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ULTRA-PRECISE CLOCK SYNCHRONIZATION VIA DISTANT ENTANGLEMENT

DARPA QUantum Information Science and Technology Kickoff Meeting Nov. 26-29, 2001 Dallas, TX. ULTRA-PRECISE CLOCK SYNCHRONIZATION VIA DISTANT ENTANGLEMENT. Selim Shahriar, Project PI Franco Wong, Co-PI Res. Lab. Of Electronics. 3/4 p pulse. Selim Shahriar, subcontract PI

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ULTRA-PRECISE CLOCK SYNCHRONIZATION VIA DISTANT ENTANGLEMENT

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  1. DARPA QUantum Information Science and Technology Kickoff Meeting Nov. 26-29, 2001 Dallas, TX ULTRA-PRECISE CLOCK SYNCHRONIZATION VIA DISTANT ENTANGLEMENT Selim Shahriar, Project PI Franco Wong, Co-PI Res. Lab. Of Electronics 3/4 p pulse Selim Shahriar, subcontract PI Dept. of Electrical and Computer Engineering Laboratory for Atomic and Photonic Technologies Center for Photonic Communications and Computing Ulvi Yurtsever, “subcontract” PI John Dowling, “subcontract” Co-PI Jet Propulsion Laboratory

  2. POGRAM SUMMARY D t TRAPPED RB ATOM QUANTUM MEMORY ULTRA-BRIGHT SOURCE FOR ENTANGLED PHOTON PAIRS DEGENERATE DISTANT ENTANGLEMENT BETWEEN PAIR OF ATOMS QUANTUM FREQUENCY TELEPORTATION VIA BSO AND ENTANGELEMENT RELATIVISTIC GENERALIZATION OF ENTANGLEMENT AND FREQUENCY TELEPORTATION CLOCK A CLOCK B D f Sub-pico-meter scale resolution measurement of amplitude as well as phase of oscillating magnetic fields would enhance the sensitivity of tracking objects such as submarines Quantum memory will be produced with a coherence time of upto several minutes, making possible high-fidelity quantum communication and teleportation Sub-picosecond scale synchronization of separated clocks will increase the resolution of GPS systems even in the presence of random fluctuations of pathlengths YR1 YR2 YR3 Bloch-Siegert Oscillation Entangled Photon Source Non-deg Teleportation Frequency Teleportation Relativist Entanglement Decoherence in Clock-Synch

  3. MEASUREMENT OF PHASE USING ATOMIC POPULATIONS: THE BLOCH-SIEGERT OSCILLATION Hamiltonian (Dipole Approx.): 3 A State Vector: 1 Coupling Parameter: g(t) = -go[exp(it+i)+c.c.]/2 Rotation Matrix:

  4. 3 Effective Schr. Eqn.: A Effective Hamiltonian: 1 Effective Coupling Parameter: (t)= -go[exp(-i2t-i2)+1]/2 Effective State Vector: 3 1

  5. 3 Periodic Solution: A Where: =exp(-i2t-i2) 1 For all n, we get the following: 3 1

  6. Energy 4 go 2 go go go go go 3 1 a1 a-2 go a2 a-1 b2 b1 b-2 b-1 0 ao bo go -2 go -4

  7. FULLY QUANTIZED VIEW: EXCITATION FIELD AS A COHERENT STATE RWA CASE: BEFORE EXCITATION: AFTER EXCITATION: ENTANGLED STATE: SEMI-CLASSICAL APPROXIMATION:

  8. Energy 4 go 2 go go go go go 3 1 a1 a-2 go a2 a-1 b2 b1 b-2 b-1 0 ao bo go -2 go -4

  9. NRWA CASE: BEFORE EXCITATION: AFTER EXCITATION: ENTANGLED STATE: where: SEMICLASSICAL APPROXIMATION: Yields the same set of coupled equations as derived semiclassically without RWA

  10. Energy go go 4 a1 go a-1 b1 b-1 2 ao bo go 0 go -2 -4

  11. Define: - (a-1-b-1) + (a-1+b-1) Which yields: go go Adiabatic following: a1 go a-1 b1 b-1 ao bo Solution: go go Similarly: Where (go/4) is small, kept to first order

