a trapped-atom quantum memory (PDF) - MIT
a trapped-atom quantum memory (PDF) - MIT
a trapped-atom quantum memory (PDF) - MIT
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TELEPORTATION OF A QUANTUM STATE<br />
USING TRAPPED RUBIDIUM ATOMS:<br />
THE GORY DETAILS<br />
Selim Shahriar and Seth Lloyd<br />
<strong>MIT</strong><br />
Philip Hemmer<br />
AFRL
OUTLINE<br />
TELEPORTATION: WHAT<br />
TELEPORTATION VIA BELL STATE MEASUREMENT<br />
ESSENTIAL TOOLS FROM LASER CONTROLLED SPIN EXCITATION<br />
COHERENCE TRANSFER VIA CAVITY QED<br />
ENTANGLING RUBIDIUM ATOMS<br />
BELL STATE MEASUREMENTS VIA SEQUENTIAL ELIMINATION<br />
EXPERIMENTAL PLAN / STATUS<br />
CLOCK SYNCHRONIZATION
TELEPORTATION: WHAT<br />
|ψ> = α |↑> + β |↓><br />
BEFORE...<br />
|φ> = |↓><br />
EARTH<br />
AFTER...<br />
ALPHA-CENTAURI<br />
|ψ> = |↓><br />
|φ> = α |↑> + β |↓>
TELEPORTATION: VIA BELL STATE MEASUREMENT<br />
|Φ> = α |↑> + β |↓><br />
|Ψ> = ( |↑ ↓ > − | ↓ ↑ > ) /√2<br />
ALICE<br />
BOB<br />
| √2 |W> = α (|↑↑↓> − |↑↓↑>) + β (|↓↑↓> − |↓↓↑>)<br />
BELL STATES<br />
DECOMPOSITION<br />
|Β 1 > = ( |↑ ↓ > − | ↓ ↑ > ) /√2<br />
|Β 2 > = ( |↑ ↓ > + | ↓ ↑ > ) /√2<br />
|Β 3 > = ( |↑ ↑ > − | ↓ ↓ > ) /√2<br />
|Β 4 > = ( |↑ ↑ > + | ↓ ↓ > ) /√2<br />
|↑ ↑ > = (|Β 4 > + |Β 3 >) /√2<br />
|↓ ↓ > = (|Β 4 > − |Β 3 >) /√2<br />
|↑ ↓ > = (|Β 2 > + |Β 1 >) /√2<br />
|↓ ↑ > = (|Β 2 > − |Β 1 >) /√2
|Φ> = α |↑> + β |↓><br />
ALICE<br />
|Β><br />
|ξ><br />
BOB<br />
| 2 |W> = |Β 1 > |ξ 1 > + |Β 2 > |ξ 2 > + |Β 3 > |ξ 3 > + |Β 4 > |ξ 4 ><br />
WHERE<br />
| |ξ 1 > = − (α |↑> + β | ↓>) = − α β = − |Φ><br />
| |ξ 2 > =<br />
| |ξ 3 > =<br />
| |ξ 4 > =<br />
-1 0<br />
0 1<br />
0 1<br />
1 0<br />
0 -1<br />
1 0<br />
|Φ><br />
|Φ><br />
|Φ>
LASER-CONTROLLED SPIN EXCITATION<br />
OFF-RESONANT<br />
|E><br />
N B<br />
|B><br />
|A><br />
Time<br />
GOOD FOR SINGLE BIT OPERATION
LASER-CONTROLLED SPIN EXCITATION<br />
RESONANT<br />
|E><br />
|E><br />
|B><br />
|A><br />
|->=<br />
(|A> - |B>)<br />
|+>=(|A> + |B>)<br />
N L<br />
(SS)<br />
EXPT. IN Rb<br />
0<br />
TWO-PHOTON DETUNING
THE DARK STATE:: GENERAL CASE<br />
|e<br />
|e<br />
Ω 1<br />
|a<br />
Ω 2<br />
|b<br />
− =<br />
Ω<br />
