapping a Quantum State of Light onto Atomic Ensemble

Spin Squeezed

Atoms

1 >

2 >

0 >

Experiment:

Hald, Sørensen, Schori, EP

PRL 83, 1319 (1999)

Very inefficient

lives only nseconds,

but a nice first try…

The beginning. Complete absorption

Squeezed Light pulse

Proposal:

Kuzmich, Mølmer, EP

PRL 79, 4782 (1997)

Atoms

slide4

…and feedback

applied

Strong

driving

Weak

quantum

Projection

measurement

on light

can be made…

Passes through one…

or more atomic samples

Dipole off-resonant

interaction entangles

light and atoms

Our light-atoms interface - the basics

Light pulse – consisting of two modes

slide5

x

-45

45

Polarization – Stokes

parameters

y

Circular polarizations

Linear polarizations

Polarization quantum variables – Light

Propagation direction

vertical

horizontal

slide6

x

Quantum state (Wigner function)

y

z

Canonical quantum variables for an atomic ensemble:

slide7

Decoherence from stray

magnetic fields

Magnetic Shields

Special coating – 104 collisions

without spin flips

Object – gas of spin polarized atoms at room temperature

Optical pumping with circular

polarized light

slide8

Various

states

t

Pulse:

  • Canonical quantum variables for light
  • Complementarity : amplitude and phase of
  • light cannot be measured together
slide9

450

-450

EOM

l/4

Polarization homodyning - measure X (or P)

Polarizing

Beamsplitter 450/-450

Strong field A(t)

x

Quantum field a -> X,P

Polarizing

cube

S1

slide10

x,p

Bell

measurement

Teleportation in the X,P representation

slide11

Projection

measurement

X

Today:

another idea for (remote) state transfer

and its experimental implementation for quantum

memory for light

See also work on quantum cloning:

J. Fiurasek, N. Cerf, and E.S. Polzik,

Phys.Rev.Lett.93, 180501 (2004)

slide12

Implementation: light-to-matter state transfer

- C

squeeze atoms first

No prior entanglement necessary

= C

F≈80%

F→100%

B. Julsgaard, J. Sherson, J. Fiurášek , I. Cirac, and E. S. Polzik

Nature, 432, 482(2004); quant-ph/0410072.

slide13

Quantum computing

with linear operations

Quantum buffer

for light

More

efficient repeaters

Quantum Key storage

in quantum cryptography

These criteria should be met for memory in:

slide14

e.-m. vacuum

Classical benchmark fidelity

for transfer of coherent states

Atoms

Best classical fidelity 50%

K. Hammerer, M.M. Wolf, E.S. Polzik, J.I. Cirac,

Phys. Rev. Lett. 94,150503 (2005),

slide15

Preparation of the input state of light

EOM

Vacuum

Input quantum

field

Coherent

Squeezed

Strong field A(t)

Quantum field - X,P

x

Polarizing

cube

S1

P

Polarization

state

X

slide16

450

-450

Physics behind the Hamiltonian:

1. Polarization rotation of light

Polarizing

Beamsplitter 450/-450

x

Quantum field

Polarizing

cube

slide17

EOM

Physics behind the Hamiltonian:

2. Dynamic Stark shift of atoms

Atoms

atoms

Strong field A(t)

Quantum field - a

x

Polarizing

cube

y

slide18

PL

atoms

Quantum memory – Step 1 - interaction

Light rotates atomic spin – Stark shift

XL

Atomic spin rotates polarization

of light – Faraday effect

Output

light

Input

light

Entanglement

slide19

PL

XL

c

light out

atoms

Feedback

to spin rotation

Compare to

the best classical

recording

Quantum memory – Step 2 - measurement + feedback

Polarization

measurement

Fidelity – > 100%

(82% without SS atoms)

slide20

Experimental realization of

quantum memory for light

slide21

Memory in rotating spin states

B

B

y

z

Atomic Quantum Noise

2,4

2,2

2,0

1,8

1,6

1,4

1,2

Atomic noise power [arb. units]

1,0

0,8

0,6

0,4

0,2

0,0

0,0

0,2

0,4

0,6

0,8

1,0

1,2

1,4

1,6

1,8

2,0

Atomic density [arb. units]

slide22

Memory in rotating spin states - continued

B

B

x

z

y

Atomic Quantum Noise

2,4

2,2

2,0

1,8

1,6

1,4

1,2

Atomic noise power [arb. units]

1,0

0,8

0,6

0,4

0,2

0,0

0,0

0,2

0,4

0,6

0,8

1,0

1,2

1,4

1,6

1,8

2,0

Atomic density [arb. units]

slide24

Rotating frame spin

Memory in atomic Zeeman coherences

Cesium

4

3

2

slide25

B

B

x

z

y

slide26

Input pulse

Readout

pulse

Magnetic

feedback

Nature, Nov. 25 (2004)

quant-ph/0410072.

