- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Letter
  • Open Access

Trade-offs between unitary and measurement induced spin squeezing in cavity QED

Diego Barberena1,2,*, Anjun Chu1,2, James K. Thompson1, and Ana Maria Rey1,2

  • *Contact author: diego.barberena@colorado.edu
PDF

Phys. Rev. Research 6, L032037 – Published 16 August, 2024

DOI: https://doi.org/10.1103/PhysRevResearch.6.L032037

Abstract

We study the combined effects of measurements and unitary evolution on the preparation of spin squeezing in an ensemble of atoms interacting with a single electromagnetic field mode inside a cavity. We derive simple criteria that determine the conditions at which measurement based entanglement generation overperforms unitary protocols. We include all relevant sources of decoherence and study both their effect on the optimal spin squeezing and the overall size of the measurement noise, which limits the dynamical range of quantum-enhanced phase measurements. Our conclusions are relevant for state-of-the-art atomic clocks that aim to operate below the standard quantum limit.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (45)

  1. C. L. Degen, F. Reinhard, and P. Cappellaro, Quantum sensing, Rev. Mod. Phys. 89, 035002 (2017).
  2. L. Pezzè, A. Smerzi, M. K. Oberthaler, R. Schmied, and P. Treutlein, Quantum metrology with nonclassical states of atomic ensembles, Rev. Mod. Phys. 90, 035005 (2018).
  3. M. Kitagawa and M. Ueda, Squeezed spin states, Phys. Rev. A 47, 5138 (1993).
  4. J. Ma, X. Wang, C. Sun, and F. Nori, Quantum spin squeezing, Phys. Rep. 509, 89 (2011).
  5. 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 (London) 588, 414 (2020).
  6. J. M. Robinson, M. Miklos, Y. M. Tso, C. J. Kennedy, T. Bothwell, D. Kedar, J. K. Thompson, and J. Ye, Direct comparison of two spin squeezed optical clocks below the quantum projection noise limit, Nat. Phys. 20, 208 (2024).
  7. D. Budker and M. Romalis, Optical magnetometry, Nat. Phys. 3, 227 (2007).
  8. T. Thiele, Y. Lin, M. O. Brown, and C. A. Regal, Self-calibrating vector atomic magnetometry through microwave polarization reconstruction, Phys. Rev. Lett. 121, 153202 (2018).
  9. H. Zheng, Z. Sun, G. Chatzidrosos, C. Zhang, K. Nakamura, H. Sumiya, T. Ohshima, J. Isoya, J. Wrachtrup, A. Wickenbrock, and D. Budker, Microwave-free vector magnetometry with nitrogen-vacancy centers along a single axis in diamond, Phys. Rev. Appl. 13, 044023 (2020).
  10. M. Kasevich and S. Chu, Atomic interferometry using stimulated Raman transitions, Phys. Rev. Lett. 67, 181 (1991).
  11. A. D. Cronin, J. Schmiedmayer, and D. E. Pritchard, Optics and interferometry with atoms and molecules, Rev. Mod. Phys. 81, 1051 (2009).
  12. G. P. Greve, C. Luo, B. Wu, and J. K. Thompson, Entanglement-enhanced matter-wave interferometry in a high-finesse cavity, Nature (London) 610, 472 (2022).
  13. A. Kuzmich, N. P. Bigelow, and L. Mandel, Atomic quantum non-demolition measurements and squeezing, Europhys. Lett. 42, 481 (1998).
  14. W. Qin, Y.-H. Chen, X. Wang, A. Miranowicz, and F. Nori, Strong spin squeezing induced by weak squeezing of light inside a cavity, Nanophotonics 9, 4853 (2020).
  15. W. Muessel, H. Strobel, D. Linnemann, D. B. Hume, and M. K. Oberthaler, Scalable spin squeezing for quantum-enhanced magnetometry with Bose-Einstein condensates, Phys. Rev. Lett. 113, 103004 (2014).
  16. J. G. Bohnet, B. C. Sawyer, J. W. Britton, M. L. Wall, A. M. Rey, M. Foss-Feig, and J. J. Bollinger, Quantum spin dynamics and entanglement generation with hundreds of trapped ions, Science 352, 1297 (2016).
  17. M. H. Schleier-Smith, I. D. Leroux, and V. Vuletić, States of an ensemble of two-level atoms with reduced quantum uncertainty, Phys. Rev. Lett. 104, 073604 (2010).
  18. I. D. Leroux, M. H. Schleier-Smith, and V. Vuletić, Implementation of cavity squeezing of a collective atomic spin, Phys. Rev. Lett. 104, 073602 (2010).
  19. K. C. Cox, G. P. Greve, J. M. Weiner, and J. K. Thompson, Deterministic squeezed states with collective measurements and feedback, Phys. Rev. Lett. 116, 093602 (2016).
  20. O. Hosten, N. J. Engelsen, R. Krishnakumar, and M. A. Kasevich, Measurement noise 100 times lower than the quantum-projection limit using entangled atoms, Nature (London) 529, 505 (2016).
