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Globally optimal interferometry with lossy twin Fock probes

Published 10 Aug 2023 in quant-ph, cond-mat.quant-gas, math-ph, and math.MP | (2308.05871v2)

Abstract: Parity or quadratic spin (e.g., $J_{z}{2}$) readouts of a Mach-Zehnder (MZ) interferometer probed with a twin Fock input state allow to saturate the optimal sensitivity attainable among all mode-separable states with a fixed total number of particles, but only when the interferometer phase $\theta$ is near zero. When more general Dicke state probes are used, the parity readout saturates the quantum Fisher information (QFI) at $\theta=0$, whereas better-than-standard quantum limit performance of the $J_{z}{2}$ readout is restricted to an $o(\sqrt{N})$ occupation imbalance. We show that a method of moments readout of two quadratic spin observables $J_{z}{2}$ and $J_{+}{2}+J_{-}{2}$ is globally optimal for Dicke state probes, i.e., the error saturates the QFI for all $\theta$. In the lossy setting, we derive the time-inhomogeneous Markov process describing the effect of particle loss on twin Fock states, showing that method of moments readout of four at-most-quadratic spin observables is sufficient for globally optimal estimation of $\theta$ when two or more particles are lost. The analysis culminates in a numerical calculation of the QFI matrix for distributed MZ interferometry on the four mode state $\vert {N\over 4},{N\over 4},{N\over 4},{N\over 4}\rangle$ and its lossy counterparts, showing that an advantage for estimation of any linear function of the local MZ phases $\theta_{1}$, $\theta_{2}$ (compared to independent probing of the MZ phases by two copies of $\vert {N\over 4},{N\over 4}\rangle$) appears when more than one particle is lost.