slide27

Light

Pin~ SYin

Xin~ SZin

p

/ 2 - rotation

Stored state versus Input state: mean amplitudes

X plane

read

write

t

output

input

Y plane

Magnetic

feedback

slide28

Stored state: variances

Absolute quantum/classical border

3.0

Perfect mapping

Atoms

<P2mem >

Light

<P2in >=1/2

<X2mem>

<X2in> =1/2

slide29

Experiment

0.68

Coherent states with 0 < n <4

Coherent states with 0 < n <8

0.66

F

Experiment

0.64

0.64

0.62

0.62

Best classical mapping

0.58

0.58

0.56

0.56

Best classical mapping

0.54

Gain

0.65

0.7

0.75

0.8

0.85

0.9

0.82

0.84

0.86

0.88

0.9

Fidelity of quantum storage

  • State overlap averaged over
  • the set of input states
decoherence limitations

1-2Hz

3-6Hz

25-40Hz

Dominating

(T is time, typical 2ms)

Atomic/shot ratio

(retaining the dominating term)

Decoherence

up to around 0.5

Theoretical entanglement

with no decoherence:

Decoherence Limitations

Typical estimate of linewidth:

G[Hz] = 5 + 0.1*q[deg] + 1.0*P[mW] + 0.5*P[mW]*q[deg]

Working values:

Important for entanglement:

Need k2 large and

h low, impossible.

slide32

Initial state of atoms

coherent

Input state

State overlap

63%

Fidelity 100% for

a qubit input state

78%

90%

Qubit fidelity

Deterministic quantum memory for a light Qubit

Initial state of atoms

squeezed

Realized by an extra QND

measurement pulse

A. Sørensen, NBI

slide33

Quantum Memory for Light demonstrated

  • Deterministic Atomic Quantum Memory proposed and
  • demonstrated for coherent states with <n> in
  • the range 0 to 10; lifetime=4msec
  • Fidelity up to 70%, markedly higher than best
  • classical mapping
slide34

Scalability – an array of dipole traps or

solid state implementation – quantum holograms

Detector

array

Spatial

array of memory

cells

I. Sokolov and EP, to be submitted

slide35

Future: Inverse Mapping

AtomsLight

Atoms Y

Detector

Proposals: Kuzmich, EP. 2001; Kraus, Giedke, Cirac 2001

Y

l/4 wave plate

Recent advanced proposals:

K. Hammerer, K. Mølmer, EP, J.I. Cirac. Phys.Rev. A., 70, 044304 (2004).

J. Sherson, K. Mølmer, A.Sørensen, J. Fiurasek, and EP

quant-ph/0505170

Light pulse

slide36

Quantum memory read-out:

single pulse in squeezed state

z

Step 1

x

y

Step 2

Exchange y and z components:

pass light through l/4 plate and

probe along spin-y axis

z

y

slide37

Light-Atoms Q-interface with cold atoms

6P

Cesium clock levels

F=4

F=3

D. Oblak

C. Alzar,

P. Petrov

slide38

Memory Summary

  • New state transfer protocol →quantum memory for light
  • Experimental demonstration for coherent states
  • Nature, 432, 482(2004)
  • Prediction for a qubit state – bridging dicrete and
  • continuous variables
  • State retrieval protocols
slide39

Figure of merit

Probe depumping

parameter:

Criteria for light-ensemble interface

  • 2-level stable state with long coherence time
  • Initialization: collective coherent spin state (CSS)
  • Coupling of the CSS to light corresponding to
  • high optical density
slide40

Multi-atom

Cat states

Color code

“easy”

hard

Atomic

teleportation

3-party

entanglement/

Secret sharing

Scaling/

solid state

implementation

Entangled

atoms

+

Entangled light

+

Light/atoms

QI exchange

Quantum

memory

for light

Distillation

by local

operations

Continuous

variable

logic

Discrete

variable

logic

slide41

cold atomic cloud

cavity enhanced interaction

  • enhanced phase shift
  • power build-up inside cavity

compensate with smaller photon number

T: mirror transmission

a: absorption

slide42

Coupling strength of the interface

z

y

x

Initial coherent spin state:

Spin squeezed state

Measurement on light

results in distribution

degree of squeezing in Jz

Figure of merit for the

quantum interface

Z

Duan, Cirac, Zoller, EP

PRL (2000)

slide43

Probe scattering

parameter:

Figure of merit for the quantum interface

slide44

0.3

Single pass interaction

30

50

10

Spontaneous emission

probability

degree of entanglement

+ h

Figure of merit for the

quantum interface

Spontaneous emission – the fundamental limit

K. Hamerrer, K. Mølmer, E. S. Polzik, J. I. Cirac.

PRA 2004, quant-ph/0312156