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