Skip to main content
SpringerLink
Log in

Cavity-enhanced metrology in an atomic spin-1 Bose–Einstein condensate

  • Research Article
  • Published:
Frontiers of Physics Aims and scope Submit manuscript

Abstract

Atom interferometer has been proven to be a powerful tool for precision metrology. Here we propose a cavity-aided nonlinear atom interferometer, based on the quasi-periodic spin mixing dynamics of an atomic spin-1 Bose–Einstein condensate trapped in an optical cavity. We unravel that the phase sensitivity can be greatly enhanced with the cavity-mediated nonlinear interaction. The influence of encoding phase, splitting time and recombining time on phase sensitivity are carefully studied. In addition, we demonstrate a dynamical phase transition in the system. Around the criticality, a small cavity light field variation can arouse a strong response of the atomic condensate, which can serve as a new resource for enhanced sensing. This work provides a robust protocol for cavity-enhanced metrology.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. D. Cronin, J. Schmiedmayer, and D. E. Pritchard, Optics and interferometry with atoms and molecules, Rev. Mod. Phys. 81(3), 1051 (2009)

    Article  ADS  Google Scholar 

  2. J. B. Fixler, G. Foster, J. McGuirk, and M. Kasevich, Atom interferometer measurement of the Newtonian constant of gravity, Science 315(5808), 74 (2007)

    Article  ADS  Google Scholar 

  3. G. Lamporesi, A. Bertoldi, L. Cacciapuoti, M. Prevedelli, and G. M. Tino, Determination of the Newtonian gravitational constant using atom interferometry, Phys. Rev. Lett. 100(5), 050801 (2008)

    Article  ADS  Google Scholar 

  4. P. W. Graham, J. M. Hogan, M. A. Kasevich, and S. Rajendran, New method for gravitational wave detection with atomic sensors, Phys. Rev. Lett. 110(17), 171102 (2013)

    Article  ADS  Google Scholar 

  5. G. Rosi, F. Sorrentino, L. Cacciapuoti, M. Prevedelli, and G. Tino, Precision measurement of the Newtonian gravitational constant using cold atoms, Nature 510(7506), 518 (2014)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  7. R. H. Parker, C. Yu, W. Zhong, B. Estey, and H. Müller, Measurement of the fine-structure constant as a test of the standard model, Science 360(6385), 191 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  8. K. Bongs, M. Holynski, J. Vovrosh, P. Bouyer, G. Condon, E. Rasel, C. Schubert, W. P. Schleich, and A. Roura, Taking atom interferometric quantum sensors from the laboratory to real-world applications, Nat. Rev. Phys. 1(12), 731 (2019)

    Article  Google Scholar 

  9. A. Peters, K. Y. Chung, and S. Chu, Measurement of gravitational acceleration by dropping atom, Nature 400(6747), 849 (1999)

    Article  ADS  Google Scholar 

  10. P. Altin, M. Johnsson, V. Negnevitsky, G. Dennis, R. P. Anderson, J. Debs, S. Szigeti, K. Hardman, S. Bennetts, G. McDonald, L. D. Turner, J. D. Close, and N. P. Robins, Precision atomic gravimeter based on Bragg diffraction, New J. Phys. 15(2), 023009 (2013)

    Article  ADS  Google Scholar 

  11. M. Snadden, J. McGuirk, P. Bouyer, K. Haritos, and M. Kasevich, Measurement of the earth’s gravity gradient with an atom interferometer-based gravity gradiometer, Phys. Rev. Lett. 81(5), 971 (1998)

    Article  ADS  Google Scholar 

  12. A. Trimeche, B. Battelier, D. Becker, A. Bertoldi, P. Bouyer, C. Braxmaier, E. Charron, R. Corgier, M. Cornelius, K. Douch, N. Gaaloul, S. Herrmann, J. Müller, E. Rasel, C. Schubert, H. Wu, and F. Pereira dos Santos, Concept study and preliminary design of a cold atom interferometer for space gravity gradiometry, Class. Quantum Gravity 36(21), 215004 (2019)

    Article  ADS  Google Scholar 

  13. F. Riehle, T. Kisters, A. Witte, J. Helmcke, and C. J. Bordé, Optical Ramsey spectroscopy in a rotating frame: Sagnac effect in a matter-wave interferometer, Phys. Rev. Lett. 67(2), 177 (1991)

    Article  ADS  Google Scholar 

  14. T. Gustavson, P. Bouyer, and M. Kasevich, Precision rotation measurements with an atom interferometer gyroscope, Phys. Rev. Lett. 78(11), 2046 (1997)

    Article  ADS  Google Scholar 

  15. J. Stockton, K. Takase, and M. Kasevich, Absolute geodetic rotation measurement using atom interferometry, Phys. Rev. Lett. 107(13), 133001 (2011)

    Article  ADS  Google Scholar 

  16. H. Strobel, W. Muessel, D. Linnemann, T. Zibold, D. B. Hume, L. Pezzè, A. Smerzi, and M. K. Oberthaler, Fisher information and entanglement of non-Gaussian spin states, Science 345(6195), 424 (2014)

    Article  ADS  Google Scholar 

  17. J. Estève, C. Gross, A. Weller, S. Giovanazzi, and M. K. Oberthaler, Squeezing and entanglement in a Bose–Einstein condensate, Nature 455(7217), 1216 (2008)

    Article  ADS  Google Scholar 

  18. B. Lücke, M. Scherer, J. Kruse, L. Pezzé, F. Deuretzbacher, P. Hyllus, O. Topic, J. Peise, W. Ertmer, J. Arlt, L. Santos, A. Smerzi, and C. Klempt, Twin matter waves for interferometry beyond the classical limit, Science 334(6057), 773 (2011)

    Article  ADS  Google Scholar 

  19. C. Gross, T. Zibold, E. Nicklas, J. Esteve, and M. K. Oberthaler, Nonlinear atom interferometer surpasses classical precision limit, Nature 464(7292), 1165 (2010)

    Article  ADS  Google Scholar 

  20. Y. Zeng, P. Xu, X. He, Y. Liu, M. Liu, J. Wang, D. Papoular, G. Shlyapnikov, and M. Zhan, Entangling two individual atoms of different isotopes via Rydberg blockade, Phys. Rev. Lett. 119(16), 160502 (2017)

    Article  ADS  Google Scholar 

  21. E. Pedrozo-Peñafiel, S. Colombo, C. Shu, A. F. Adiyatullin, Z. Li, E. Mendez, B. Braverman, A. Kawasaki, D. Akamatsu, Y. Xiao, and V. Vuletić, Entanglement on an optical atomic-clock transition, Nature 588(7838), 414 (2020)

    Article  ADS  Google Scholar 

  22. L. Pezzè, A. Smerzi, M. K. Oberthaler, R. Schmied, and P. Treutlein, Quantum metrology with nonclassical states of atomic ensembles, Rev. Mod. Phys. 90(3), 035005 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  23. G. Jin, Y. Liu, and L. You, Optimal phase sensitivity of atomic Ramsey interferometers with coherent spin states, Front. Phys. 6(3), 251 (2011)

    Article  ADS  Google Scholar 

  24. J. Wrubel, A. Schwettmann, D. P. Fahey, Z. Glassman, H. Pechkis, P. Griffin, R. Barnett, E. Tiesinga, and P. Lett, Spinor Bose–Einstein-condensate phase-sensitive amplifier for SU(1, 1) interferometry, Phys. Rev. A 98(2), 023620 (2018)

    Article  ADS  Google Scholar 

  25. T. W. Mao, Q. Liu, X. W. Li, J. H. Cao, F. Chen, W. X. Xu, M. K. Tey, Y. X. Huang, and L. You, Quantum enhanced sensing by echoing spin-nematic squeezing in atomic Bose–Einstein condensate, Nat. Phys. 19(11), 1585 (2023)

    Article  Google Scholar 

  26. X. Y. Luo, Y. Q. Zou, L. N. Wu, Q. Liu, M. F. Han, M. K. Tey, and L. You, Deterministic entanglement generation from driving through quantum phase transitions, Science 355(6325), 620 (2017)

    Article  ADS  MathSciNet  Google Scholar 

  27. P. Feldmann, M. Gessner, M. Gabbrielli, C. Klempt, L. Santos, L. Pezzè, and A. Smerzi, Interferometric sensitivity and entanglement by scanning through quantum phase transitions in spinor Bose–Einstein condensates, Phys. Rev. A 97(3), 032339 (2018)

    Article  ADS  Google Scholar 

  28. Y. Q. Zou, L. N. Wu, Q. Liu, X. Y. Luo, S. F. Guo, J. H. Cao, M. K. Tey, and L. You, Beating the classical precision limit with spin-1 Dicke states of more than 10 000 atoms, Proc. Natl. Acad. Sci. USA 115(25), 6381 (2018)

    Article  ADS  Google Scholar 

  29. E. Davis, G. Bentsen, and M. Schleier-Smith, Approaching the Heisenberg limit without single-particle detection, Phys. Rev. Lett. 116(5), 053601 (2016)

    Article  ADS  Google Scholar 

  30. F. Fröwis, P. Sekatski, and W. Dür, Detecting large quantum Fisher information with finite measurement precision, Phys. Rev. Lett. 116(9), 090801 (2016)

    Article  ADS  MathSciNet  Google Scholar 

  31. T. Macrì, A. Smerzi, and L. Pezzè, Loschmidt echo for quantum metrology, Phys. Rev. A 94(1), 010102 (2016)

    Article  ADS  Google Scholar 

  32. D. Linnemann, H. Strobel, W. Muessel, J. Schulz, R. J. Lewis-Swan, K. V. Kheruntsyan, and M. K. Oberthaler, Quantum-enhanced sensing based on time reversal of nonlinear dynamics, Phys. Rev. Lett. 117(1), 013001 (2016)

    Article  ADS  Google Scholar 

  33. M. Gabbrielli, L. Pezzè, and A. Smerzi, Spin-mixing interferometry with Bose–Einstein condensates, Phys. Rev. Lett. 115(16), 163002 (2015)

    Article  ADS  Google Scholar 

  34. Q. Liu, L. N. Wu, J. H. Cao, T. W. Mao, X. W. Li, S. F. Guo, M. K. Tey, and L. You, Nonlinear interferometry beyond classical limit enabled by cyclic dynamics, Nat. Phys. 18(2), 167 (2022)

    Article  ADS  Google Scholar 

  35. W. T. He, C. W. Lu, Y. X. Yao, H. Y. Zhu, and Q. Ai, Criticality-based quantum metrology in the presence of decoherence, Front. Phys. 18(3), 31304 (2023)

    Article  ADS  Google Scholar 

  36. A. W. Chin, S. F. Huelga, and M. B. Plenio, Quantum metrology in non-Markovian environments, Phys. Rev. Lett. 109(23), 233601 (2012)

    Article  ADS  Google Scholar 

  37. M. Jarzyna and R. Demkowicz-Dobrzański, True precision limits in quantum metrology, New J. Phys. 17(1), 013010 (2015)

    Article  ADS  Google Scholar 

  38. L. Zhou, H. Pu, H. Y. Ling, and W. Zhang, Cavity-mediated strong matter wave bistability in a spin-1 condensate, Phys. Rev. Lett. 103(16), 160403 (2009)

    Article  ADS  Google Scholar 

  39. L. Zhou, H. Pu, H. Y. Ling, K. Zhang, and W. Zhang, Spin dynamics and domain formation of a spinor Bose–Einstein condensate in an optical cavity, Phys. Rev. A 81(6), 063641 (2010)

    Article  ADS  Google Scholar 

  40. A. Kuzmich, L. Mandel, and N. P. Bigelow, Generation of spin squeezing via continuous quantum nondemolition measurement, Phys. Rev. Lett. 85(8), 1594 (2000)

    Article  ADS  Google Scholar 

  41. A. Kuzmich, L. Mandel, J. Janis, Y. Young, R. Ejnisman, and N. Bigelow, Quantum nondemolition measurements of collective atomic spin, Phys. Rev. A 60(3), 2346 (1999)

    Article  ADS  Google Scholar 

  42. A. Kuzmich and E. S. Polzik, Atomic continuous variable processing and light-atoms quantum interface, in: Quantum Information with Continuous Variables, Springer, pp 231–265, 2003

  43. R. Miller, T. Northup, K. Birnbaum, A. Boca, A. Boozer, and H. Kimble, Trapped atoms in cavity QED: Coupling quantized light and matter, J. Phys. At. Mol. Opt. Phys. 38(9), S551 (2005)

    Article  ADS  Google Scholar 

  44. H. Ritsch, P. Domokos, F. Brennecke, and T. Esslinger, Cold atoms in cavity-generated dynamical optical potentials, Rev. Mod. Phys. 85(2), 553 (2013)

    Article  ADS  Google Scholar 

  45. H. Tanji-Suzuki, I. D. Leroux, M. H. Schleier-Smith, M. Cetina, A. T. Grier, J. Simon, and V. Vuletić, Interaction between atomic ensembles and optical resonators: Classical description, in: Advances in Atomic, Molecular, and Optical Physics, Vol. 60, Elsevier, pp 201–237, 2011

  46. M. Eckstein, M. Kollar, and P. Werner, Thermalization after an interaction quench in the Hubbard model, Phys. Rev. Lett. 103(5), 056403 (2009)

    Article  ADS  Google Scholar 

  47. A. Gambassi and P. Calabrese, Quantum quenches as classical critical films, Europhys. Lett. 95(6), 66007 (2011)

    Article  ADS  Google Scholar 

  48. P. Smacchia, M. Knap, E. Demler, and A. Silva, Exploring dynamical phase transitions and prethermalization with quantum noise of excitations, Phys. Rev. B 91(20), 205136 (2015)

    Article  ADS  Google Scholar 

  49. J. Lang, B. Frank, and J. C. Halimeh, Concurrence of dynamical phase transitions at finite temperature in the fully connected transverse-field Ising model, Phys. Rev. B 97(17), 174401 (2018)

    Article  ADS  Google Scholar 

  50. S. S. Mirkhalaf, E. Witkowska, and L. Lepori, Supersensitive quantum sensor based on criticality in an antiferromagnetic spinor condensate, Phys. Rev. A 101(4), 043609 (2020)

    Article  ADS  Google Scholar 

  51. S. S. Mirkhalaf, D. B. Orenes, M. W. Mitchell, and E. Witkowska, Criticality-enhanced quantum sensing in ferromagnetic Bose–Einstein condensates: Role of readout measurement and detection noise, Phys. Rev. Lett. 103(2), 023317 (2021)

    Google Scholar 

  52. Q. Guan and R. J. Lewis-Swan, Identifying and harnessing dynamical phase transitions for quantum-enhanced sensing, Phys. Rev. Res. 3(3), 033199 (2021)

    Article  Google Scholar 

  53. L. Zhou, J. Kong, Z. Lan, and W. Zhang, Dynamical quantum phase transitions in a spinor Bose–Einstein condensate and criticality enhanced quantum sensing, Phys. Rev. Res. 5(1), 013087 (2023)

    Article  Google Scholar 

  54. C. Law, H. Pu, and N. Bigelow, Quantum spins mixing in spinor Bose–Einstein condensates, Phys. Rev. Lett. 81(24), 5257 (1998)

    Article  ADS  Google Scholar 

  55. B. Megyeri, G. Harvie, A. Lampis, and J. Goldwin, Directional bistability and nonreciprocal lasing with cold atoms in a ring cavity, Phys. Rev. Lett. 121(16), 163603 (2018)

    Article  ADS  Google Scholar 

  56. S. C. Schuster, P. Wolf, D. Schmidt, S. Slama, and C. Zimmermann, Pinning transition of Bose–Einstein condensates in optical ring resonators, Phys. Rev. Lett. 121(22), 223601 (2018)

    Article  ADS  Google Scholar 

  57. S. Yi, Ö. Müstecaplıoğlu, C. P. Sun, and L. You, Single mode approximation in a spinor-1 atomic condensate, Phys. Rev. A 66(1), 011601 (2002)

    Article  ADS  Google Scholar 

  58. W. Zhang, D. Zhou, M. S. Chang, M. Chapman, and L. You, Coherent spin mixing dynamics in a spin-1 atomic condensate, Phys. Rev. A 72(1), 013602 (2005)

    Article  ADS  Google Scholar 

  59. C. Gerving, T. Hoang, B. Land, M. Anquez, C. Hamley, and M. Chapman, Non-equilibrium dynamics of an unstable quantum pendulum explored in a spin-1 Bose–Einstein condensate, Nat. Commun. 3(1), 1169 (2012)

    Article  ADS  Google Scholar 

  60. M. S. Chang, Q. Qin, W. Zhang, L. You, and M. S. Chapman, Coherent spinor dynamics in a spin-1 Bose condensate, Nat. Phys. 1(2), 111 (2005)

    Article  Google Scholar 

  61. P. B. Blakie, A. Bradley, M. Davis, R. Ballagh, and C. Gardiner, Dynamics and statistical mechanics of ultra-cold Bose gases using c-field techniques, Adv. Phys. 57(5), 363 (2008)

    Article  ADS  Google Scholar 

  62. C. W. Helstrom, Minimum mean-squared error of estimates in quantum statistics, Phys. Lett. A 25(2), 101 (1967)

    Article  ADS  Google Scholar 

  63. S. L. Braunstein and C. M. Caves, Statistical distance and the geometry of quantum states, Phys. Rev. Lett. 72(22), 3439 (1994)

    Article  ADS  MathSciNet  Google Scholar 

  64. A. S. Holevo, Probabilistic and Statistical Aspects of Quantum Theory, Vol. 1, Springer Science & Business Media, 2011

  65. W. M. Zhang, D. H. Feng, and R. Gilmore, Coherent states: Theory and some applications, Rev. Mod. Phys. 62(4), 867 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  66. E. Yukawa, M. Ueda, and K. Nemoto, Classification of spin-nematic squeezing in spin-1 collective atomic systems, Phys. Rev. A 88(3), 033629 (2013)

