a trapped-atom quantum memory (PDF) - MIT

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a trapped-atom quantum memory (PDF) - MIT

TELEPORTATION OF A QUANTUM STATE

USING TRAPPED RUBIDIUM ATOMS:

THE GORY DETAILS

Selim Shahriar and Seth Lloyd

MIT

Philip Hemmer

AFRL


OUTLINE

TELEPORTATION: WHAT

TELEPORTATION VIA BELL STATE MEASUREMENT

ESSENTIAL TOOLS FROM LASER CONTROLLED SPIN EXCITATION

COHERENCE TRANSFER VIA CAVITY QED

ENTANGLING RUBIDIUM ATOMS

BELL STATE MEASUREMENTS VIA SEQUENTIAL ELIMINATION

EXPERIMENTAL PLAN / STATUS

CLOCK SYNCHRONIZATION


TELEPORTATION: WHAT

|ψ> = α |↑> + β |↓>

BEFORE...

|φ> = |↓>

EARTH

AFTER...

ALPHA-CENTAURI

|ψ> = |↓>

|φ> = α |↑> + β |↓>


TELEPORTATION: VIA BELL STATE MEASUREMENT

|Φ> = α |↑> + β |↓>

|Ψ> = ( |↑ ↓ > − | ↓ ↑ > ) /√2

ALICE

BOB

| √2 |W> = α (|↑↑↓> − |↑↓↑>) + β (|↓↑↓> − |↓↓↑>)

BELL STATES

DECOMPOSITION

|Β 1 > = ( |↑ ↓ > − | ↓ ↑ > ) /√2

|Β 2 > = ( |↑ ↓ > + | ↓ ↑ > ) /√2

|Β 3 > = ( |↑ ↑ > − | ↓ ↓ > ) /√2

|Β 4 > = ( |↑ ↑ > + | ↓ ↓ > ) /√2

|↑ ↑ > = (|Β 4 > + |Β 3 >) /√2

|↓ ↓ > = (|Β 4 > − |Β 3 >) /√2

|↑ ↓ > = (|Β 2 > + |Β 1 >) /√2

|↓ ↑ > = (|Β 2 > − |Β 1 >) /√2


|Φ> = α |↑> + β |↓>

ALICE

|Β>

|ξ>

BOB

| 2 |W> = |Β 1 > |ξ 1 > + |Β 2 > |ξ 2 > + |Β 3 > |ξ 3 > + |Β 4 > |ξ 4 >

WHERE

| |ξ 1 > = − (α |↑> + β | ↓>) = − α β = − |Φ>

| |ξ 2 > =

| |ξ 3 > =

| |ξ 4 > =

-1 0

0 1

0 1

1 0

0 -1

1 0

|Φ>

|Φ>

|Φ>


LASER-CONTROLLED SPIN EXCITATION

OFF-RESONANT

|E>

N B

|B>

|A>

Time

GOOD FOR SINGLE BIT OPERATION


LASER-CONTROLLED SPIN EXCITATION

RESONANT

|E>

|E>

|B>

|A>

|->=

(|A> - |B>)

|+>=(|A> + |B>)

N L

(SS)

EXPT. IN Rb

0

TWO-PHOTON DETUNING


THE DARK STATE:: GENERAL CASE

|e

|e

Ω 1

|a

Ω 2

|b

− =

Ω

− +

( − )

