Skip to main content
SpringerLink
Log in

Introduction to Optical Cavities, Atomic Clocks, Cold Atoms and Gravitational Waves

  • Chapter
  • First Online:
Optical Cavities for Optical Atomic Clocks, Atom Interferometry and Gravitational-Wave Detection

Part of the book series: Springer Theses ((Springer Theses))

  • 651 Accesses

Abstract

The Fabry-Perot interferometer (Fig. 1.1) is perhaps the most deceptively simple setup in optics. In an idealised form it consists of two spherical or plane partially reflective surfaces facing each other and separated by a fixed or variable distance.

These are some of the things that hydrogen atoms do, given fifteen billion years of cosmic evolution.

—Carl Sagan.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    The Fabry-Perot interferometer was conceived as a parallel plate interferometer. It was not until the late 1950’s that interferometry using spherical surfaces was introduced.

  2. 2.

    Perot A and Fabry Ch 1899, Sur l’application de phénomènes d’interférence à la solution de divers problèmes de spectroscopie et de mètrologie. ‘Bull. Astronomique 16:5−32’.

  3. 3.

    Fabry Ch and Perot A 1899, Théorie et applications d’une nouvelle méthode de spectroscopie interférentielle, Ann. Chim. Phys. 16:115−44.

  4. 4.

    Perot A and Fabry Ch 1899, Méthodes interférentielles pour la mesure des grandes épaisseurs et la comparaison des longueurs d’onde, Ann. Chim. Phys. 16:289−338.

  5. 5.

    Fabry Ch and Perot A 1897, Sur les franges des lames minces argentées et leur application à la mesure de petites épaisseurs d’air, Ann. Chim. Phis. 12:459−501.

  6. 6.

    Perot A and Fabry Ch 1901, Sur un nouveau modèle d’interféromètre, Ann. Chim. Phys. 22.

  7. 7.

    Connes P 1958, L’étalon Fabry-Perot sphérique, J. Phys. Radium 19:262−9.

  8. 8.

    Metrology is the science of measurement, encompassing several fields across physics, mathematics and chemistry. It deals with the establishment of units of measurement, as well as the development of the measurement methods and standards of measurement.

  9. 9.

    Gouy L G 1890, Sur une propriete nouvelle des ondes lumineuses, C. R. Acad. Sci. Paris 110:1251.

  10. 10.

    For a variable with zero mean \((\Delta x)^2 = \left\langle x^2\right\rangle \).

  11. 11.

    We can recast other parameters in terms of q(z). For example, \(w^2(z) = \frac{\lambda }{\pi } \frac{\left| q(z) \right| ^2}{\mathrm {Im}\left[ q(z) \right] } \),    \( R(z) = \frac{\left| q(z) \right| ^2}{ \mathrm {Re}\left[ q(z) \right] } \),    \( \zeta (z) = \arctan \left( \frac{\mathrm {Re}\left[ q(z) \right] }{\mathrm {Im}\left[ q(z) \right] } \right) \),    \( w_0^2 = \frac{\lambda }{\pi } \mathrm {Im}\left[ q(z) \right] \).

References

  1. Perot A, Fabry C (1899) On the application of interference phenomena to the solution of various problems of spectroscopy and metrology. Astrophys J 9:87

    Article  ADS  Google Scholar 

  2. Fabry C, Perot A (1901) On a new form of interferometer. Astrophys J 13:265

    Article  ADS  Google Scholar 

  3. National Physical Laboratory. http://npl.co.uk/. Accessed 16 July 2018

  4. Fox AG, Li T (1961) Resonant modes in a maser interferometer. Bell Syst Tech J 40(2):453–488

    Article  Google Scholar 

  5. Fox AG, Li T (1963) Modes in a maser interferometer with curved and tilted mirrors. Proc IEEE 51(1):80–89

    Article  Google Scholar 

  6. Kogelnik H, Li T (1996) Laser beams and resonators. Appl Opt 5:1550–1567

    Article  ADS  Google Scholar 

  7. Siegman A, Arrathoon R (1967) Modes in unstable optical resonators and lens waveguides. IEEE J Quantum Electron 3(4):156–163

