Post on 08-Jan-2016
description
ULTRA-PRECISE CLOCK SYNCHRONIZATION VIA DISTANT ENTANGLEMENT
Selim Shahriar, Project PIFranco Wong, Co-PIRes. Lab. Of Electronics
DARPA QUantum Information Scienceand Technology Site Visit at
Northwestern University
Selim Shahriar, subcontract PIDept. of Electrical and Computer EngineeringLaboratory for Atomic and Photonic TechnologiesCenter for Photonic Communications and Computing
Ulvi Yurtsever, “subcontract” PIJet Propulsion Laboratory
Http://lapt.ece.nwu.edu/research/Projects/clocksynch
L. Maccone, V. Giovanetti, others
V. Gopal, P. Pradhan,G. Cardoso, M. Raginsky,A. Heifetz, J. Shen, K. Salit,A. Hasan, A. Gangat, M. Hall,
J. Dowling, others
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, and remote frequency-locking will increase the resolution of GPS systems
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
fSUB-SHOT-NOISE TIME SIGNALING VIA ENTANGLEDFREQUENCY SOURCE
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, SUCH AS SUB-SHOT-NOISE TIME SIGNALING VIA ENTANGLED FREQUENCY SOURCE
DETERMINE THE NON-TRIVIAL ROLE OF SPECIAL AND GENERAL RELATIVITYIN THESE PROCESSES
NWU/MIT
NWU/MIT
JPL
A
1
3
)(
)(0^
tg
tgH
A
A
C
Ct
3
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:
)(
~|)(
~)(~
|ttHi
t
t
0)(
)(0*
~
t
tH
A
A
C
CtQt
3
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
eetin
nn
tin
nn ngPnPgt
,|||)0(|
etin
nnn
n neTiSinngTCosPTt ]1,|)(,|)([)(|
}1|{|)(}|{|)()(| eetin
nn
tin
nn nPeTiSinnPgTCosTt
}1|{|)(}|{|)()(|)1(
eeetni
nn
titin
nn nPeTiSinnPgTCosTt
AFTER EXCITATION: ENTANGLED STATE:
SEMI-CLASSICAL APPROXIMATION:
}|{]|)(|)([)(| eetin
nn
tinPeTiSingTCosTt
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
eetin
nn
tin
nn ngPnPgt
,|||)0(|
AFTER EXCITATION: ENTANGLED STATE:
BEFORE EXCITATION:
eti
eg egTt ||||)(|
]2|)(|)([|)2(
eetni
n
tin
nn
ng nTSininTCosP
]3|)(1|)([|)3()1(
eetni
n
tni
nn
ne 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/( tii
where
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 Degree
Am
plitu
de
T
tt1 t2
T
A
1
3
Phase-sensitivity maximum at pulse
Must 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
ti
AAie 321121
2
1 *)(
A
ti
AAie 321121
2
1 *)(
B
ti
BBie 321121
2
1 *)(
B
ti
BBie 321121
2
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
ti
AAie 321121
2
1 *)(
A
ti
AAie 321121
2
1 *)(
B
ti
BBie 321121
2
1 *)(
B
ti
BBie 321121
2
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(212
12 tSinpS
For Normal Excitation: (|1>A goes to |+>A, etc.)
)22(212
11 tSinpS
For Time-Reversed Excitation: (|+>A goes to |1>A, etc.)
)2(212
1 Sin
Experimental Apparatus constructed and Tested
EXPERIMENTAL TEST USING RUBIDIUM ATOMIC BEAM
Reassembly in progress at NWU
Potential Concern: BSO wash-out due to velocity spread
RF-COIL FL- DETECTOR
Identified a Photon-Echo Type process that eliminates the effect of velocityspread
Expect results in a few months
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
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, SUCH AS SUB-SHOT-NOISE TIME SIGNALING VIA ENTANGLED FREQUENCY SOURCE
DETERMINE THE NON-TRIVIAL ROLE OF SPECIAL AND GENERAL RELATIVITYIN THESE PROCESSES
NWU/MIT
NWU/MIT
JPL
QUANTUM FREQUENCY/WAVELENGTH TRANSFER:
ALICE
BOB
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
SUMMARY OF PROGRESS/NWU GROUP
Identified concrete technique for full-fidelity teleportation via measurementof all four Bell states
Identified concrete scheme for frequency locking
Demonstrated Atomic Fountain and FORT, as precursor to singletrapped atoms
Identified concrete scheme for measuring BSO in an atomic beam
“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)
“Frequency Locking Via Phase Mapping Of Remote Clocks Using Quantum Entanglement” M.S. Shahriar, (sub to PRL; quant-ph eprint)
“Physical Limitation to Quantum Clock Synchronization,” V. Giovanneti, L. Maccone, S. Lloyd, and M.S. Shahriar, (to appear in PRA)
“Determination Of The Phase Of An Electromagnetic Field Via Incoherent Detection Of Fluorescence,” M.S. Shahriar and P. Pradhan, (sub to PRL; quant-ph eprint)
MOST RELEVANT PUBLICATIONS/PREPRINTS/NWU GROUP
OTHER RELEVANT PUBLICATIONS/PREPRINTS/NWU GROUP
.
.M.S. Shahriar and P. Pradhan, “Fundamental Limitation On Qubit Operations Due To
The Bloch-Siegert Oscillation,” to be presented at QCMC 2002, Boston, MA.
.P. Pradhan, J. Morzinsky and M.S. Shahriar, “Determination of the Phase of an Electromagnetic Field via Incoherent Detection of Fluorescence using the Bloch-Siegert Oscillation,” to be presented at the Progress In Electromagnetic Research Symposium 2002, Cambridge, MA (July 2002).
.M.S. Shahriar and P. Pradhan, “Measurement of the Phase of an Electromagnetic Field via Incoherent Detection of Fluorescence,” to be presented at the OSA Annual Meeting, 2002.
.M.S. Shahriar and P. Pradhan, “Determination and Teleportation Of The Phase Of An Electromagnetic Field Via Incoherent Detection Of Fluorescence,” presented at the APS annual meeting, March, 2002.
.M.S. Shahriar, “Bloch-Siegert oscillation for detection and quantum teleportation of the phase of an oscillating field,” proceedings of the Conference on Quantum Optics 8, Rochester, NY, July 2001.
.M.S. Shahriar, “Frequency Locking Via Phase Mapping Of Remote Clocks Using Quantum Entanglement,” submitted to Phys. Rev. Lett. (http://xxx.lanl.gov/pdf/quant-ph/0010007).