    Article  ADS  Google Scholar 

  67. C. D. Hamley, C. Gerving, T. Hoang, E. Bookjans, and M. S. Chapman, Spin-nematic squeezed vacuum in a quantum gas, Nat. Phys. 8(4), 305 (2012)

    Article  Google Scholar 

  68. S. Pang and T. A. Brun, Quantum metrology for a general Hamiltonian parameter, Phys. Rev. A 90(2), 022117 (2014)

    Article  ADS  Google Scholar 

  69. A. Goussev, R. A. Jalabert, H. M. Pastawski, and D. A. Wisniacki, Loschmidt echo and time reversal in complex systems, Philos. Trans. R. Soc. A 374(2069), 20150383 (2016)

    Article  ADS  Google Scholar 

  70. T. Gorin, T. Prosen, T. H. Seligman, and M. Žnidarič, Dynamics of Loschmidt echoes and fidelity decay, Phys. Rep. 435(2–5), 33 (2006)

    Article  ADS  Google Scholar 

  71. F. Gerbier, A. Widera, S. Fölling, O. Mandel, and I. Bloch, Resonant control of spin dynamics in ultracold quantum gases by microwave dressing, Phys. Rev. A 73(4), 041602 (2006)

    Article  ADS  Google Scholar 

  72. S. Leslie, J. Guzman, M. Vengalattore, J. D. Sau, M. L. Cohen, and D. Stamper-Kurn, Amplification of fluctuations in a spinor Bose–Einstein condensate, Phys. Rev. A 79(4), 043631 (2009)

    Article  ADS  Google Scholar 

  73. P. Kunkel, M. Prüfer, H. Strobel, D. Linnemann, A. Frölian, T. Gasenzer, M. Gärttner, and M. K. Oberthaler, Spatially distributed multipartite entanglement enables EPR steering of atomic clouds, Science 360(6387), 413 (2018)

    Article  ADS  MathSciNet  Google Scholar 

  74. E. J. Davis, G. Bentsen, L. Homeier, T. Li, and M. H. Schleier-Smith, Photon-mediated spin-exchange dynamics of spin-1 atoms, Phys. Rev. Lett. 122(1), 010405 (2019)

    Article  ADS  Google Scholar 

  75. M. A. Norcia, R. J. Lewis-Swan, J. R. Cline, B. Zhu, A. M. Rey, and J. K. Thompson, Cavity-mediated collective spin exchange interactions in a strontium superradiant laser, Science 361(6399), 259 (2018)

    Article  ADS  Google Scholar 

  76. S. J. Masson, M. Barrett, and S. Parkins, Cavity QED engineering of spin dynamics and squeezing in a spinor gas, Phys. Rev. Lett. 119(21), 213601 (2017)

    Article  ADS  Google Scholar 

  77. D. S. Ding, Z. K. Liu, B. S. Shi, G. C. Guo, K. Mølmer, and C. S. Adams, Enhanced metrology at the critical point of a many-body Rydberg atomic system, Nat. Phys. 18(12), 1447 (2022)

    Article  Google Scholar 

  78. M. Olsen and A. Bradley, Numerical representation of quantum states in the positive-P and Wigner representations, Opt. Commun. 282(19), 3924 (2009)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (Grant Nos. 12074120 and 11904063) and the Key Scientific Research Project of Colleges and Universities in Henan Province (No. 23A140001).

Author information

Authors and Affiliations

  1. School of Physics, Hefei University of Technology, Hefei, 230009, China

    Renfei Zheng & Bing Chen

  2. State Key Laboratory of Precision Spectroscopy, Department of Physics, School of Physics and Electronic Science, East China Normal University, Shanghai, 200241, China

    Renfei Zheng & Lu Zhou

  3. School of Physics and Materials Science, Guangzhou University, 230 Wai Huan Xi Road, Guangzhou Higher Education Mega Center, Guangzhou, 510006, China

    Jieli Qin

  4. Department of Physics, Henan Normal University, Xinxiang, 453007, China

    Xingdong Zhao

  5. Collaborative Innovation Center of Extreme Optics, Shanxi University, Taiyuan, 030006, China

    Lu Zhou

Authors
  1. Renfei Zheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jieli Qin
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Bing Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Xingdong Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Lu Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Xingdong Zhao or Lu Zhou.

Ethics declarations

Declarations The authors declare that they have no competing interests and there are no conflicts.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zheng, R., Qin, J., Chen, B. et al. Cavity-enhanced metrology in an atomic spin-1 Bose–Einstein condensate. Front. Phys. 19, 32204 (2024). https://doi.org/10.1007/s11467-023-1372-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11467-023-1372-5

Keywords

Search

Navigation