    Article  ADS  Google Scholar 

  8. Krupke W, Sooy W (1969) Properties of an unstable confocal resonator CO 2 laser system. IEEE J Quantum Electron

    Google Scholar 

  9. Siegman AE (1974) Unstable optical resonators. Appl Opt 13:353–367

    Article  ADS  Google Scholar 

  10. Essen L (1956) Atomic time and the definition of the second. Nature 178:34–35

    Article  ADS  Google Scholar 

  11. Gill P (2005) Optical frequency standards. Metrologia 42(3):S125–S137

    Article  ADS  Google Scholar 

  12. Kasevich MA, Riis E, Chu S, Devoe RG (1989) Rf spectroscopy in an atomic fountain. Phys Rev Lett 63(6):612–615

    Article  ADS  Google Scholar 

  13. Clairon A, Salomon C, Guellati S, Phillips WD (1991) Ramsey resonance in a Zacharias fountain. Europhys Lett 16(2):165–170

    Article  ADS  Google Scholar 

  14. Gill P (2011) When should we change the definition of the second? Philos Trans R Soc A Math Phys Eng Sci 369(1953):4109–4130

    Article  ADS  Google Scholar 

  15. Dovale Álvarez M, Williams RA (2015) Design of NPL’s new long optical cavity, tech. rep. National Physical Laboratory

    Google Scholar 

  16. Hänsch TW, Schawlow AL (1975) Cooling of gases by laser radiation. Opt Commun 13:68–69

    Article  ADS  Google Scholar 

  17. Wineland DJ, Itano WM (1979) Laser cooling of atoms. Phys Rev A 20:1521–1540

    Article  ADS  Google Scholar 

  18. Dimopoulos S, Graham PW, Hogan JM, Kasevich MA (2007) Testing general relativity with atom interferometry. Phys Rev Lett 98(11):111102

    Google Scholar 

  19. Dimopoulos S, Graham PW, Hogan JM, Kasevich MA (2008) General relativistic effects in atom interferometry. Phys Rev D 78(4 ):042003

    Google Scholar 

  20. Dimopoulos S, Graham PW, Hogan JM, Kasevich MA, Rajendran S (2008) Atomic gravitational wave interferometric sensor. Phys Rev D 78(12):122002

    Google Scholar 

  21. Graham PW, Hogan JM, Kasevich MA, Rajendran S (2013) New method for gravitational wave detection with atomic sensors. Phys Rev Lett 110(17):171102

    Google Scholar 

  22. Chaibi W, Geiger R, Canuel B, Bertoldi A, Landragin A, Bouyer P (2016) Low frequency gravitational wave detection with ground based atom interferometer arrays. Phys Rev D 93(2):021101

    Google Scholar 

  23. Canuel B, Pelisson S, Amand L, Bertoldi A, Cormier E, Fang B, Gaffet S, Geiger R, Harms J, Holleville D, Landragin A, Lefèvre G, Lhermite J, Mielec N, Prevedelli M, Riou I, Bouyer P (2016) Miga: combining laser and matter wave interferometry for mass distribution monitoring and advanced geodesy. Proc SPIE 9900, Quantum Opt 990008

    Google Scholar 

  24. Canuel B, Bertoldi A, Amand L, di Borgo EP, Chantrait T, Danquigny C, Dovale  Álvarez M, Fang B, Freise A, Geiger R, Gillot J, Henry S, Hinderer J, Holleville D, Junca J, Lefèvre G, Merzougui M, Mielec N, Monfret T, Pelisson S, Prevedelli M, Reynaud S, Riou I, Rogister Y, Rosat S, Cormier E, Landragin A, Chaibi W, Gaffet S, Bouyer P (2018) Exploring gravity with the MIGA large scale atom interferometer. Sci Rep 8:1–23

    Google Scholar 

  25. Kasevich M, Chu S (1991) Atomic interferometry using stimulated raman transitions. Phys Rev Lett 67(2):181

    Article  ADS  Google Scholar 

  26. Fixler JB, Foster GT, McGuirk JM, Kasevich MA (2007) Atom interferometer measurement of the newtonian constant of gravity. Science 315(5808):74–77

    Article  ADS  Google Scholar 

  27. Rosi G, Sorrentino F, Cacciapuoti L, Prevedelli M, Tino GM (2014) Precision measurement of the newtonian gravitational constant using cold atoms. Nature 510(7506):518–521

