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ULTRA-PRECISE CLOCK SYNCHRONIZATION VIA DISTANT ENTANGLEMENT

DARPA QUantum Information Science and Technology Site Visit at Northwestern University. ULTRA-PRECISE CLOCK SYNCHRONIZATION VIA DISTANT ENTANGLEMENT. Http://lapt.ece.nwu.edu/research/Projects/clocksynch. Selim Shahriar, Project PI Franco Wong, Co-PI Res. Lab. Of Electronics.

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ULTRA-PRECISE CLOCK SYNCHRONIZATION VIA DISTANT ENTANGLEMENT

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  1. DARPA QUantum Information Science and Technology Site Visit at Northwestern University ULTRA-PRECISE CLOCK SYNCHRONIZATION VIA DISTANT ENTANGLEMENT Http://lapt.ece.nwu.edu/research/Projects/clocksynch Selim Shahriar, Project PI Franco Wong, Co-PI Res. Lab. Of Electronics 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, 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 Jet Propulsion Laboratory J. Dowling, others

  2. SUB-SHOT-NOISE TIME SIGNALING VIA ENTANGLED FREQUENCY SOURCE 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 Quantum memory will be produced with a coherence time of upto several minutes, making possible high-fidelity quantum communication and teleportation 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 Sub-picosecond scale synchronization of separated clocks, and remote frequency-locking will increase the resolution of GPS systems POGRAM SUMMARY D t YR1 YR2 YR3 Bloch-Siegert Oscillation Entangled Photon Source Non-deg Teleportation Frequency Teleportation Relativist Entanglement Decoherence in Clock-Synch

  3. 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, SUCH AS SUB-SHOT-NOISE TIME SIGNALING VIA ENTANGLED FREQUENCY SOURCE DETERMINE THE NON-TRIVIAL ROLE OF SPECIAL AND GENERAL RELATIVITY IN THESE PROCESSES CLOCK SYNCHRONIZATION: NWU/MIT NWU/MIT JPL

  4. 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:

  5. 3 Effective Schr. Eqn.: A Effective Hamiltonian: 1 Effective Coupling Parameter: (t)= -go[exp(-i2t-i2)+1]/2 Effective State Vector: 3 1

  6. 3 Periodic Solution: A Where: =exp(-i2t-i2) 1 For all n, we get the following: 3 1

  7. 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

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

  9. 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

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

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

  12. 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

  13. 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

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

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

  16. 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

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

  18. 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

  19. TRANSFER PHOTON ENTANGLEMENT TO ATOMIC ENTANGLEMENT

  20. B EXPLICIT SCHEME IN 87RB C D A

  21. 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

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

  23. 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

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

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

  26. 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.)

  27. EXPERIMENTAL TEST USING RUBIDIUM ATOMIC BEAM RF-COIL FL- DETECTOR Experimental Apparatus constructed and Tested Reassembly in progress at NWU Potential Concern: BSO wash-out due to velocity spread Identified a Photon-Echo Type process that eliminates the effect of velocity spread Expect results in a few months

  28. 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

  29. 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

  30. 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, SUCH AS SUB-SHOT-NOISE TIME SIGNALING VIA ENTANGLED FREQUENCY SOURCE DETERMINE THE NON-TRIVIAL ROLE OF SPECIAL AND GENERAL RELATIVITY IN THESE PROCESSES CLOCK SYNCHRONIZATION: NWU/MIT NWU/MIT JPL

  31. QUANTUM FREQUENCY/WAVELENGTH TRANSFER: ALICE Dl BOB

  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. SUMMARY OF PROGRESS/NWU GROUP Identified concrete technique for full-fidelity teleportation via measurement of all four Bell states Identified concrete scheme for measuring BSO in an atomic beam Identified concrete scheme for frequency locking Demonstrated Atomic Fountain and FORT, as precursor to single trapped atoms

  37. MOST RELEVANT PUBLICATIONS/PREPRINTS/NWU GROUP “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)

  38. 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).

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