ultra-precise clock synchronization via distant entanglement
DESCRIPTION
DARPA QUantum Information Science and Technology Kickoff Meeting Nov. 26-29, 2001 Dallas, TX. ULTRA-PRECISE CLOCK SYNCHRONIZATION VIA DISTANT ENTANGLEMENT. Selim Shahriar, Project PI Franco Wong, Co-PI Res. Lab. Of Electronics. 3/4 p pulse. Selim Shahriar, subcontract PI - PowerPoint PPT PresentationTRANSCRIPT
ULTRA-PRECISE CLOCK SYNCHRONIZATION VIA DISTANT ENTANGLEMENT
Selim Shahriar, Project PIFranco Wong, Co-PIRes. Lab. Of Electronics
DARPA QUantum Information Scienceand Technology Kickoff Meeting
Nov. 26-29, 2001 Dallas, TX
Selim Shahriar, subcontract PIDept. of Electrical and Computer EngineeringLaboratory for Atomic and Photonic TechnologiesCenter for Photonic Communications and Computing
3/4 pulse
Ulvi Yurtsever, “subcontract” PIJohn Dowling, “subcontract” Co-PIJet Propulsion Laboratory
POGRAM SUMMARY
TRAPPED RB ATOM QUANTUM MEMORY
ULTRA-BRIGHT SOURCE FOR ENTANGLEDPHOTON PAIRS
DEGENERATE DISTANT ENTANGLEMENT BETWEEN PAIR OF ATOMS
QUANTUM FREQUENCY TELEPORTATION VIA BSO AND ENTANGELEMENT
Sub-picosecond scale synchronization of separated clocks will increase the resolution of GPS systems even in the presence of random fluctuations of pathlengths
Quantum memory will be produced with a coherence time of upto several minutes, making possible high-fidelityquantum communication and teleportation
Sub-pico-meter scale resolution measurement of amplitudeas well as phase of oscillating magnetic fields would enhance the sensitivity of tracking objects such as submarines
RELATIVISTIC GENERALIZATION OF ENTANGLEMENT AND FREQUENCY TELEPORTATION
Non-deg Teleportation
Bloch-Siegert Oscillation
Frequency Teleportation
Relativist Entanglement
Decoherence in Clock-Synch
YR1 YR3YR2
Entangled Photon Source
CLOCK A CLOCK B
f
A
1
3
)()(0^
tgtg
H
A
A
CC
t3
1)(
g(t) = -go[exp(it+i)+c.c.]/2
Hamiltonian (Dipole Approx.):
State Vector:
Coupling Parameter:
)exp(0
01ˆ iti
Q
Rotation Matrix:
MEASUREMENT OF PHASE USING ATOMIC POPULATIONS:THE BLOCH-SIEGERT OSCILLATION
A
1
3
(t)= -go[exp(-i2t-i2)+1]/2
Effective Schr. Eqn.:
Effective Hamiltonian:
Effective Coupling Parameter:
Effective State Vector:
)(~|)(~)(~| ttHitt
0)()(0
*
~
tt
H
A
A
CC
tQt3
1~~
)(~|ˆ)(~|
1 3
A
1
3Periodic Solution:
Where:
For all n, we get the following:
1 3
n
nnt
)(~|
=exp(-i2t-i2)
n
nn b
a
2/)(2 1
nnonn bbigania
2/)(2 1
nnonn aaigbnib
2/)(2 1
nnonn bbigania
2/)(2 1
nnonn aaigbnib
goao bo
goa-1 b-1
goa1 b1
goa-2 b-2
goa2 b2
go
go
go
0
2
-2
4
-4
go
Energy
1 3
FULLY QUANTIZED VIEW: EXCITATION FIELD AS A COHERENT STATE
ee tin
nn
tin
nn ngPnPgt ,|||)0(|
e tinnn
nn neTiSinngTCosPTt ]1,|)(,|)([)(|
}1|{|)(}|{|)()(| ee tin
nn
tin
nn nPeTiSinnPgTCosTt
}1|{|)(}|{|)()(| )1(eee tni
nn
titin