    Article  ADS  Google Scholar 

  28. Weiss DS, Young BC, Chu S (1994) Precision measurement of \(\hbar /m_{\rm {cs}}\) based on photon recoil using laser-cooled atoms and atomic interferometry. Appl Phys B 59(3):217–256

    Article  ADS  Google Scholar 

  29. Cadoret M, de Mirandes E, Cladé P, Guellati-Khélifa S, Schwob C, Nez F, Julien L, Biraben F (2008) Combination of bloch oscillations with a ramsey-bordé interferometer: new determination of the fine structure constant. Phys Rev Lett 101(23):230801

    Google Scholar 

  30. Bouchendira R, Cladé P, Guellati-Khélifa S, Nez F, Biraben F (2011) New determination of the fine structure constant and test of the quantum electrodynamics. Phys Rev Lett 106(8):080801

    Google Scholar 

  31. Schlippert D, Hartwig J, Albers H, Richardson LL, Schubert C, Roura A, Schleich WP, Ertmer W, Rasel EM (2014) Quantum test of the universality of free fall. Phys Rev Lett 112(20):203002

    Google Scholar 

  32. Tarallo MG, Mazzoni T, Poli N, Sutyrin DV, Zhang X, Tino GM (2014) Test of einstein equivalence principle for 0-spin and half-integer-spin atoms: search for spin-gravity coupling effects. Phys Rev Lett 113(2):023005

    Google Scholar 

  33. Peters A, Chung KY, Chu S (1999) Measurement of gravitational acceleration by dropping atoms. Nature 400(6747):849

    Article  ADS  Google Scholar 

  34. Hu Z, Sun BL, Duan XC, Zhou MK, Chen LL, Zhan S, Zhang QZ, Luo J (2013) Demonstration of an ultrahigh-sensitivity atom-interferometry absolute gravimeter. Phys Rev A 88(4):043610

    Google Scholar 

  35. McGuirk JM, Foster GT, Fixler JB, Snadden MJ, Kasevich MA (2002) Sensitive absolute-gravity gradiometry using atom interferometry. Phys Rev A 65(3):033608

    Google Scholar 

  36. Sorrentino F, Bodart Q, Cacciapuoti L, Lien Y-H, Prevedelli M, Rosi G, Salvi L, Tino GM (2014) Sensitivity limits of a raman atom interferometer as a gravity gradiometer. Phys Rev A 89(2):023607

    Google Scholar 

  37. Gustavson TL, Bouyer P, Kasevich MA (1997) Precision rotation measurements with an atom interferometer gyroscope. Phys Rev Lett 78(11):2046

    Article  ADS  Google Scholar 

  38. Canuel B, Leduc F, Holleville D, Gauguet A, Fils J, Virdis A, Clairon A, Dimarcq N, Borde CJ, Landragin A, Bouyer P (2006) Six-axis inertial sensor using cold-atom interferometry. Phys Rev Lett 97(1):010402

    Google Scholar 

  39. Stockton JK, Takase K, Kasevich MA (2011) Absolute geodetic rotation measurement using atom interferometry. Phys Rev Lett 107(13):133001

    Google Scholar 

  40. Dutta I, Savoie D, Fang B, Venon B, Garrido Alzar CL, Geiger R, Landragin A (2016) Continuous cold-atom inertial sensor with 1 nrad/sec rotation stability. Phys Rev Lett 116(18):183003

    Google Scholar 

  41. Wolf P, Lemonde P, Lambrecht A, Bize S, Landragin A, Clairon A (2007) From optical lattice clocks to the measurement of forces in the casimir regime. Phys Rev A 75

    Google Scholar 

  42. Kovachy T, Asenbaum P, Overstreet C, Donnelly CA, Dickerson SM, Sugarbaker A, Hogan JM, Kasevich MA (2015) Quantum superposition at the half-metre scale. Nature 528:530–533

    Article  ADS  Google Scholar 

  43. Martynov DV et al. (2016) Sensitivity of the advanced LIGO detectors at the beginning of gravitational wave astronomy. Phys Rev D 93:433–19

    Google Scholar 

  44. Hamilton P, Jaffe M, Brown JM, Maisenbacher L, Estey B, Müller H (2015) Atom interferometry in an optical cavity. Phys Rev Lett 114(10):100405