Ω a Ω b / Ω

2 1

2

Ω= Ω + Ω

1

2

2


2

− = ( Ω a − Ω b )/ Ω + Ω

2 1 1

2

2

|e

|e

|e

|e

|e

Ω 1

Ω 1

Ω 2

3 1

Ω 1

Ω 2

1 1

Ω 1

Ω 2

1 3

Ω 2

|a

− ∝ b

|b

|a

|b

1

3 a − b

|a

a

|b

|a

|b

− b a − 1 3 b

|a

a

|b


ADIABATIC TRANSFER VIA THE DARK STATE

|e

|e

Ω 1

Ω 2

Ω

|b |- |+

|a

AMPLITUDE

1

0

Ω 1

Ω 2

TIME

|-> = (Ω 2 |a> - Ω 1 |b>)/Ω

|+> = (Ω 1 |a> + Ω 2 |b>)/Ω

|a> - |e>

|+> - |e>

|b> - |e>

EQUIVALENT TO A π-PULSE

|->=|b>

|->=|a>

TOPOLGICALLY ROBUST

|a> + |e>

|+> + |e>

|b> + |e>


COHERENCE TRANSFER VIA CAVITY QED

ATOM

A

ATOM

B

Ω 1 Ω 2

g

g

g

Ω 2

α

0

Ω 1

A B

0

α

β

1

1

β

A

B


TRANSFERRING TWO BITS INTO A SINGLE ATOM VIA CAVITY QED

1

ATOM A

α 1

ATOM B

1

1

ATOM A

0

ATOM B

0

β 1

α 2

0

β 2

0

1

α 1

0

β 1

0

g

g

Ω 1 Ω 2

α 2

β 2

e n

0

0

Ω 1 Ω 2

0

0

g

g

1

0

e n

α 1 α 2

α 1 β 2

β 1 β 2


ADIABATIC COHERENCE TRANSFER VIA CAVITY-QED DARK STATE

1 2

Ω 1 Ω 2

g

INTENSITY

1

0

Ω 2

Ω 1

TIME

ATOM 1 ATOM 2

|e 1 > |e 2 >

Ω 1

g

Ω 2

|a 1 > |b 1 > |a 2 > |b 2 >

α β 0 1

g

NO CAVITY

PHOTONS

|b 1 b 2 0>

β

ONE CAVITY PHOTON

|e 1 b 2 0> |b 1 e 2 0>

g g

Ω 1

Ω 2

|a 1 b 2 0> |b 1 b 2 1> |b 1 a 2 0>

Ω 2 g −Ω 1 Ω 2 Ω 1 g

α

|ψ> = (α |a 1 > + β |b 1 >) ⊗ |b 2 > ⊗ |0> |ψ> = (α |b 1 a 2 0> + β |b 1 b 2 0>) = |b 1 > ⊗ (α |a 2 > + β |b 2 >) ⊗ |0>


TRANSFER PHOTON ENTANGLEMENT TO ATOMIC ENTANGLEMENT

Ref 1: quant-ph/003147

Ref 2: J. Opt. B: Quantum Semiclass. Opt. 2 (2000) L1-L4


EXPLICIT SCHEME IN 87 RB

C

B

D

A


ATOMS 2 AND 3 ARE NOW ENTANGLED

ΑΤΟΜ 2 ΑΤΟΜ 3

a

b

a

b

c

d

c

d

|ψ 23 >={ |a> 2 |b> 3 - |b> 2 |a> 3 }/√2


ATOM 1 IN ARBITRARY STATE: TO BE TELEPORTED

2

3

a

c

b

d

a

c

b

d

|ψ 23 >={|a> 2 |b> 3 - |b> 2 |a> 3 }/√2

a

c

b

d

|ϕ 1 > ={α|c> 1 +β|a> 1 }

1


TRANSFERRING TWO BITS INTO A SINGLE ATOM VIA CAVITY QED

1

ATOM A

α 1

ATOM B

1

1

ATOM A

0

ATOM B

0

β 1

α 2

0

β 2

0

1

α 1

0

β 1

0

g

g

Ω 1 Ω 2

α 2

β 2

e n

0

0

Ω 1 Ω 2

0

0

g

g

1

0

e n

α 1 α 2

α 1 β 2

β 1 β 2


TRANSFER STATES OF 1 AND 2 INTO 2 ONLY


QUANTUM STATE AFTER THE TRANSFER

BEFORE TRANSFER

|ψ 23 >={|a> 2 |b> 3 - |b> 2 |a> 3 }/√2

|ϕ 1 > ={α|c> 1 +β|a> 1 }

2

3

AFTER TRANSFER

a

c

b

d

a

c

b

d

|ψ 1 > = |c> 1

|φ 23 >={|A + >(α|b 3 >+β|a 3 >) +

|A - >(α|b 3 >-β|a 3 >) +

|B + >(β|b 3 >+α|a 3 >)+

| B - >(-β|b 3 >+α|a 3 >)}/2

a

b

BELL STATES

c

d

|A ± >={|c 2 >±|b 2 >}/√2,

|B ± >={|d 2 >±|a 2 >}/√2.

1


ROTATE SUPERPOSITION-BASIS BELL STATES INTO PURE-BASIS BELL STATES

π/2 pulses

a

b

a

b

c

d

c

d

2

2

OLD BELL STATES

|A + >=|c 2 >+|b 2 >

|A - >=|c 2 >-|b 2 >

|B + >=|d 2 >+|a 2 >

|B - >=|d 2 >-|a 2 >.

NEW BELL STATES

|a + >=|c 2 >

|a - >=|b 2 >

|b + >=|d 2 >

|b - >=|a 2 >.


MEASURING BELL STATES VIA SEQUENTIAL ELIMINATION


LOADING ATOMS INTO A FORT USING A FOUNTAIN

ALL DIODE LASERS POSSIBLE

CAN BE VERY COMPACT (5 CM 3 )


WAVELENGTH SCALE CONFINEMENT


PHOTOGRAPH OF THE TRAP


TIME-OF-FLIGHT TEMPERATURE DATA FROM OUR TRAP


POSSIBLE REALIZATION OF BASIC TEST FOR CLOCK SYNCHRONIZATION

OPA1

I 1

I 2

I 1

=I 2

Ω

I 1

I 2

Ω’

I 1

≠I

2

ALICE’s CLOCKS

OPA2

BOB’s CLOCKS

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