nn nPeTiSinnPgTCosTt
AFTER EXCITATION: ENTANGLED STATE:
SEMI-CLASSICAL APPROXIMATION:
}|{]|)(|)([)(| ee tin
nn
ti nPeTiSingTCosTt
BEFORE EXCITATION:
RWA CASE:
2/)(2 1
nnonn bbigania
2/)(2 1
nnonn aaigbnib
goao bo
goa-1 b-1
goa1 b1
goa-2 b-2
goa2 b2
go
go
go
0
2
-2
4
-4
go
Energy
1 3
ee tin
nn
tin
nn ngPnPgt ,|||)0(|
AFTER EXCITATION: ENTANGLED STATE:
BEFORE EXCITATION:
e tieg egTt ||||)(|
]2|)(|)([| )2(ee tnin
tinn
nng nTSininTCosP
]3|)(1|)([| )3()1( ee tnin
tnin
nne nTCosinTSinPi
where:
NRWA CASE:
SEMICLASSICAL APPROXIMATION:
Yields the same set of coupled equations as derived semiclassically without RWA
0
2
-2
4
-4
goao bo
goa-1 b-1
goa1 b1
go
go
Energy
2/1 bbiga ooo
2/1aaigb ooo
2/2 111 oo bbigaia
2/2 111 aigbib o
2/2 111 bigaia o
2/2 111 oo aaigbib
goao bo
goa-1 b-1
goa1 b1
go
go
2/1 bbiga ooo
2/1aaigb ooo
2/2 111 oo bbigaia
2/2 111 aigbib o
2/2 111 bigaia o
2/2 111 oo aaigbib
- (a-1-b-1)
+ (a-1+b-1)
2/)2/2( ooo aiggi
Define:
Which yields:
2/)2/2( ooo aiggi
oo aa ;
oaba 11 ;0
0; 11 bba o
Adiabatic following:
Solution:
Similarly:
Where (go/4) is small, kept to first order
goao bo
goa-1 b-1
goa1 b1
go
go
2/1 bbiga ooo
2/1aaigb ooo
2/2 111 oo bbigaia
2/2 111 aigbib o
2/2 111 bigaia o
2/2 111 oo aaigbib
2/2/ oooo aibiga
2/2/ oooo biaigb
Reduced Equations:
Where
=g2o/4 is the Bloch-Siegert Shift.
)2/()();2/()( tgiSintbtgCosta oooo
)2/()();2/()( 11 tgCostbtgSinita oo
The NET solution is:
goao bo
goa-1 b-1
goa1 b1
go
go
2/1 bbiga ooo
2/1aaigb ooo
2/2 111 oo bbigaia
2/2 111 aigbib o
2/2 111 bigaia o
2/2 111 oo aaigbib
A
1
3
)2/(2)2/()(1 tgSintgCostC ooA
)]2/(2)2/([)( *)(3 tgCostgSinietC oo
tiA
In the original picture, the solution is:
)]22(exp[)2/( tiiwhere
Conventional Result
A
1
3)2/(2)2/()(1 tgSintgCostC ooA
)]2/(2)2/([)( *)(3 tgCostgSinietC oo
tiA
)]22(exp[)2/( tii
IMPLICATIONS:
tt1 t2
When is ignored, result of measurement of pop. of state 1 is independent of t1 and t2, and depends only on (t2- t1)
When is NOT ignored, result of measurement of pop. of state 1 depends EXPLICITLY ON t1, as well as on (t2- t1)Explit dependence on t1 enables measurement of the field phase at t1
tt1 t2
T
A
1
3
T
33
RABI OSCILLATION
BLOCH-SIEGERT OSCILLATION
0 50 100 150 200 250 300 3500.92
0.922
0.924
0.926
0.928
0.93
0.932
0.934
0.936
0.938
Initial Phase in DegreeA
mpl
itude
T
tt1 t2
T
A
1
3
Phase-sensitivity maximum at pulseMust be accounted for when doing QC if is not negligible
Pulse=0.931=0.05
TRANSFER PHOTON ENTANGLEMENT TO ATOMIC ENTANGLEMENT
EXPLICIT SCHEME IN 87RBC
A
B
D
ATOMS 2 AND 3 ARE NOW ENTANGLED
|23>={ |a>2|b>3 - |b>2|a>3}/2
a b
c d
a b
c d
NET RESULT OF THIS PROCESS: DEGENERATE ENTANGLEMENT
ALICEBOB
A
1 2
3
B
1 2
3|
NON-DEGENERATE ENTANGLEMENT:
VCO VCO
A
1 2
3
B
1 2
3
|(t)>=[|1>A|3>Bexp(-it-i) - |3>A|1>Bexp(-it-i)]/2.