− +<br />
( − )<br />
Ω a Ω b / Ω<br />
2 1<br />
2<br />
Ω= Ω + Ω<br />
1<br />
2<br />
2
2<br />
− = ( Ω a − Ω b )/ Ω + Ω<br />
2 1 1<br />
2<br />
2<br />
|e<br />
|e<br />
|e<br />
|e<br />
|e<br />
Ω 1<br />
Ω 1<br />
Ω 2<br />
3 1<br />
Ω 1<br />
Ω 2<br />
1 1<br />
Ω 1<br />
Ω 2<br />
1 3<br />
Ω 2<br />
|a<br />
− ∝ b<br />
|b<br />
|a<br />
|b<br />
1<br />
3 a − b<br />
|a<br />
a<br />
|b<br />
|a<br />
|b<br />
− b a − 1 3 b<br />
|a<br />
a<br />
|b
ADIABATIC TRANSFER VIA THE DARK STATE<br />
|e<br />
|e<br />
Ω 1<br />
Ω 2<br />
Ω<br />
|b |- |+<br />
|a<br />
AMPLITUDE<br />
1<br />
0<br />
Ω 1<br />
Ω 2<br />
TIME<br />
|-> = (Ω 2 |a> - Ω 1 |b>)/Ω<br />
|+> = (Ω 1 |a> + Ω 2 |b>)/Ω<br />
|a> - |e><br />
|+> - |e><br />
|b> - |e><br />
EQUIVALENT TO A π-PULSE<br />
|->=|b><br />
|->=|a><br />
TOPOLGICALLY ROBUST<br />
|a> + |e><br />
|+> + |e><br />
|b> + |e>
COHERENCE TRANSFER VIA CAVITY QED<br />
ATOM<br />
A<br />
ATOM<br />
B<br />
Ω 1 Ω 2<br />
g<br />
g<br />
g<br />
Ω 2<br />
α<br />
0<br />
Ω 1<br />
A B<br />
0<br />
α<br />
β<br />
1<br />
1<br />
β<br />
A<br />
B
TRANSFERRING TWO BITS INTO A SINGLE ATOM VIA CAVITY QED<br />
1<br />
ATOM A<br />
α 1<br />
ATOM B<br />
1<br />
1<br />
ATOM A<br />
0<br />
ATOM B<br />
0<br />
β 1<br />
α 2<br />
0<br />
β 2<br />
0<br />
1<br />
α 1<br />
0<br />
β 1<br />
0<br />
g<br />
g<br />
Ω 1 Ω 2<br />
α 2<br />
β 2<br />
e n<br />
0<br />
0<br />
Ω 1 Ω 2<br />
0<br />
0<br />
g<br />
g<br />
1<br />
0<br />
e n<br />
α 1 α 2<br />
α 1 β 2<br />
β 1 β 2
ADIABATIC COHERENCE TRANSFER VIA CAVITY-QED DARK STATE<br />
1 2<br />
Ω 1 Ω 2<br />
g<br />
INTENSITY<br />
1<br />
0<br />
Ω 2<br />
Ω 1<br />
TIME<br />
ATOM 1 ATOM 2<br />
|e 1 > |e 2 ><br />
Ω 1<br />
g<br />
Ω 2<br />
|a 1 > |b 1 > |a 2 > |b 2 ><br />
α β 0 1<br />
g<br />
NO CAVITY<br />
PHOTONS<br />
|b 1 b 2 0><br />
β<br />
ONE CAVITY PHOTON<br />
|e 1 b 2 0> |b 1 e 2 0><br />
g g<br />
Ω 1<br />
Ω 2<br />
|a 1 b 2 0> |b 1 b 2 1> |b 1 a 2 0><br />
Ω 2 g −Ω 1 Ω 2 Ω 1 g<br />
α<br />
|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<br />
Ref 1: quant-ph/003147<br />
Ref 2: J. Opt. B: Quantum Semiclass. Opt. 2 (2000) L1-L4
