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Impact

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Perhaps the most significant consequence of the Dick analysis is due to its presentation of a mathematical framework that enabled researchers to accurately calculate the effect based on the methodology and technology used for many very different atomic clocks. Since the effect is generally the most significant limitation to stability for advanced frequency standards,[1][2] a great deal of work since that time has focused on amelioration strategies. Additionally, the effect methodology and the sensitivity function have enabled significant progress in a number of technical areas.

  • The value for the limiting instability due to the effect is determined by the interrogation protocol combined with phase noise properties of the LO. Consequences of the theory have been worked out for several different kinds of atomic clocks.[3][4][5]
  • Laboratories working on microwave Atomic fountain clocks have turned to cryogenic[6][7] or optical[8] LO techniques to replace the quartz ultrastable oscillator (USO) previously used as a reference for microwave atomic frequency standards. While the instability of the quartz USO could be reduced by feedback to effectively realize the inherent atomic stability in a clock, its phase noise, transformed by the effect, was now the primary source of the clock's instability, as shown by the graph in the previous section. Cryogenic and optical techniques can provide both the stability and phase noise required to realize the inherent stability of the atomic standard.
These atomic clocks typically operate by tossing a ball of laser-cooled atoms upward through a microwave cavity that acts to start the clock in each individual atom. As the atoms return downward, they again traverse this same cavity where they receive a second microwave pulse that stops their clocks. The ball then falls through an optical interrogation apparatus below the cavity that "reads out" the phase difference between the microwaves (the LO) and the atoms that developed during their flying time. This is repeated again and again; a sequential process that gives rise to the effect.[9]
On a smaller scale, the stability of Rb vapor clocks using a pulsed optically pumped (POP) technique has improved to such an extent that the effect due to a quartz USO LO has become the limiting performance factor. Developments in a combined USO--DRO (dielectric resonator oscillator) LO technology[10] now enable improved performance.
  • Optical clocks have achieved the highest stability of any clocks, and are on track to replace Cesium fountain clocks as the definition of the second.[11] However, as (Katori, 2011)[1] states: "In optical lattice clocks, however, owing to the significantly low QPN (quantum projection noise), the Dick effect becomes the major obstacle in achieving higher stability". Analysis of the effect and its consequence as applied to optical standards has been treated in a major review (Ludlow, et al., 2015)[2] that lamented "the pernicious influence of the Dick effect", and in several other papers.[12][13]
  • The timing for two complete atomic systems (while using only one LO) can be interleaved,[14][15] thus eliminating the dead time associated with atomic state preparation and detection. This substantially reduces the effect, and could possibly eliminate it. The efficacy of his approach was verified by Biedermann et al. in an experiment with a deliberately degraded LO[16][17] Subsequently, this approach has been applied by Shioppo et al.[3][18] to achieve the highest stability to date for any clock in tests using two laser-cooled Yb optical standards, and, on a much smaller scale, in a Rb vapor microwave clock.[19] It has been proposed that zero dead time might be accomplished in a single fountain by use of a juggling protocol.[20] A theoretical paper also proposes to use not only two complete atomic systems, but to add a third (again with a single LO) to not only eliminate the effect but also to reduce the otherwise limiting stability due to photon– or atom–counting effects.[21]
  • An alternative that can eliminate the effect is a continuously operating fountain.[22] Such a clock has been demonstrated, enabled by the development of a source of laser-cooled atoms with continuous flow.[23] This clock uses a different configuration from the usual fountain in order to physically separate the rising atoms from the falling ones. This is achieved by angling the launch direction away from vertical; the atoms' internal clocks are started in one microwave cavity; then stopped in a second one after executing a parabolic arc. The second cavity, together with a second laser interrogation system, are laterally displaced from the launch system and cavity.
  • The microwave or optical signals used to start and stop the atoms' internal clocks typically have a rectangular time dependence. Shaped pulses[14][24] can reduce the effect by eliminating discontinuities in the slope of the sensitivity function that result from a sudden turn on and turn off of the electromagnetic signal. This, in turn, reduces sensitivity to the high-frequency components of LO phase noise, and so reduces the effect. Additionally, when applied to multiple clocks with interleaved timing, properly shaped pulses could eliminate the effect entirely.[14]
  • Compare frequency standards.[25][26][27][28]
  • Atomic clocks have been used and proposed for applications in space, both for applications that require only performance already available from earth-based technology and those that would require performance only available from a clock operating in space.[29][30] A good example is the PHARAO laser-cooled Cs atomic frequency standard [31] which has been delivered to the European Space Agency for incorporation into the ACES multiple-clock physics payload, and is scheduled to be launched to the ISS. A significant part of the performance advantage for space-based clocks is due to a reduction of the effect; this due to the longer interrogation times and higher duty factors available when the atomic clock is operated in zero G.
  • Atom interferometry[24][32] with applications as an atomic gravimeter,[33] and for gravitational wave detection.[34]
  1. ^ a b Katori, H. (2011). "Optical lattice clocks and quantum metrology". Nature Photonics. 5 (4): 203–210. Bibcode:2011NaPho...5..203K. doi:10.1038/nphoton.2011.45.
  2. ^ a b Ludlow, A.D.; Boyd, M.M.; Ye, J.; Peik, E.; Schmidt, P.O. (June 26, 2015). "Optical atomic clocks". Reviews of Modern Physics. 87 (2): 637–701. arXiv:1407.3493. Bibcode:2015RvMP...87..637L. doi:10.1103/RevModPhys.87.637. S2CID 119116973.
  3. ^ a b Schioppo, M.; Brown, R. C.; McGrew, W. F.; Hinkley, N.; Fasano, R. J.; Beloy, K.; Yoon, T. H.; Milani, G.; Nicolodi, D.; Sherman, J. A.; Phillips, N. B.; Oates, C. W.; Ludlow, A. D. (2017). "Ultrastable optical clock with two cold-atom ensembles". Nature Photonics. 11 (1): 48–52. arXiv:1607.06867. Bibcode:2017NaPho..11...48S. doi:10.1038/nphoton.2016.231. S2CID 118541117.
  4. ^ Danet, J. M.; Lours, M.; Guérandel, S.; De Clercq, E. (2014). "Dick effect in a pulsed atomic clock using coherent population trapping". IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control. 61 (4): 567–574. arXiv:1406.6673. doi:10.1109/TUFFC.2014.2945. S2CID 363993.
  5. ^ Al Masoudi, A.; Dorcher, S.; Hafner, S.; Sterr, U.; Lisdat, C. (December 2015). "Noise and instability of an optical lattice clock". Physical Review A. 92 (63814): 063814. arXiv:1507.04949. Bibcode:2015PhRvA..92f3814A. doi:10.1103/PhysRevA.92.063814. S2CID 119217208.
  6. ^ Mann, A.G.; Santarelli, G.; Chang, S.; Liuten, A.N.; Laurent, P.; Salomon, C.; Blair, D.G.; Clairon, A. (May 29, 1998). A High Stability Atomic Fountain Clock using a Cryogenic Sapphire Interrogation Oscillator. 1998 IEEE International Frequency Control Symposium. Pasadena, California. doi:10.1109/FREQ.1998.717871.
    Santarelli, G.; Laurent, P.; Lemonde, P.; Clairon, A.; Mann, A.G.; Chang, S.; Liuten, A.N.; Salomon, C. (1999). "Quantum Projection Noise in an Atomic Fountain: A High Stability Cesium Frequency Standard" (PDF). Physical Review Letters. 82 (23): 4619–4622. Bibcode:1999PhRvL..82.4619S. doi:10.1103/PhysRevLett.82.4619. S2CID 26451919.
  7. ^ Takamizawa, A.; Yanagimachi, S.; Tanabe, T.; Hagimoto, K.; Hirano, I.; Watabe, K.; Ikegami, T.; Hartnett, J. (2014). "Atomic fountain clock with very high frequency stability employing a pulse-tube-cryocooled sapphire oscillator". IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control. 61 (9): 1463–1469. doi:10.1109/TUFFC.2014.3060. PMID 25167146. S2CID 27535524.
  8. ^ Weyers, S.; Lipphardt, B.; Schnatz, H. (March 11, 2009). "Reaching the quantum limit in a fountain clock using a microwave oscillator phase locked to an ultrastable laser" (PDF). Physical Review A. 79 (31803): 031803. arXiv:0901.2788. Bibcode:2009PhRvA..79c1803W. doi:10.1103/PhysRevA.79.031803. S2CID 119267225.
  9. ^ Cite error: The named reference Dick 1987 was invoked but never defined (see the help page).
  10. ^ Li, W.B.; Hao, Q.; Du, Y.B.; Huang, S.Q.; Yun, P.; Lu, Z.H. (2019). "Demonstration of a Sub-Sampling Phase Lock Loop Based Microwave Source for Reducing Dick Effect in Atomic Clocks". Chinese Physics Letters. 36 (7): 070601. arXiv:1810.03803. Bibcode:2019ChPhL..36g0601L. doi:10.1088/0256-307X/36/7/070601. S2CID 250853211.
