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Squeezing of nonlinear spin observables by one axis twisting in the presence of decoherence: An analytical study
[Compression des observables de spin non linéaires par torsion à un axe en présence de décohérence  : Une étude analytique]
Comptes Rendus. Physique, Volume 23 (2022), pp. 1-26.

Dans un ensemble d’atomes à deux niveaux descriptible par un spin collectif, on peut utiliser les états intriqués pour améliorer la sensibilité des mesures interférométriques. Bien que les états de spin non gaussiens puissent produire des améliorations quantiques plus importantes que les habituels état comprimés de spin, gaussiens, leur utilisation nécessite la mesure d’observables non linéaires en les trois composantes du spin collectif. Nous expliquons ici comment maximiser le gain quantique en utilisant des états non gaussiens surcomprimés produits par un hamiltonien non linéaire de torsion à un axe, et nous montrons que les techniques de mesure après intéraction, connues pour amplifier les signaux de sorties dans les protocoles quantiques de détermination de quantités physiques, sont efficaces pour mesurer les observables de spin non linéaires. En tenant compte des processus de décohérence pertinents pour les expériences de physique atomique, nous déterminons analytiquement le gain quantique optimal en fonction des paramètres de bruit pour un nombre d’atomes arbitraire.

In an ensemble of two-level atoms that can be described in terms of a collective spin, entangled states can be used to enhance the sensitivity of interferometric precision measurements. While non-Gaussian spin states can produce larger quantum enhancements than spin-squeezed Gaussian states, their use requires the measurement of observables that are nonlinear functions of the three components of the collective spin. In this paper we develop strategies that achieve the optimal quantum enhancements using non-Gaussian states produced by a nonlinear one-axis-twisting Hamiltonian, and show that measurement-after-interaction techniques, known to amplify the output signals in quantum parameter estimation protocols, are effective in measuring nonlinear spin observables. Including the presence of the relevant decoherence processes from atomic experiments, we determine analytically the quantum enhancement of non-Gaussian over-squeezed states as a function of the noise parameters for arbitrary atom numbers.

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DOI : 10.5802/crphys.103
Keywords: spin squeezing, non gaussian states, scaling laws, quantum metrology, decoherence
Mot clés : compression de spin, état non gaussiens, lois d’échelle, métrologie quantique, décohérence

Youcef Baamara 1 ; Alice Sinatra 1 ; Manuel Gessner 2, 1

1 Laboratoire Kastler Brossel, ENS-Université PSL, CNRS, Université de la Sorbonne and Collège de France, 24 rue Lhomond, 75231 Paris, France
2 ICFO-Institut de Ciències Fotòniques, The Barcelona Institute of Science and Technology, Av. Carl Friedrich Gauss 3, 08860, Castelldefels Barcelona, Spain
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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Youcef Baamara; Alice Sinatra; Manuel Gessner. Squeezing of nonlinear spin observables by one axis twisting in the presence of decoherence: An analytical study. Comptes Rendus. Physique, Volume 23 (2022), pp. 1-26. doi : 10.5802/crphys.103. https://comptes-rendus.academie-sciences.fr/physique/articles/10.5802/crphys.103/

[1] Carlton M. Caves Quantum-mechanical noise in an interferometer, Phys. Rev. D, Volume 23 (1981) no. 8, pp. 1693-1708 | DOI

[2] D. J. Wineland; John J. Bollinger; W. M. Itano; F. L. Moore; D. J. Heinzen Spin squeezing and reduced quantum noise in spectroscopy, Phys. Rev. A, Volume 46 (1992) no. 11, p. R6797-R6800 | DOI

[3] John J. Bollinger; W. M. Itano; D. J. Wineland; D. J. Heinzen Optimal frequency measurements with maximally correlated states, Phys. Rev. A, Volume 54 (1996) no. 6, p. R4649-R4652 | DOI

[4] V. Giovannetti; S. Lloyd; L. Maccone Advances in quantum metrology, Nature Photon., Volume 5 (2011), pp. 222-229 | DOI

[5] Luca Pezzè; Augusto Smerzi; Markus K. Oberthaler; Roman Schmied; Philipp Treutlein Quantum metrology with nonclassical states of atomic ensembles, Rev. Mod. Phys., Volume 90 (2018) no. 3, 035005, 70 pages | DOI

[6] Masahiro Kitagawa; Masahito Ueda Squeezed spin states, Phys. Rev. A, Volume 47 (1993) no. 6, pp. 5138-5143 | DOI

[7] Luca Pezzè; Augusto Smerzi Entanglement, Nonlinear Dynamics, and the Heisenberg Limit, Phys. Rev. Lett., Volume 102 (2009) no. 10, 100401, 4 pages | DOI

[8] Philipp Hyllus; Wiesław Laskowski; Roland Krischek; Christian Schwemmer; Witlef Wieczorek; Harald Weinfurter; Luca Pezzè; Augusto Smerzi Fisher information and multiparticle entanglement, Phys. Rev. A, Volume 85 (2012) no. 2, 022321, 10 pages | DOI

[9] Géza Tóth Multipartite entanglement and high-precision metrology, Phys. Rev. A, Volume 85 (2012) no. 2, 022322, 8 pages | DOI

[10] Géza Tóth; Iagoba Apellaniz Quantum metrology from a quantum information science perspective, J. Phys. A, Math. Gen., Volume 47 (2014) no. 42, 424006 | DOI

[11] Zhihong Ren; Weidong Li; Augusto Smerzi; Manuel Gessner Metrological Detection of Multipartite Entanglement from Young Diagrams, Phys. Rev. Lett., Volume 126 (2021) no. 8, 080502, 6 pages | DOI

[12] Anders Sørensen; L. M. Duan; J. I. Cirac; P. Zoller Many-particle entanglement with Bose–Einstein condensates, Nature, Volume 409 (2001), pp. 63-66 | DOI

[13] Yun Li; Philipp Treutlein; J. Reichel; A. Sinatra Spin squeezing in a bimodal condensate: spatial dynamics and particle losses, Eur. Phys. J. B, Volume 68 (2009), pp. 365-381 | DOI

[14] C. Gross; Tilman Zibold; E. Nicklas; Jérôme Estève; Markus K. Oberthaler Nonlinear atom interferometer surpasses classical precision limit, Nature, Volume 464 (2010), pp. 1165-1169 | DOI

[15] Max F. Reidel; Pascal Böhi; Yun Li; Theodor W. Hänsch; Alice Sinatra; Philipp Treutlein Atom chip based generation of entanglement for quantum metrology, Nature, Volume 464 (2010), p. 1170--1173 | DOI

[16] Ian D. Leroux; Monika H. Schleier-Smith; Vladan Vuletić Implementation of cavity squeezing of a collective atomic spin, Phys. Rev. Lett., Volume 104 (2010) no. 7, 073602, 4 pages | DOI

[17] R. J. Sewell; M. Koschorreck; M. Napolitano; B. Dubost; N. Behbood; M. W. Mitchell Magnetic Sensitivity Beyond the Projection Noise Limit by Spin Squeezing, Phys. Rev. Lett., Volume 109 (2012) no. 25, 253605, 5 pages | DOI

[18] Onur Hosten; Nils J. Engelsen; Rajiv Krishnakumar; Mark A. Kasevich Measurement noise 100 times lower than the quantum-projection limit using entangled atoms, Nature, Volume 529 (2016), pp. 505-508 | DOI

[19] Kevin C. Cox; Graham P. Greve; Joshua M. Weiner; James K. Thompson Deterministic squeezed states with collective measurements and feedback, Phys. Rev. Lett., Volume 116 (2016) no. 9, 093602, 5 pages | DOI

[20] Thomas Chalopin; Chayma Bouazza; Alexandre Evrard; Vasiliy Makhalov; Davide Dreon; Jean Dalibard; Leonid A. Sidorenkov; Sylvain Nascimbene Quantum-enhanced sensing using non-classical spin states of a highly magnetic atom, Nat. Commun., Volume 9 (2018) no. 1, 4955 | DOI

[21] Simone Colombo; Edwin Pedrozo-Peñafiel; Albert F. Adiyatullin; Zeyang Li; Enrique Mendez; Chi Shu; Vladan Vuletić Time-Reversal-Based Quantum Metrology with Many-Body Entangled States (2021) (https://arxiv.org/abs/2106.03754)

[22] Bernard Yurke; Samuel L. McCall; John R. Klauder SU(2) and SU(1,1) interferometers, Phys. Rev. A, Volume 33 (1986) no. 6, pp. 4033-4054 | DOI

[23] Emily Davis; Gregory Bentsen; Monika H. Schleier-Smith Approaching the Heisenberg Limit without Single-Particle Detection, Phys. Rev. Lett., Volume 116 (2016) no. 5, 053601, 5 pages | DOI

[24] Florian Fröwis; Pavel Sekatski; Wolfgang Dür Detecting Large Quantum Fisher Information with Finite Measurement Precision, Phys. Rev. Lett., Volume 116 (2016) no. 9, 090801, 5 pages | DOI

[25] Tommaso Macrì; Augusto Smerzi; Luca Pezzè Loschmidt echo for quantum metrology, Phys. Rev. A, Volume 94 (2016) no. 1, 010102(R), 5 pages | DOI

[26] Onur Hosten; Rajiv Krishnakumar; Nils J. Engelsen; Mark A. Kasevich Quantum phase magnification, Science, Volume 352 (2016) no. 6293, pp. 1552-1555 | DOI

[27] Samuel P. Nolan; Stuart S. Szigeti; Simon A. Haine Optimal and Robust Quantum Metrology Using Interaction-Based Readouts, Phys. Rev. Lett., Volume 119 (2017) no. 19, 193601, 7 pages | DOI

[28] Simon A. Haine Using interaction-based readouts to approach the ultimate limit of detection-noise robustness for quantum-enhanced metrology in collective spin systems, Phys. Rev. A, Volume 98 (2018) no. 3, 030303(R), 7 pages | DOI

[29] Marius Schulte; Victor J. Martínez-Lahuerta; Scharnagl Maja S.; Klemens Hammerer Ramsey interferometry with generalized one-axis twisting echoes, Quantum, Volume 4 (2020), 268, 19 pages | DOI

[30] S. F. Huelga; C. Macchiavello; T. Pellizzari; A. K. Ekert; M. B. Plenio; J. I. Cirac Improvement of Frequency Standards with Quantum Entanglement, Phys. Rev. Lett., Volume 79 (1997) no. 20, pp. 3865-3868 | DOI

[31] Thomas Monz; Philipp Schindler; Julio T. Barreiro; Michael Chwalla; Daniel Nigg; William A. Coish; Maximilian Harlander; Wolfgang Hänsel; Markus Hennrich; Rainer Blatt 14-qubit entanglement: Creation and coherence, Phys. Rev. Lett., Volume 106 (2011) no. 13, 130506, 4 pages | DOI

[32] R. Demkowicz-Dobrzański; J. Kołodyński; M. Guţǎ The elusive Heisenberg limit in quantum-enhanced metrology, Nat. Commun., Volume 3 (2012), 1063 | DOI

[33] K. Pawlowski; Matteo Fadel; Philipp Treutlein; Yvan Castin; A. Sinatra Mesoscopic quantum superpositions in bimodal Bose–Einstein condensates: Decoherence and strategies to counteract it, Phys. Rev. A, Volume 95 (2017) no. 6, 063609, 22 pages | DOI

[34] Helmut Strobel; Wolfgang Muessel; Daniel Linnemann; Tilman Zibold; David B. Hume; Luca Pezzè; Augusto Smerzi; Markus K. Oberthaler Fisher information and entanglement of non-Gaussian spin states, Science, Volume 345 (2014) no. 6195, pp. 424-427 | DOI

[35] Justin G. Bohnet; Brian C. Sawyer; Joseph W. Britton; Michael L. Wall; Ana Maria Rey; Michael Foss-Feig; John J. Bollinger Quantum spin dynamics and entanglement generation with hundreds of trapped ions, Science, Volume 352 (2016) no. 6291, pp. 1297-1301 | DOI

[36] Alexandre Evrard; Vasiliy Makhalov; Thomas Chalopin; Leonid A. Sidorenkov; Jean Dalibard; Raphael Lopes; Sylvain Nascimbene Enhanced Magnetic Sensitivity with Non-Gaussian Quantum Fluctuations, Phys. Rev. Lett., Volume 122 (2019) no. 17, 173601, 6 pages | DOI

[37] Kai Xu; Yu-Ran Zhang; Zheng-Hang Sun; Hekang Li; Pengtao Song; Zhongcheng Xiang; Kaixuan Huang; Hao Li; Yun-Hao Shi; Chi-Tong Chen; Xiaohui Song; Dongning Zheng; Franco Nori; H. Wang; Heng Fan Metrological characterisation of non-Gaussian entangled states of superconducting qubits (2021) | arXiv

[38] Manuel Gessner; Augusto Smerzi; Luca Pezzè Metrological Nonlinear Squeezing Parameter, Phys. Rev. Lett., Volume 122 (2019) no. 9, 090503, 7 pages | DOI

[39] Youcef Baamara; Alice Sinatra; Manuel Gessner Scaling laws for the sensitivity enhancement of non-Gaussian spin states, Phys. Rev. Lett., Volume 127 (2021) no. 16, 160501, 7 pages | DOI

[40] Alice Sinatra; Jean-Christophe Dornstetter; Yvan Castin Spin squeezing in Bose–Einstein condensates: Limits imposed by decoherence and non-zero temperature, Front. Phys., Volume 7 (2012), pp. 86-97 | DOI

[41] B. Lücke; M. Scherer; J. Kruse; Luca Pezzè; F. Deuretzbacher; P. Hyllus; O. Topic; J. Peise; W. Ertmer; J. Arlt; L. Santos; Augusto Smerzi; C. Klempt Twin Matter Waves for Interferometry Beyond the Classical Limit, Science, Volume 334 (2011) no. 6509, pp. 773-776 | DOI

[42] Samuel L. Braunstein; Carlton M. Caves Statistical distance and the geometry of quantum states, Phys. Rev. