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: smshahri@mit.edu)

RELEVANT PUBLICATIONS/PREPRINTS