Skip to main content
Log in

Numerical Simulations of Arm-locking for Taiji Space Gravitational Waves Detection

  • Original Article
  • Published:
Microgravity Science and Technology Aims and scope Submit manuscript

Abstract

The laser frequency stabilization is one of the most important key technologies for the interferometer measurement system of space gravitational waves detection. As a proposed frequency stabilization technique, the scheme of arm-locking is to convert the stability of interferometer arm-length into the stability of laser frequency. Some numerical simulations of arm-locking for Taiji mission were investigated in the paper. Meanwhile, an innovative controller consisted of a compensation filter and two-stage integrators in parallel was presented to suppress the laser frequency noise without increasing gain and prevent the high gain from suppressing the gravitational waves signal. The single arm-locking simulation results showed that the laser noise of closed loop was lower than 3.19 μm/√Hz@10 mHz only in the frequency range of 0.1 mHz – 0.03 Hz. But the dual arm-locking simulation results showed that the laser noise of closed loop was lower than 3.19 μm/√Hz@10 mHz in the full frequency range of 0.1 mHz – 1 Hz, meeting the requirement of Taiji mission. Preliminary results represented the feasibility and effectiveness of arm-locking on laser frequency stabilization for the Taiji mission.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig.7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  • Abbott, B.P., Abbott, R., Abbott, T., Abernathy, M., Acernese, F., Ackley, K., Adams, C., Adams, T., Addesso, P., Adhikari, R.: GW151226: observation of gravitational waves from a 22-solar-mass binary black hole coalescence. Phys. Rev. Lett. 116(24), 241103 (2016a)

    Article  Google Scholar 

  • Abbott, B.P., Abbott, R., Abbott, T., Abernathy, M., Acernese, F., Ackley, K., Adams, C., Adams, T., Addesso, P., Adhikari, R.: Observation of gravitational waves from a binary black hole merger. Phys. Rev. Lett. 116(6), 061102 (2016b)

    Article  MathSciNet  Google Scholar 

  • Abbott, B.P., Abbott, R., Abbott, T.D., Acernese, F., Ackley, K., Adams, C., Adams, T., Addesso, P., Adhikari, R., Adya, V.: GW170817: implications for the stochastic gravitational-wave background from compact binary coalescences. Phys. Rev. Lett. 120(9), 091101 (2018)

    Article  Google Scholar 

  • Abramovici, A., Althouse, W.E., Drever, R.W., Gürsel, Y., Kawamura, S., Raab, F.J., Shoemaker, D., Sievers, L., Spero, R.E., Thorne, K.S.: LIGO: The laser interferometer gravitational-wave observatory. science 256(5055), 325–333 (1992)

  • Acernese, F., Antonucci, F., Aoudia, S., Arun, K., Astone, P., Ballardin, G., Barone, F., Barsuglia, M., Bauer, T.S., Beker, M.: Performances of the Virgo interferometer longitudinal control system. Astropart. Phys. 33(2), 75–80 (2010)

    Article  Google Scholar 

  • Ando, M., Kawamura, S., Seto, N., Sato, S., Nakamura, T., Tsubono, K., Takashima, T., Funaki, I., Numata, K., Kanda, N.: DECIGO and DECIGO pathfinder. Class. Quantum Gravity 27(8), 084010 (2010)

    Article  Google Scholar 

  • Arain, M.A., Mueller, G.: Design of the Advanced LIGO recycling cavities. Opt. Express 16(14), 10018–10032 (2008)

    Article  Google Scholar 

  • Beker, M., Blom, M., van den Brand, J., Bulten, H.J., Hennes, E., Rabeling, D.: Seismic attenuation technology for the Advanced Virgo gravitational wave detector. Physics Procedia 37, 1389–1397 (2012)

    Article  Google Scholar 

  • Black, E.D.: An introduction to Pound–Drever–Hall laser frequency stabilization. Am. J. Phys. 69(1), 79–87 (2001)

    Article  Google Scholar 

  • Cornish, N.J.: Detecting a stochastic gravitational wave background with the Laser Interferometer Space Antenna. Physical Review D 65(2), 022004 (2001)

    Article  MathSciNet  Google Scholar 

  • Cyranoski, D.: Chinese gravitational-wave hunt hits crunch time. Nature 531(7593), 150–151 (2016)

    Article  Google Scholar 

  • Danzmann, K., Prince, T., Binetruy, P., Bender, P., Buchman, S., Centrella, J., Cerdonio, M., Cornish, N., Cruise, M., Cutler, C.J., Finn, L.S., Gundlach, J., Hogan, C., Hough, J., Hughes, S.A., Jennrich, O., Jetzer, P., Lobo, A., Madau, P., Madau, Y., Phinney, S., Richstone, D.O., Schutz, B., Stebbins, R., Sumner, T., Thorne, K., Vinet, J.Y., Vitale, S.: LISA: Unveiling a hidden Universe. Assessment Study Report ESA/SRE (Yellow Book). In. Tech. Rep, (2011)

  • de Vine, G., Ware, B., McKenzie, K., Spero, R.E., Klipstein, W.M., Shaddock, D.A.: Experimental Demonstration of Time-Delay Interferometry for the Laser Interferometer Space Antenna. Physical Review Letters 104(21) (2010). doi:https://doi.org/10.1103/PhysRevLett.104.211103

  • Dong, Y., Liu, H., Luo, Z., Li, Y., Jin, G.: A comprehensive simulation of weak-light phase-locking for space-borne gravitational wave antenna. Science China Technological Sciences 59(5), 730–737 (2016)

    Article  Google Scholar 

  • Gair, J.R., Vallisneri, M., Larson, S.L., Baker, J.G.: Testing general relativity with low-frequency, space-based gravitational-wave detectors. Living Rev. Relativ. 16(1), 7 (2013)

