ultra-precise clock synchronization via distant entanglement

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).