    Google Scholar 

  45. Hamilton P, Jaffe M, Haslinger P, Simmons Q, Müller H, Khoury J (2015) Atom-interferometry constraints on dark energy. Science 349:849–851

    Article  ADS  Google Scholar 

  46. Jaffe M, Haslinger P, Xu V, Hamilton P, Upadhye A, Elder B, Khoury J, Müller H (2017) Testing sub-gravitational forces on atoms from a miniature, in-vacuum source mass. Nat Phys 13:938

    Article  Google Scholar 

  47. Haslinger P, Jaffe M, Xu V, Schwartz O, Sonnleitner M, Ritsch-Marte M, Ritsch H, Müller H (2018) Attractive force on atoms due to blackbody radiation. Nat Phys 1–5

    Google Scholar 

  48. Dovale Álvarez M, Brown DD, Jones AW, Mow-Lowry CM, Miao H, Freise A (2017) Fundamental limitations of cavity-assisted atom interferometry. Phys Rev A 96:053820–10

    Google Scholar 

  49. Dovale Álvarez M, Mow-Lowry CM, Freise A (2018) 4-mirror large-waist stable cavity for enhanced atom interferometry, tech. rep. University of Birmingham

    Google Scholar 

  50. Abbott BP et al. (2016) Observation of gravitational waves from a binary black hole merger. Phys Rev Lett 116:061102–061116

    Google Scholar 

  51. Abbott BP et al. (2017) GW170817: observation of gravitational waves from a binary neutron star inspiral. Phys Rev Lett 119:61–18

    Google Scholar 

  52. Abbott BP et al. (2017) Multi-messenger observations of a binary neutron star merger. Astrophys J Lett 848

    Google Scholar 

  53. Abernathy M, Acernese F, Ajith P, Allen B, Amaro-Seoane P, et al. (2011) Einstein gravitational wave telescope conceptual design study. Available from European Gravitational Observatory, document number ET-0106C-10

    Google Scholar 

  54. Amaro-Seoane P et al. (2017) Laser interferometer space antenna. arXiv:1702.00786

  55. Collaboration LS (2015) Advanced ligo. Class Quantum Grav 32:074001

    Google Scholar 

  56. Wang H, Dovale Álvarez M, Brown DD, Cooper S, Green A, Töyrä D, Miao H, Mow-Lowry C, Freise A (2017) Near-unstable fabry-perot cavities for future gravitational wave detectors. Manuscr Prep

    Google Scholar 

  57. Green AC, Brown DD, Dovale Álvarez M, Collins C, Miao H, Mow-Lowry CM, Freise A (2017) The influence of dual-recycling on parametric instabilities at advanced LIGO. ClIcal Quantum Gravity 34:205004–205017

    Article  ADS  Google Scholar 

  58. Born M, Wolf E (1999) Principles of optics. Cambridge University Press

    Google Scholar 

  59. Rakhmanov M, Savage RL, Reitze DH, Tanner DB (2002) Dynamic resonance of light in Fabry-Perot cavities. Phys Lett A 305(5):239–244

    Article  ADS  Google Scholar 

  60. Sánchez-Soto LL, Monzón JJ, Leuchs G (2016) The many facets of the Fabry–Perot. Eur J Phys 37:1–15

    Article  ADS  Google Scholar 

  61. Feng S, Winful HG (2001) Physical origin of the gouy phase shift. Opt Lett 26(8):485–487

    Article  ADS  Google Scholar 

  62. Bond C, Brown DD, Freise A, Strain KA (2017) Interferometer techniques for gravitational-wave detection. Living Rev Relativ 19:1–217

    Google Scholar 

  63. Siegman AE (1986) Lasers. University Science Books

    Google Scholar 

  64. Acernese F et al. (2015) Advanced Virgo: a second-generation interferometric gravitational wave detector. Classical Quantum Gravity 32(2):024001

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Max Planck Institut für Gravitationsphysik, Hannover, Germany

    Miguel Dovale Álvarez

Authors
  1. Miguel Dovale Álvarez
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Miguel Dovale Álvarez .

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Álvarez, M.D. (2019). Introduction to Optical Cavities, Atomic Clocks, Cold Atoms and Gravitational Waves. In: Optical Cavities for Optical Atomic Clocks, Atom Interferometry and Gravitational-Wave Detection. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-030-20863-9_1

Download citation

Publish with us

Policies and ethics

Search

Navigation