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