  12. Reduced Equations: Where go go =g2o/4 is the Bloch-Siegert Shift. a1 go a-1 b1 b-1 ao bo The NET solution is: go go

  13. go go a1 go a-1 b1 b-1 ao bo go go

  14. In the original picture, the solution is: 3 A where 1 Conventional Result s= 0

  15. 3 A IMPLICATIONS: 1 t t1 t2 When s is ignored, result of measurement of pop. of state 1 is independent of t1 and t2, and depends only on (t2- t1) When s 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 x, the field phase at t1

  16. r33 x=0 3 A T t t1 t2 RABI OSCILLATION 1 BLOCH-SIEGERT OSCILLATION x T

  17. s=0.05 Pulse=0.931p 3 T A T x 0.938 t t1 t2 0.936 0.934 1 0.932 Amplitude 0.93 0.928 0.926 0.924 0.922 0.92 0 50 100 150 200 250 300 350 Initial Phase in Degree Phase-sensitivity maximum at p/2 pulse Must be accounted for when doing QC if s is not negligible x

  18. TRANSFER PHOTON ENTANGLEMENT TO ATOMIC ENTANGLEMENT

  19. B EXPLICIT SCHEME IN 87RB C D A

  20. ATOMS 2 AND 3 ARE NOW ENTANGLED ATOM 2 ATOM 3 a a b b c c d d |23>={ |a>2|b>3- |b>2|a>3}/2

  21. NET RESULT OF THIS PROCESS: DEGENERATE ENTANGLEMENT |Y>=(|1>|2 > - |2>|1>) /2 3 3 A B BOB ALICE 1 1 2 2

  22. NON-DEGENERATE ENTANGLEMENT: |(t)>=[|1>A|3>Bexp(-it-i) - |3>A|1>Bexp(-it-i)]/2. 3 3 A B 1 1 2 2 BB=BboCos( t+ ) BA=BaoCos( t+ ) VCO VCO

  23. |(t)>=[|1>A|3>Bexp(-it-i) - |3>A|1>Bexp(-it-i)]/2. Can be re-expressed as: Where:

  24. Recalling the NRWA solution: 3 A The following states result from p/2 excitation starting from different initial states: 1

  25. Post-Selection Measure |1>A ALICE: Measure |1>B x BOB: t t pSProbability of success on both measurements t1 t2 For Normal Excitation: (|1>A goes to |+>A, etc.) For Time-Reversed Excitation: (|+>A goes to |1>A, etc.)

  26. LIMITATIONS: The relative phase between A and B can not be measured this way Absolute time difference between two remote clocks can not be measured without 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 transmitting a timing signal

  27. TELEPORATION OF THE PHASE INFORMATION: BOB ALICE A B C C C 3 3 STRONG EXCITATION FOR p/2 PULSE WEAK EXCITATION FOR p PULSE TELEPORT 1 1 2 2

  28. APPLICATION TO CLOCK SYNCHRONIZATION: THE BASIC PROBLEM: APPROACH: D t CLOCK A CLOCK B D f MASTER SLAVE ELIMINATE Df BY QUANTUM FREQUENCY TRANSFER THIS IS EXPECTED TO STABILIZE Dt DETERMINE AND ELIMINATE Dt 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

  29. QUANTUM FREQUENCY/WAVELENGTH TRANSFER: ALICE Dl BOB

  30. 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

  31. 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 mW pump

  32. EVENTUAL CONFIGURATION:

  33. CURRENT GEOMETRY:

  34. 782.1 NM FORT:

  35. THERMAL ATOMIC BEAM TO OBSERVE BSO PHASE SCAN: USE ZEEMAN SUBLEVELS PROBLEMS DUE TO THERMAL VELOCITY SPREAD OVERCOME VIA DETECTION CLOSE TO THE END OF RF COIL 1 MHz RF POPULATION MEASUREMENT VIA FLUORESENCE STATE PREPARATION

  36. RELEVANT PUBLICATIONS/PREPRINTS “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)

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