BA=BaoCos( t+ ) BB=BboCos( t+ )
|(t)>=[|1>A|3>Bexp(-it-i) - |3>A|1>Bexp(-it-i)]/2.Can be re-expressed as:
BABA
t 2
1)(
Where:
A
tiAA
ie 3211212
1 *)(
A
tiAA
ie 3211212
1 *)(
B
tiBB
ie 3211212
1 *)(
B
tiBB
ie 3211212
1 *)(
A
1
3Recalling the NRWA solution:
)2/(2)2/()(1 tgSintgCostC ooA )]2/(2)2/([)( *)(
3 tgCostgSinietC ooti
A
)]22(exp[)2/( tii
A
tiAA
ie 3211212
1 *)(
A
tiAA
ie 3211212
1 *)(
B
tiBB
ie 3211212
1 *)(
B
tiBB
ie 3211212
1 *)(
The following states result from excitation starting from different initial states:
tt1 t2
t
ALICE:
BOB:
Measure |1>A
Measure |1>B
Post-Selection
pSProbability of success on both measurements
)22(2121
2 tSinpS
For Normal Excitation: (|1>A goes to |+>A, etc.)
)22(2121
1 tSinpS
For Time-Reversed Excitation: (|+>A goes to |1>A, etc.)
)2(2121 Sin
The relative phase between A and B can not be measured this way
LIMITATIONS:
Absolute time difference between two remote clocks can not be measuredwithout sending timing signals. Quantum Mechanics does not allow one to get around this constraint.
Teleportation of a quantum state representing a superposition of non-degenerate energy states can not be achieved without transmittinga timing signal
TELEPORATION OF THE PHASE INFORMATION:
A B
C
ALICE BOB
1 2
3
C
STRONGEXCITATIONFOR PULSE
1 2
3
C
WEAKEXCITATIONFOR PULSE
TELEPORT
APPLICATION TO CLOCK SYNCHRONIZATION:
THE BASIC PROBLEM:
APPROACH:
CLOCK A CLOCK B
f
MASTER SLAVE
ELIMINATE f BY QUANTUM FREQUENCY TRANSFER
THIS IS EXPECTED TO STABILIZE
DETERMINE AND ELIMINATE TO HIGH-PRECISION VIA OTHER METHODS, USING LONGTIME AVERAGING TO REDUCE EFEFCTS OF PATHLENGTH FLUCTUATIONS(SNR CONSIDERATION IMPLIES THAT A CLASSICAL METHOD WOULD BE THE BEST FOR THIS TASK
QUANTUM FREQUENCY/WAVELENGTH TRANSFER:
ALICE
BOB
High-Stability, Portable Entanglement Source
•PPKTP optical parametric amplifier at frequency degeneracy•Polarization-entangled outputs after beamsplitter•High-stability cavity design: vibration-resistant, no mirror mounts•Portable system: locked-down cavity setup and fiber-coupled pump•Fine tuning: pump wavelength, crystal’s temperature, cavity PZT
P Z TT E c o o l e r
P P K T P
F i b e r - c o u p l e dP u m p
3 9 7 n m
7 9 5 n m
5 0 / 5 0
P o l a r i z a t i o n -E n t a n g l e d
O u t p u t s
Degenerate Parametric Amplifier Source
Type-II KTP parametric amplifier at frequency degeneracy:
•Pumped at 532 nm with outputs at 1064 nm
•Pair generation rate: 1.7 x 106 /s at 100 W pump
Launch laser beam
Pulsed ServoBeam
Pulsed Probe Beam
FORTBeam
CopperBlockFor VibrationIsolation
EVENTUAL CONFIGURATION:
Valve
Probe Beam
SRI PhotonCounter
CooledPMT
CURRENT GEOMETRY:
782.1 NM FORT:
THERMAL ATOMIC BEAM TO OBSERVE BSO PHASE SCAN:
MHz RF
STATE PREPARATION POPULATION MEASUREMENTVIA FLUORESENCE
USE ZEEMAN SUBLEVELS
PROBLEMS DUE TO THERMALVELOCITY SPREAD OVERCOMEVIA DETECTION CLOSE TO THEEND OF RF COIL
“Long Distance, Unconditional Teleportation of Atomic States Via Complete Bell State Measurements,” S. Lloyd, M.S. Shahriar, and P.R. Hemmer, Phys. Rev. Letts.87, 167903 (2001)
“Phase-Locking of Remote Clocks using Quantum Entanglement,” M.S. Shahriar, (quant-ph eprint)
“Physical Limitation to Quantum Clock Synchronization,” V. Giovanneti, L. Maccone, S. Lloyd, and M.S. Shahriar, (quant-ph eprint)
“Measurement of the Local Phase of An Oscillating Field via Incoherent Fluorescence Detection,” M.S. Shahriar and P. Pradhan, (in preparation; draft available upon request: [email protected])
RELEVANT PUBLICATIONS/PREPRINTS