EXPLICIT SCHEME IN 87 RB<br />
C<br />
B<br />
D<br />
A
ATOMS 2 AND 3 ARE NOW ENTANGLED<br />
ΑΤΟΜ 2 ΑΤΟΜ 3<br />
a<br />
b<br />
a<br />
b<br />
c<br />
d<br />
c<br />
d<br />
|ψ 23 >={ |a> 2 |b> 3 - |b> 2 |a> 3 }/√2
ATOM 1 IN ARBITRARY STATE: TO BE TELEPORTED<br />
2<br />
3<br />
a<br />
c<br />
b<br />
d<br />
a<br />
c<br />
b<br />
d<br />
|ψ 23 >={|a> 2 |b> 3 - |b> 2 |a> 3 }/√2<br />
a<br />
c<br />
b<br />
d<br />
|ϕ 1 > ={α|c> 1 +β|a> 1 }<br />
1
TRANSFERRING TWO BITS INTO A SINGLE ATOM VIA CAVITY QED<br />
1<br />
ATOM A<br />
α 1<br />
ATOM B<br />
1<br />
1<br />
ATOM A<br />
0<br />
ATOM B<br />
0<br />
β 1<br />
α 2<br />
0<br />
β 2<br />
0<br />
1<br />
α 1<br />
0<br />
β 1<br />
0<br />
g<br />
g<br />
Ω 1 Ω 2<br />
α 2<br />
β 2<br />
e n<br />
0<br />
0<br />
Ω 1 Ω 2<br />
0<br />
0<br />
g<br />
g<br />
1<br />
0<br />
e n<br />
α 1 α 2<br />
α 1 β 2<br />
β 1 β 2
TRANSFER STATES OF 1 AND 2 INTO 2 ONLY
QUANTUM STATE AFTER THE TRANSFER<br />
BEFORE TRANSFER<br />
|ψ 23 >={|a> 2 |b> 3 - |b> 2 |a> 3 }/√2<br />
|ϕ 1 > ={α|c> 1 +β|a> 1 }<br />
2<br />
3<br />
AFTER TRANSFER<br />
a<br />
c<br />
b<br />
d<br />
a<br />
c<br />
b<br />
d<br />
|ψ 1 > = |c> 1<br />
|φ 23 >={|A + >(α|b 3 >+β|a 3 >) +<br />
|A - >(α|b 3 >-β|a 3 >) +<br />
|B + >(β|b 3 >+α|a 3 >)+<br />
| B - >(-β|b 3 >+α|a 3 >)}/2<br />
a<br />
b<br />
BELL STATES<br />
c<br />
d<br />
|A ± >={|c 2 >±|b 2 >}/√2,<br />
|B ± >={|d 2 >±|a 2 >}/√2.<br />
1
ROTATE SUPERPOSITION-BASIS BELL STATES INTO PURE-BASIS BELL STATES<br />
π/2 pulses<br />
a<br />
b<br />
a<br />
b<br />
c<br />
d<br />
c<br />
d<br />
2<br />
2<br />
OLD BELL STATES<br />
|A + >=|c 2 >+|b 2 ><br />
|A - >=|c 2 >-|b 2 ><br />
|B + >=|d 2 >+|a 2 ><br />
|B - >=|d 2 >-|a 2 >.<br />
NEW BELL STATES<br />
|a + >=|c 2 ><br />
|a - >=|b 2 ><br />
|b + >=|d 2 ><br />
|b - >=|a 2 >.
MEASURING BELL STATES VIA SEQUENTIAL ELIMINATION
LOADING ATOMS INTO A FORT USING A FOUNTAIN<br />
ALL DIODE LASERS POSSIBLE<br />
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<br />
OPA1<br />
I 1<br />
I 2<br />
I 1<br />
=I 2<br />
Ω<br />
I 1<br />
I 2<br />
Ω’<br />
I 1<br />
≠I<br />
2<br />
ALICE’s CLOCKS<br />
OPA2<br />
BOB’s CLOCKS