Ultraprecise Clock SynchromnizationVia Distant Entanglement
Team:Dr. George Cardoso (Post-Doc)Dr. Prabhakar Pradhan (Post-Doc)Dr. Max RaginskyJacob Morzinski (Grad Student/MIT)Dr. Ulvi Yurtsever (JPL)Dr. Franco Wong (MIT)
Supported By:DARPA, NRO
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
EXAMPLE: GPS
User clock need not be very stable long-term
Differential Positioning enables high accuracy
WHAT ARE THE ISSUES?
CASE 1: Sattelite to Sattelite Synchronization
No propagation related problem
Clock frequencies can drift with respect each other
Signal-to-Noise Ratio determines timing resolution and accuracy
Special and General Relativity have to be accounted for accurately
Doppler shifts have to be taken into account
WHAT ARE THE ISSUES?
CASE 2: Sattelite to Ground Synchronization
Fluctuation in the propagating medium is the key problem
Clock frequencies can drift with respect each other
Signal-to-Noise Ratio determines timing resolution and accuracy
Special and General Relativity have to be accounted for accurately
Doppler shifts have to be taken into account
HOW AND WHERE QM MAY HELP?
Entangled states may help V. Giovannetti, S. Lloyd, L. Maccone, Nature, Vol. 412, 26 July, 2001
V. Giovannetti, S. Lloyd, L. Maccone, and F.N.C. Wong,Phys. Rev. Letts. 87, 117902 (2001)
TIMING RESOLUTION AND ACCURACY
Fundamentally constrained by Signal-to-Noise Ratio
However, the net SNR is much smaller than what can beachieved via entangled states
HOW AND WHERE QM MAY HELP?
Entanglement does not help overcome this limit
V. Giovannetti, S. Lloyd, L. Maccone, and M. S. Shahriar, Phys. Rev. A 65, 062319 ,2002
R. Jozsa, D.S. Abrams, J.P. Dowling, and C.P. Williams, Phys. Rev. Letts. 85, 2010(2000)
M.S. Shahriar, “Phase Mapping of Remote ClocksUsing Quantum Entanglement,” quant-ph/0010007
U. Yurtsever and J.P. Dowling, quant-ph/0010097
PROPAGATION LENGTH FLUCTUATION
Limits accuracy to time-scales longer than the characteristictime-scale of the fluctuation
Constraint tied to the basic notion of synchrony
HOW AND WHERE QM MAY HELP?
Entanglement may help in frequency lockingindependent of propagation length fluctuation
S.Lloyd, M.S. Shahriar, J.H. Shapiro, and P.R. Hemmer, Phys. Rev. Lett. 87, 167903 (2001)
M.S. Shahriar, P. Pradhan, and J. Morzinski, “Measurement of the Phase of an Electromagnetic Field via Incoherent Detection of Fluorescence,” quant-ph/0205120
M.S. Shahriar, “Frequency Locking Via Phase Mapping Of Remote Clocks Using Quantum Entanglement,” quant-ph/0209064
DRIFTS IN CLOCK FREQUENCIES
This is the fundamental cause for asynchrony
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
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
)]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
A
1
3
Phase-sensitivity maximum at pulseMust be accounted for when doing QC if is not negligible
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+ )
STATE OF THE NON-DEGENERATE ENTANGLEMENT: SUMMARY
A
1 2
3
B
1 2
3
BABA
t 2
1)(
tt1 t2
t
ALICE:
BOB:
t3 t4
NEXT STEP IN THE PROTOCOL:
A
1 2
3
B
1 2
3
BAt 1)(
t
t
ALICE:
BOB:
t3 t4
t1 t2
t5 t6
POST-SELECTION
FINAL STEP IN THE PROTOCOL:
A
1 2
3
B
1 2
3
BAt 31)(
t
t
ALICE:
BOB:
t3 t4
t1 t2
t5 t6
POST-SELECTION
t7 t8
RESULT OF THE PROTOCOL:
BOB
f
1 and repumping
Atomic beam
,
fluorescence detection
),(, 21 ggBSOBSO
Fluorescence
Frequency = 4 t
Mixer
Fluorescence with Frequency
Frequency 2
From AOMdrives
FrequencyDoubler
Phase constant
0 1 2 3
-100
-80
-60
-40
-20
33 dB
frequency (MHz)
R
elat
ive
stre
ngth
(dB
)
Reference Signal
BSO Signal
Observation of the BSO Signal