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References (61)
  1. M. J. Holland and K. Burnett, “Interferometric detection of optical phase shifts at the Heisenberg limit,” Phys. Rev. Lett. 71, 1355–1358 (1993).
  2. Carlton M. Caves, “Quantum-mechanical noise in an interferometer,” Phys. Rev. D 23, 1693–1708 (1981).
  3. D. Ganapathy et al. (LIGO O4 Detector Collaboration), “Broadband Quantum Enhancement of the LIGO Detectors with Frequency-Dependent Squeezing,” Phys. Rev. X 13, 041021 (2023).
  4. L. McCuller, C. Whittle, D. Ganapathy, K. Komori, M. Tse, A. Fernandez-Galiana, L. Barsotti, P. Fritschel, M. MacInnis, F. Matichard, K. Mason, N. Mavalvala, R. Mittleman, Haocun Yu, M. E. Zucker,  and M. Evans, “Frequency-Dependent Squeezing for Advanced LIGO,” Phys. Rev. Lett. 124, 171102 (2020).
  5. Merlin Cooper, Laura J. Wright, Christoph Söller,  and Brian J. Smith, “Experimental generation of multi-photon Fock states,” Opt. Express 21, 5309–5317 (2013).
  6. Savas Dimopoulos, Peter W. Graham, Jason M. Hogan, Mark A. Kasevich,  and Surjeet Rajendran, “Atomic gravitational wave interferometric sensor,” Phys. Rev. D 78, 122002 (2008).
  7. Mahiro Abe et al., “Matter-wave Atomic Gradiometer Interferometric Sensor (MAGIS-100),” Quantum Science and Technology 6, 044003 (2021).
  8. Mark Kasevich and Steven Chu, “Atomic interferometry using stimulated raman transitions,” Phys. Rev. Lett. 67, 181–184 (1991).
  9. Saijun Wu, Ying-Ju Wang, Quentin Diot,  and Mara Prentiss, “Splitting matter waves using an optimized standing-wave light-pulse sequence,” Phys. Rev. A 71, 043602 (2005).
  10. H. M. Wiseman and John A. Vaccaro, “Entanglement of indistinguishable particles shared between two parties,” Phys. Rev. Lett. 91, 097902 (2003).
  11. 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, 773–776 (2011).
  12. Bernard Yurke, Samuel L. McCall,  and John R. Klauder, “SU(2) and SU(1,1) interferometers,” Phys. Rev. A 33, 4033–4054 (1986).
  13. A. Holevo, Probabilistic and Statistical Aspects of Quantum Theory (North-Holland, Amsterdam, 1982).
  14. Sixia Yu, “Quantum Fisher Information as the Convex Roof of Variance,” arXiv preprint arXiv:1302.5311  (2013).
  15. Matthias D. Lang and Carlton M. Caves, “Optimal quantum-enhanced interferometry,” Phys. Rev. A 90, 025802 (2014).
  16. Kasper Duivenvoorden, Barbara M. Terhal,  and Daniel Weigand, “Single-mode displacement sensor,” Phys. Rev. A 95, 012305 (2017).
  17. Cyril Vaneph, Tommaso Tufarelli,  and Marco G. Genoni, “Quantum estimation of a two-phase spin rotation,” Quantum Measurements and Quantum Metrology 1, 12–20 (2013).
  18. Akio Fujiwara, “Estimation of SU(2) operation and dense coding: An information geometric approach,” Phys. Rev. A 65, 012316 (2001).
  19. Manuel Gessner, Augusto Smerzi,  and Luca Pezzè, “Multiparameter squeezing for optimal quantum enhancements in sensor networks,” Nature Communications 11, 3817 (2020).
  20. Matteo Fadel, Benjamin Yadin, Yuping Mao, Tim Byrnes,  and Manuel Gessner, “Multiparameter quantum metrology and mode entanglement with spatially split nonclassical spin ensembles,” New Journal of Physics 25, 073006 (2023).
  21. Andreas Bärtschi and Stephan Eidenbenz, “Short-Depth Circuits for Dicke State Preparation,” in 2022 IEEE International Conference on Quantum Computing and Engineering (QCE) (2022) pp. 87–96.
  22. Dariusz Kajtoch and Emilia Witkowska, “Quantum dynamics generated by the two-axis countertwisting hamiltonian,” Phys. Rev. A 92, 013623 (2015).
  23. Zhang Jiang, Eleanor G. Rieffel,  and Zhihui Wang, “Near-optimal quantum circuit for Grover’s unstructured search using a transverse field,” Phys. Rev. A 95, 062317 (2017).
  24. Karsten Lange, Jan Peise, Bernd Lücke, Ilka Kruse, Giuseppe Vitagliano, Iagoba Apellaniz, Matthias Kleinmann, Géza Tóth,  and Carsten Klempt, “Entanglement between two spatially separated atomic modes,” Science 360, 416–418 (2018a).
  25. Roland Krischek, Christian Schwemmer, Witlef Wieczorek, Harald Weinfurter, Philipp Hyllus, Luca Pezzé,  and Augusto Smerzi, “Useful multiparticle entanglement and sub-shot-noise sensitivity in experimental phase estimation,” Phys. Rev. Lett. 107, 080504 (2011).
  26. Lu Zhou, Jia Kong, Zhihao Lan,  and Weiping Zhang, “Dynamical quantum phase transitions in a spinor Bose-Einstein condensate and criticality enhanced quantum sensing,” Phys. Rev. Res. 5, 013087 (2023).
  27. Artur Niezgoda, Dariusz Kajtoch, Joanna Dziekańska,  and Emilia Witkowska, “Optimal quantum interferometry robust to detection noise using spin-1 atomic condensates,” New Journal of Physics 21, 093037 (2019).
  28. Q. Guan, G. W. Biedermann, A. Schwettmann,  and R. J. Lewis-Swan, “Tailored generation of quantum states in an entangled spinor interferometer to overcome detection noise,” Phys. Rev. A 104, 042415 (2021).
  29. Tian-Wei Mao, Qi Liu, Xin-Wei Li, Jia-Hao Cao, Feng Chen, Wen-Xin Xu, Meng Khoon Tey, Yi-Xiao Huang,  and Li You, “Quantum-enhanced sensing by echoing spin-nematic squeezing in atomic Bose–Einstein condensate,” Nature Physics 19, 1585–1590 (2023).
  30. Masahiro Kitagawa and Masahito Ueda, “Squeezed spin states,” Phys. Rev. A 47, 5138–5143 (1993).
  31. Bernd Lücke, Jan Peise, Giuseppe Vitagliano, Jan Arlt, Luis Santos, Géza Tóth,  and Carsten Klempt, “Detecting Multiparticle Entanglement of Dicke States,” Phys. Rev. Lett. 112, 155304 (2014).