    Article  Google Scholar 

  • Grote, H., Collaboration, L.S.: The GEO 600 status. Class. Quantum Gravity 27(8), 084003 (2010)

    Article  MathSciNet  Google Scholar 

  • Hu, W., Wu, Y.: The Taiji Program in Space for gravitational wave physics and the nature of gravity. In. Oxford University Press, (2017)

  • Hughes, S.P.: General method for optimal guidance of spacecraft formations. Journal of guidance, control, and dynamics 31(2), 414–423 (2008)

    Article  Google Scholar 

  • Kawamura, S., Nakamura, T., Ando, M., Seto, N., Tsubono, K., Numata, K., Takahashi, R., Nagano, S., Ishikawa, T., Musha, M.: The Japanese space gravitational wave antenna—DECIGO. Class. Quantum Gravity 23(8), S125 (2006)

    Article  Google Scholar 

  • Luo, J., Chen, L.S., Duan, H.Z., Gong, Y.G., Hu, S.C., Ji, J.H., Liu, Q., Mei, J.W., Milyukov, V., Sazhin, M., Shao, C.G., Toth, V.T., Tu, H.B., Wang, Y.M., Wang, Y., Yeh, H.C., Zhan, M.S., Zhang, Y.H., Zharov, V., Zhou, Z.B.: TianQin: a space-borne gravitational wave detector. Classical And Quantum Gravity 33(3), 19 (2016). https://doi.org/10.1088/0264-9381/33/3/035010

    Article  Google Scholar 

  • Luo, Z., Wang, Y., Wu, Y., Hu, W., Jin, G.: The Taiji program: A concise overview. Progress of Theoretical and Experimental Physics (2020)

  • McKenzie, K., Spero, R.E., Shaddock, D.A.: Performance of arm locking in LISA. Physical Review D 80(10), 102003 (2009)

    Article  Google Scholar 

  • Pitkin, M., Reid, S., Rowan, S., Hough, J.: Gravitational wave detection by interferometry (ground and space). Living Rev. Relativ. 14(1), 5 (2011)

    Article  Google Scholar 

  • Robertson, D., Hough, J.: Interferometry for LISA. Class. Quantum Gravity 13(11A), A271 (1996)

    Article  Google Scholar 

  • Scientific, L., Abbott, B., Abbott, R., Abbott, T., Acernese, F., Ackley, K., Adams, C., Adams, T., Addesso, P., Adhikari, R.: GW170104: observation of a 50-solar-mass binary black hole coalescence at redshift 0.2. Physical Review Letters 118(22), 221101 (2017)

  • Sheard, B.S., Gray, M.B., McClelland, D.E., Shaddock, D.A.: Laser frequency stabilization by locking to a LISA arm. Phys. Lett. A 320(1), 9–21 (2003). https://doi.org/10.1016/j.physleta.2003.10.076

    Article  Google Scholar 

  • Sheard, B.S., Gray, M.B., Shaddock, D.A., McClelland, D.E.: Laser frequency noise suppression by arm-locking in LISA: progress towards a bench-top demonstration. Class. Quantum Gravity 22(10), S221–S226 (2005). https://doi.org/10.1088/0264-9381/22/10/013

    Article  Google Scholar 

  • Sutton, A., Shaddock, D.A.: Laser frequency stabilization by dual arm locking for LISA. Physical Review D 78(8), 082001 (2008). https://doi.org/10.1103/PhysRevD.78.082001

    Article  Google Scholar 

  • Thorpe, J.I., Cruz, R.J., Sankar, S., Mueller, G.: Electronic phase delay—a first step towards a bench-top model of LISA. Class. Quantum Gravity 22(10), S227 (2005)

    Article  Google Scholar 

  • Thorpe, J.I., McKenzie, K.: Arm locking with the GRACE follow-on laser ranging interferometer. Physical Review D 93(4), 042003 (2016). https://doi.org/10.1103/PhysRevD.93.042003

    Article  Google Scholar 

  • Thorpe, J.I., Mueller, G.: Experimental verification of arm-locking for LISA using electronic phase delay. Phys. Lett. A 342(3), 199–204 (2005). https://doi.org/10.1016/j.physleta.2005.05.053

    Article  Google Scholar 

  • Tröbs, M., Heinzel, G.: Improved spectrum estimation from digitized time series on a logarithmic frequency axis. Measurement 39(2), 120–129 (2006)

    Article  Google Scholar 

  • Wang, G., Ni, W.-T.: Numerical simulation of time delay interferometry for TAIJI and new LISA. Research in Astronomy and Astrophysics 19(4), 058 (2019)

    Article  Google Scholar 

  • Willke, B., Aufmuth, P., Aulbert, C., Babak, S., Balasubramanian, R., Barr, B., Berukoff, S., Bose, S., Cagnoli, G., Casey, M.M.: The GEO 600 gravitational wave detector. Class. Quantum Gravity 19(7), 1377 (2002)

    Article  Google Scholar 

Download references

Acknowledgements

This work was supported by the Youth Innovation Promotion Association, Chinese Academy of Sciences, Grant No.2018024, and the National Science Foundation of China, Grant No.61575209, and the Strategic Priority Research Program of the Chinese Academy of Sciences, Grant No. XDB23030200.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yuqiong Li.

Additional information

Publisher’s Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, H., Li, Y. & Jin, G. Numerical Simulations of Arm-locking for Taiji Space Gravitational Waves Detection. Microgravity Sci. Technol. 33, 41 (2021). https://doi.org/10.1007/s12217-021-09875-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s12217-021-09875-7

Keyword

Navigation