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 Site Visit at Northwestern University 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 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

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, 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-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 SUB-SHOT-NOISE TIME SIGNALING VIA ENTANGLED FREQUENCY SOURCE

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

4. 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

5. 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

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

7. 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

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

9. 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

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

11. 0 22 -2  44 -4  gogo aoao bobo gogo a -1 b -1 gogo a1a1 b1b1 gogo gogo Energy

12. 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

13. 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:

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

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

16. 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

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

18. 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

19. TRANSFER PHOTON ENTANGLEMENT TO ATOMIC ENTANGLEMENT

20. EXPLICIT SCHEME IN 87 RB C A B D

21. 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  

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

23. 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+  )

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

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

26. 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.) 

27. 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-COILFL- DETECTOR Identified a Photon-Echo Type process that eliminates the effect of velocity spread Expect results in a few months

28. 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

29. 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

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

31. QUANTUM FREQUENCY/WAVELENGTH TRANSFER: ALICE BOB 

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

37. “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

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).