  32. R. A. Campos, Christopher C. Gerry,  and A. Benmoussa, “Optical interferometry at the Heisenberg limit with twin Fock states and parity measurements,” Phys. Rev. A 68, 023810 (2003).
  33. Karol Gietka and Jan Chwedeńczuk, “Atom interferometer in a double-well potential,” Phys. Rev. A 90, 063601 (2014).
  34. Julian Grond, Ulrich Hohenester, Igor Mazets,  and Jörg Schmiedmayer, “Atom interferometry with trapped Bose–Einstein condensates: impact of atom–atom interactions,” New Journal of Physics 12, 065036 (2010).
  35. U. Dorner, R. Demkowicz-Dobrzanski, B. J. Smith, J. S. Lundeen, W. Wasilewski, K. Banaszek,  and I. A. Walmsley, “Optimal quantum phase estimation,” Phys. Rev. Lett. 102, 040403 (2009).
  36. Luca Pezzè, Augusto Smerzi, Markus K. Oberthaler, Roman Schmied,  and Philipp Treutlein, “Quantum metrology with nonclassical states of atomic ensembles,” Rev. Mod. Phys. 90, 035005 (2018).
  37. Philipp Hyllus, Otfried Gühne,  and Augusto Smerzi, “Not all pure entangled states are useful for sub-shot-noise interferometry,” Phys. Rev. A 82, 012337 (2010).
  38. D Meiser and M J Holland, “Robustness of Heisenberg-limited interferometry with balanced Fock states,” New Journal of Physics 11, 033002 (2009).
  39. J. J. Bollinger, Wayne M. Itano, D. J. Wineland,  and D. J. Heinzen, “Optimal frequency measurements with maximally correlated states,” Phys. Rev. A 54, R4649–R4652 (1996).
  40. Christopher C. Gerry, “Heisenberg-limit interferometry with four-wave mixers operating in a nonlinear regime,” Phys. Rev. A 61, 043811 (2000).
  41. Christopher C. Gerry, R. A. Campos,  and A. Benmoussa, “Comment on “Interferometric Detection of Optical Phase Shifts at the Heisenberg Limit”,” Phys. Rev. Lett. 92, 209301 (2004).
  42. Vittorio Giovannetti, Seth Lloyd,  and Lorenzo Maccone, “Quantum metrology,” Phys. Rev. Lett. 96, 010401 (2006).
  43. Taesoo Kim, Olivier Pfister, Murray J. Holland, Jaewoo Noh,  and John L. Hall, “Influence of decorrelation on Heisenberg-limited interferometry with quantum correlated photons,” Phys. Rev. A 57, 4004–4013 (1998).
  44. T J Volkoff and Michael J Martin, “Saturating the one-axis twisting quantum Cramér-Rao bound with a total spin readout,” Journal of Physics Communications 8, 015004 (2024).
  45. Emily Davis, Gregory Bentsen,  and Monika Schleier-Smith, “Approaching the Heisenberg Limit without Single-Particle Detection,” Phys. Rev. Lett. 116, 053601 (2016).
  46. T. J. Volkoff and Michael J. Martin, “Asymptotic optimality of twist-untwist protocols for Heisenberg scaling in atom-based sensing,” Phys. Rev. Res. 4, 013236 (2022).
  47. Juha Javanainen and Martin Wilkens, “Phase and Phase Diffusion of a Split Bose-Einstein Condensate,” Phys. Rev. Lett. 78, 4675–4678 (1997).
  48. B. C. Sanders and G. J. Milburn, “Optimal quantum measurements for phase estimation,” Phys. Rev. Lett. 75, 2944–2947 (1995).
  49. G.-B. Jo, Y. Shin, S. Will, T. A. Pasquini, M. Saba, W. Ketterle, D. E. Pritchard, M. Vengalattore,  and M. Prentiss, “Long Phase Coherence Time and Number Squeezing of Two Bose-Einstein Condensates on an Atom Chip,” Phys. Rev. Lett. 98, 030407 (2007).
  50. Mihai D. Vidrighin, Gaia Donati, Marco G. Genoni, Xian-Min Jin, W. Steven Kolthammer, M. S. Kim, Animesh Datta, Marco Barbieri,  and Ian A. Walmsley, “Joint estimation of phase and phase diffusion for quantum metrology,” Nature Communications 5, 3532 (2014).
  51. Marco G. Genoni, Stefano Olivares,  and Matteo G. A. Paris, “Optical phase estimation in the presence of phase diffusion,” Phys. Rev. Lett. 106, 153603 (2011).
  52. Luca Pezzé and Augusto Smerzi, “Phase sensitivity of a Mach-Zehnder interferometer,” Phys. Rev. A 73, 011801 (2006).
  53. H. Uys and P. Meystre, “Quantum states for Heisenberg-limited interferometry,” Phys. Rev. A 76, 013804 (2007).
  54. Iagoba Apellaniz, Bernd Lücke, Jan Peise, Carsten Klempt,  and Géza Tóth, “Detecting metrologically useful entanglement in the vicinity of Dicke states,” New Journal of Physics 17, 083027 (2015).
  55. Samuel L. Braunstein and Carlton M. Caves, “Statistical distance and the geometry of quantum states,” Phys. Rev. Lett. 72, 3439–3443 (1994).
  56. Wenchao Ge, Kurt Jacobs, Zachary Eldredge, Alexey V. Gorshkov,  and Michael Foss-Feig, “Distributed quantum metrology with linear networks and separable inputs,” Phys. Rev. Lett. 121, 043604 (2018).
  57. Timothy J. Proctor, Paul A. Knott,  and Jacob A. Dunningham, “Multiparameter estimation in networked quantum sensors,” Phys. Rev. Lett. 120, 080501 (2018).
  58. Tyler J. Volkoff, “Distillation of maximally correlated bosonic matter from many-body quantum coherence,” Quantum 4, 330 (2020).
  59. Manuel Gessner, Luca Pezzè,  and Augusto Smerzi, “Sensitivity bounds for multiparameter quantum metrology,” Phys. Rev. Lett. 121, 130503 (2018).
  60. T. J. Volkoff and Mohan Sarovar, “Optimality of Gaussian receivers for practical Gaussian distributed sensing,” Phys. Rev. A 98, 032325 (2018).
  61. Karsten Lange, Jan Peise, Bernd Lücke, Ilka Kruse, Giuseppe Vitagliano, Iagoba Apellaniz, Matthias Kleinmann, Géza Tóth,  and Carsten Klempt, “Entanglement between two spatially separated atomic modes,” Science 360, 416–418 (2018b).

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Authors (2)

  1. T. J. Volkoff 
  2. Changhyun Ryu 

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