  11. ^ Yao, J.; Sherman, J.A.; Fortier, T.; Leopardi, H.; Parker, T.; McGrew, W.; Zhang, X.; Nicolodi, D.; Fasano, R.; Shaffer, S.; Beloy, K.; Savory, J.; Romisch, S.; Oates, C.; Diddams, S.; Ludlow, A.; Levine, J. (October 30, 2019). "Optical-Clock-Based Time Scale". Physical Review Applied. 12 (44069): 044069. arXiv:1902.06858. Bibcode:2019PhRvP..12d4069Y. doi:10.1103/PhysRevApplied.12.044069. PMC 7580056. PMID 33102625. S2CID 86468489.
  12. ^ Quessada, A.; Kovacich, R. P.; Courtillot, I.; Clairon, A.; Santarelli, G.; Lemonde, P. (April 2, 2003). "The Dick effect for an optical frequency standard". Journal of Optics B: Quantum and Semiclassical Optics. 5 (2): S150–S154. Bibcode:2003QuSOp...5S.150Q. doi:10.1088/1464-4266/5/2/373.
  13. ^ Westergaard, P.G.; Lodewyck, J.; Lemonde, P. (March 2010). "Minimizing the Dick effect in an optical lattice clock". IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control. 57 (3): 623–628. arXiv:0909.0909. doi:10.1109/TUFFC.2010.1457. PMID 20211780. S2CID 10581032.
  14. ^ a b c Cite error: The named reference Dick etal 1990 was invoked but never defined (see the help page).
  15. ^ Cheng, P.; Sun, X.; Zhang, J.; Wang, L. (2018). "Suppression of Dick Effect in Ramsey-CPT Atomic Clock by Interleaving Lock". IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control. 65 (11): 2195–2200. arXiv:1707.07559. doi:10.1109/TUFFC.2018.2864622. PMID 30106720. S2CID 52006126.
  16. ^ Biedermann, Grant (2008). Gravity tests, differential accelerometry and interleaved clocks with cold atom interferometers (PDF) (PhD). Stanford University.
  17. ^ Biedermann, G.W.; Takese, K.; Wu, X.; Deslauriers, K.; Roy, S.; Kasevich, M. A. (2013). "Zero-Dead-Time Operation of Interleaved Atomic Clocks". Physical Review Letters. 341 (17): 1215–1218. Bibcode:2013PhRvL.111q0802B. doi:10.1103/PhysRevLett.111.170802. PMID 24206471.
  18. ^ Hinkley, N.; Sherman, J. A.; Phillips, N. B.; Schioppo, M.; Lemke, N.D.; Beloy, K.; Pizzocaro, M.; Oates, C. W.; Ludlow, A. D. (2013). "An atomic clock with 10-18 instability". Science. 341 (6151): 1215–1218. arXiv:1305.5869. Bibcode:2013Sci...341.1215H. doi:10.1126/science.1240420. PMID 23970562. S2CID 206549862.
  19. ^ Lin, H.; Lin, J.; Deng, J.; Zhang, S.; Wang, W. (2017). "Pulsed optically pumped atomic clock with zero-dead-time". Review of Scientific Instruments. 88 (123103): 123103. Bibcode:2017RScI...88l3103L. doi:10.1063/1.5008627. PMID 29289225.
  20. ^ Meunier, M.; Dutta, I.; Geiger, R.; Guerlin, C.; Garrido Alzar, C.L.; Landragin, A. (December 22, 2014). "Stability enhancement by joint phase measurements in a single cold atomic fountain". Physical Review A. 90 (63633): 063633. arXiv:1501.01943. Bibcode:2014PhRvA..90f3633M. doi:10.1103/PhysRevA.90.063633. S2CID 26876528.
  21. ^ Li, W.; Wu, S.; Smerzi, A.; Pezzè, L. (2022). "Improved absolute clock stability by the joint interrogation of two atomic ensembles". Physical Review A. 105 (5): 053116. arXiv:2104.14309. doi:10.1103/PhysRevA.105.053116. S2CID 233444191.
  22. ^ Joyet, A.; Mileti, G.; Dudle, G.; Thomann, P. (2001). "Theoretical study of the Dick effect in a continuously operated Ramsey resonator" (PDF). IEEE Transactions on Instrumentation and Measurement. 50 (1): 150–156. Bibcode:2001ITIM...50..150J. doi:10.1109/19.903893.
  23. ^ Devenoges, L.; Stefanov, A.; Joyet, A.; Thomann, P.; Di Domenico, G. (2012). "Improvement of the Frequency Stability Below the Dick Limit With a Continuous Atomic Fountain Clock" (PDF). IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control. 59 (2): 211–216. doi:10.1109/TUFFC.2012.2181. PMID 24626029. S2CID 15285482.
  24. ^ a b Fang, B.; Mielec, M.; Savole, D.; Altorio, A.; Landragin, A.; Geiger, R. (February 20, 2018). "Improving the phase response of an atom interferometer by means of temporal pulse shaping". New Journal of Physics. 20 (2): 023020. arXiv:1712.08110. Bibcode:2018NJPh...20b3020F. doi:10.1088/1367-2630/aaa37c. S2CID 54042350.
  25. ^ Takamoto, M.; Takano, T.; Katori, H. (2011). "Frequency comparison of optical lattice clocks beyond the Dick limit". Nature Photonics. 5 (5): 288–292. Bibcode:2011NaPho...5..288T. doi:10.1038/nphoton.2011.34.
  26. ^ Bize, S.; Sortais, Y.; Lemonde, P.; Zhang, S.; Laurent, P.; Santarelli, G.; Salomon, C.; Clairon, A. (September 2000). "Interrogation oscillator noise rejection in the comparison of atomic fountains". IEEE Transactions on Ultrasonics, Ferroelectrics, and Frequency Control. 47 (5): 1253–1255. doi:10.1109/58.869073. PMID 18238668. S2CID 11952522.
  27. ^ Oelker, E.; Hutson, R.B; Kennedy, C.J.; Sonderhouse, L.; Bothwell, T.; Goban, A.; Kedar, D.; Sanner, C.; Robinson, J.M.; Marti, G.E.; Matei, D.G.; Legero, T.; Giunta, M.; Holzwarth, R.; Riehle, F.; Sterr, U.; Ye, J. (2019). "Demonstration of 4.8 × 10−17 stability at 1 s for two independent optical clocks". Nature Photonics. 13 (10): 714–719. arXiv:1902.02741. doi:10.1038/s41566-019-0493-4. S2CID 201255893.
  28. ^ Lu. X.; Zhou, C.; Li, T.; Wang, Y.; Chang, H. (2020). "Synchronous frequency comparison beyond the Dick limit based on dual-excitation spectrum in an optical lattice clock". Applied Physics Letters. 117 (23): 231101. doi:10.1063/5.0025097.
  29. ^ Li, L.; Qui, Q.Z.; Wang, B.; Li, T.; Zhao, J.B.; Ji, J.W.; Ren, W.; Zhao, X.; Ye, M.F; Yao, Y.Y.; Lu, D.S.; Liu, L. (2016). "Initial Tests of a Rubidium Space Cold Atom Clock". Chin Phys Lett. 33 (6): 063201. Bibcode:2016ChPhL..33f3201L. doi:10.1088/0256-307X/33/6/063201. S2CID 250872294.
  30. ^ Derevianko, A.; Gibble, K.; Hollberg, L.; Newbury, N. R.; Oates, C.; Safronova, M. S.; Sinclair, L. C.; Yu, N. (2022). "Fundamental physics with a state-of-the-art optical clock in space". IOP Publishing. 7 (4): 044002. arXiv:2112.10817. Bibcode:2022QS&T....7d4002D. doi:10.1088/2058-9565/ac7df9. S2CID 245353766.
  31. ^ Laurent, P.; Esnaut, F. X.; Gibble, K.; Peterman, P.; Lévèque, T.; Delaroche, C.; Grosjean, O.; Moric, I.; Abgrall, M.; Massonnet, D.; Salomon, C. (2020). "Qualification and frequency accuracy of the space-based primary frequency standard PHARAO" (PDF). Metrologia. 57 (5): 055005. Bibcode:2020Metro..57e5005L. doi:10.1088/1681-7575/ab948b. S2CID 219450624.
  32. ^ Chienet, P.; Canuel, B.; Dos Santos, F. P.; Gauguet, F.; Yver=Leduc, F.; Landragin, A. (May 2, 2008). "Measurement of the Sensitivity Function in a Time-Domain Atomic Interferometer" (PDF). IEEE Transactions on Instrumentation and Measurement. 57 (6): 1141–1148. arXiv:physics/0510197. Bibcode:2008ITIM...57.1141C. doi:10.1109/TIM.2007.915148. S2CID 5651070.
  33. ^ Le Gouet, J.; Mehlstäubler, T.E.; Kim, J.; Merlet, S.; Clairon, A.; Landragin, A.; Pereira Dos Santos, F. (August 2008). "Limits to the sensitivity of a low noise compact atomic gravimeter". Applied Physics B. 92 (2): 133–144. arXiv:0801.1270. Bibcode:2008ApPhB..92..133L. doi:10.1007/s00340-008-3088-1. S2CID 52357750.
  34. ^ Tang, B.; Zhang, B.C.; Zhou, L.; Wang, J.; Zhan, M.S. (2015). "Sensitivity function analysis of gravitational wave detection with single-laser and large-momentum-transfer atomic sensors". Research in Astronomy and Astrophysics. 15 (333): 333–347. arXiv:1312.7652. Bibcode:2015RAA....15..333T. doi:10.1088/1674-4527/15/3/004. S2CID 118689204.
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