  21. B. Braverman, A. Kawasaki, E. Pedrozo-Peñafiel, S. Colombo, C. Shu, Z. Li, E. Mendez, M. Yamoah, L. Salvi, D. Akamatsu, Y. Xiao, and V. Vuletić, Near-unitary spin squeezing in Yb171, Phys. Rev. Lett. 122, 223203 (2019).
  22. Y.-L. Zhang, C.-L. Zou, X.-B. Zou, L. Jiang, and G.-C. Guo, Detuning-enhanced cavity spin squeezing, Phys. Rev. A 91, 033625 (2015).
  23. V. B. Braginsky, Y. I. Vorontsov, and K. S. Thorne, Quantum nondemolition measurements, Science 209, 547 (1980).
  24. V. B. Braginsky and F. Y. Khalili, Quantum nondemolition measurements: the route from toys to tools, Rev. Mod. Phys. 68, 1 (1996).
  25. Z. Li, B. Braverman, S. Colombo, C. Shu, A. Kawasaki, A. F. Adiyatullin, E. Pedrozo-Peñafiel, E. Mendez, and V. Vuletić, Collective spin-light and light-mediated spin-spin interactions in an optical cavity, PRX Quantum 3, 020308 (2022).
  26. L. A. Fuderer, J. J. Hope, and S. A. Haine, Hybrid method of generating spin-squeezed states for quantum-enhanced atom interferometry, Phys. Rev. A 108, 043722 (2023).
  27. B. Braverman, A. Kawasaki, and V. Vuletić, Impact of non-unitary spin squeezing on atomic clock performance, New J. Phys. 20, 103019 (2018).
  28. E. Davis, G. Bentsen, and M. Schleier-Smith, Approaching the Heisenberg limit without single-particle detection, Phys. Rev. Lett. 116, 053601 (2016).
  29. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.6.L032037 for derivations of the atom-light model in Eq.  (1)– (3), calculation of the bounds given in Eqs.  (7), (9), (13), and an application of our results to a variety of experimental platforms.
  30. H. M. Wiseman and G. J. Milburn, Quantum Measurement and Control (Cambridge University Press, Cambridge, 2009).
  31. K. Jacobs and D. A. Steck, A straightforward introduction to continuous quantum measurement, Contemp. Phys. 47, 279 (2006).
  32. L. B. Madsen and K. Mølmer, Spin squeezing and precision probing with light and samples of atoms in the Gaussian description, Phys. Rev. A 70, 052324 (2004).
  33. Z. Zhang, Y. Zhang, H. Guo, L. Wang, G. Chen, C. Shan, and K. Mølmer, Stochastic mean-field theory for conditional spin squeezing by homodyne probing of atom-cavity photon dressed states, arXiv:2306.00868 [quant-ph].
  34. D. J. Wineland, J. J. Bollinger, W. M. Itano, F. L. Moore, and D. J. Heinzen, Spin squeezing and reduced quantum noise in spectroscopy, Phys. Rev. A 46, R6797(R) (1992).
  35. A. Chu, P. He, J. K. Thompson, and A. M. Rey, Quantum enhanced cavity QED interferometer with partially delocalized atoms in lattices, Phys. Rev. Lett. 127, 210401 (2021).
  36. M. H. Schleier-Smith, I. D. Leroux, and V. Vuletić, Squeezing the collective spin of a dilute atomic ensemble by cavity feedback, Phys. Rev. A 81, 021804(R) (2010).
  37. M. H. Schleier-Smith, I. D. Leroux, and V. Vuletić, Erratum: Squeezing the collective spin of a dilute atomic ensemble by cavity feedback [Phys. Rev. A 81, 021804(R) (2010)], Phys. Rev. A 83, 039907(E) (2011).
  38. H. Bao, J. Duan, S. Jin, X. Lu, P. Li, W. Qu, M. Wang, I. Novikova, E. E. Mikhailov, K.-F. Zhao, K. Mølmer, H. Shen, and Y. Xiao, Spin squeezing of 1011 atoms by prediction and retrodiction measurements, Nature (London) 581, 159 (2020).
  39. Z. Chen, J. G. Bohnet, S. R. Sankar, J. Dai, and J. K. Thompson, Conditional spin squeezing of a large ensemble via the vacuum Rabi splitting, Phys. Rev. Lett. 106, 133601 (2011).
  40. O. Hosten, R. Krishnakumar, N. J. Engelsen, and M. A. Kasevich, Quantum phase magnification, Science 352, 1552 (2016).
  41. 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, 013001 (2016).
  42. S. Colombo, E. Pedrozo-Peñafiel, A. F. Adiyatullin, Z. Li, E. Mendez, C. Shu, and V. Vuletić, Time-reversal-based quantum metrology with many-body entangled states, Nat. Phys. 18, 925 (2022).
  43. Z. Li, S. Colombo, C. Shu, G. Velez, S. Pilatowsky-Cameo, R. Schmied, S. Choi, M. Lukin, E. Pedrozo-Peñafiel, and V. Vuletić, Improving metrology with quantum scrambling, Science 380, 1381 (2023).
  44. J. Borregaard, E. J. Davis, G. S. Bentsen, M. H. Schleier-Smith, and A. S. Sørensen, One- and two-axis squeezing of atomic ensembles in optical cavities, New J. Phys. 19, 093021 (2017).
  45. J. Hu, W. Chen, Z. Vendeiro, A. Urvoy, B. Braverman, and V. Vuletić, Vacuum spin squeezing, Phys. Rev. A 96, 050301(R) (2017).

Outline

Information

Phys. Rev. Research 6, L032037– Published 16 August, 2024
  • Received 8 October 2023
  • Accepted 31 May 2024
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation