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

2. POGRAM SUMMARY   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 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-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 RELATIVISTIC GENERALIZATION OF ENTANGLEMENT AND FREQUENCY TELEPORTATION Non-deg Teleportation Bloch-Siegert Oscillation Frequency Teleportation Relativist Entanglement Decoherence in Clock-Synch YR1YR3YR2 Entangled Photon Source CLOCK ACLOCK B  f

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

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

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

6. gogo aoao bobo gogo a -1 b -1 gogo a1a1 b1b1 gogo a -2 b -2 gogo a2a2 b2b2 gogo gogo gogo 0 22 -2  44 -4  gogo Energy 1 3

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

8. gogo aoao bobo gogo a -1 b -1 gogo a1a1 b1b1 gogo a -2 b -2 gogo a2a2 b2b2 gogo gogo gogo 0 22 -2  44 -4  gogo Energy 1 3

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

10. 0 22 -2  44 -4  gogo aoao bobo gogo a -1 b -1 gogo a1a1 b1b1 gogo gogo Energy

11. gogo aoao bobo gogo a -1 b -1 gogo a1a1 b1b1 gogo gogo  -  (a -1 -b -1 )  +  (a -1 +b -1 ) Define: Which yields: Adiabatic following: Solution: Similarly: Where  (g o /4  ) is small, kept to first order

12. gogo aoao bobo gogo a -1 b -1 gogo a1a1 b1b1 gogo gogo Reduced Equations: Where  =g 2 o /4  is the Bloch-Siegert Shift. The NET solution is:

13. gogo aoao bobo gogo a -1 b -1 gogo a1a1 b1b1 gogo gogo

14. A 1 3 In the original picture, the solution is: where  Conventional Result

15. A 1 3 IMPLICATIONS: t t1t1 t2t2 When  is ignored, result of measurement of pop. of state 1 is independent of t 1 and t 2, and depends only on (t 2 - t 1 ) When  is NOT ignored, result of measurement of pop. of state 1 depends EXPLICITLY ON t 1, as well as on (t 2 - t 1 ) Explit dependence on t 1 enables measurement of  the field phase at t 1

16. t t1t1 t2t2 T  A 1 3 T  33 RABI OSCILLATION BLOCH-SIEGERT OSCILLATION 

17. 050100150200250300350 0.92 0.922 0.924 0.926 0.928 0.93 0.932 0.934 0.936 0.938 Initial Phase in Degree Amplitude  T t t1t1 t2t2 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

18. TRANSFER PHOTON ENTANGLEMENT TO ATOMIC ENTANGLEMENT

19. EXPLICIT SCHEME IN 87 RB C A B D

20. 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  

21. NET RESULT OF THIS PROCESS: DEGENERATE ENTANGLEMENT ALICE BOB A 1 2 3 B 1 2 3 |         

22. NON-DEGENERATE ENTANGLEMENT: VCO A 1 2 3 B 1 2 3 |  (t)>=[|1> A |3> B exp(-i  t-i  ) - |3> A |1> B exp(-i  t-i  )]/  2. B A =B ao Cos(  t+  ) B B =B bo Cos(  t+  )

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

24. A 1 3 Recalling the NRWA solution: The following states result from  excitation starting from different initial states:

25. t t1t1 t2t2 t ALICE: BOB: Measure |1> A Measure |1> B Post-Selection p S  Probability of success on both measurements For Normal Excitation: (|1> A goes to |+> A, etc.) For Time-Reversed Excitation: (|+> A goes to |1> A, etc.) 

26. The relative phase between A and B can not be measured this way LIMITATIONS: 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: AB C ALICE BOB 1 2 3 C STRONG EXCITATION FOR  PULSE 1 2 3 C WEAK EXCITATION FOR  PULSE TELEPORT

28. APPLICATION TO CLOCK SYNCHRONIZATION: THE BASIC PROBLEM: APPROACH: CLOCK ACLOCK 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

29. QUANTUM FREQUENCY/WAVELENGTH TRANSFER: ALICE 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 10 6 /s at 100  W pump

32. EVENTUAL CONFIGURATION:

33. CURRENT GEOMETRY:

34. 782.1 NM FORT:

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

36. “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