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Ultraprecise Clock Synchromnization Via Distant Entanglement

Ultraprecise Clock Synchromnization Via Distant Entanglement. Team: Dr. George Cardoso (Post-Doc) Dr. Prabhakar Pradhan (Post-Doc) Dr. Max Raginsky Jacob Morzinski (Grad Student/MIT) Dr. Ulvi Yurtsever (JPL) Dr. Franco Wong (MIT). Supported By: DARPA, NRO. CLOCK SYNCHRONIZATION:.

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Ultraprecise Clock Synchromnization Via Distant Entanglement

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  1. Ultraprecise Clock Synchromnization Via Distant Entanglement Team: Dr. George Cardoso (Post-Doc) Dr. Prabhakar Pradhan (Post-Doc) Dr. Max Raginsky Jacob Morzinski (Grad Student/MIT) Dr. Ulvi Yurtsever (JPL) Dr. Franco Wong (MIT) Supported By: DARPA, NRO

  2. CLOCK SYNCHRONIZATION: THE BASIC PROBLEM: APPROACH: D t CLOCK A CLOCK B D f NWU/MIT MASTER SLAVE NWU/MIT 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 JPL

  3. EXAMPLE: GPS User clock need not be very stable long-term Differential Positioning enables high accuracy

  4. 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

  5. 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

  6. HOW AND WHERE QM MAY HELP? However, the net SNR is much smaller than what can be achieved via entangled states TIMING RESOLUTION AND ACCURACY Fundamentally constrained by Signal-to-Noise Ratio 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)

  7. HOW AND WHERE QM MAY HELP? Constraint tied to the basic notion of synchrony PROPAGATION LENGTH FLUCTUATION Limits accuracy to time-scales longer than the characteristic time-scale of the fluctuation 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 Clocks Using Quantum Entanglement,” quant-ph/0010007 U. Yurtsever and J.P. Dowling, quant-ph/0010097

  8. HOW AND WHERE QM MAY HELP? DRIFTS IN CLOCK FREQUENCIES This is the fundamental cause for asynchrony Entanglement may help in frequency locking independent 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

  9. 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:

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

  11. 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

  12. x 3 A 1 t t t1 t2 x t Phase-sensitivity maximum at p/2 pulse Must be accounted for when doing QC if s is not negligible

  13. 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

  14. STATE OF THE NON-DEGENERATE ENTANGLEMENT: SUMMARY 3 3 A B 1 1 2 2 ALICE: 2 - 3 t t1 t3 t4 t2 BOB: 2 - 3 t

  15. NEXT STEP IN THE PROTOCOL: 3 3 A B 1 1 2 2 ALICE: 2 - 3 1 - 3 t t3 t1 t4 t2 t5 t6 BOB: 2 - 3 t POST-SELECTION

  16. FINAL STEP IN THE PROTOCOL: 3 3 A B 1 1 2 2 ALICE: 2 - 3 1 - 3 1 - 3 t t3 t1 t4 t2 t5 t7 t6 t8 BOB: 2 - 3 t POST-SELECTION

  17. RESULT OF THE PROTOCOL: Df 0 BOB

  18. and repumping Atomic beam fluorescence detection Fluorescence Frequency = t

  19. Frequency Fluorescence with Frequency From AOM 2D drives Frequency Doubler Phase constant Mixer

  20. Observation of the BSO Signal Reference Signal -20 BSO Signal -40 33 dB -60 Relative strength (dB) -80 -100 0 1 2 3 frequency (MHz)

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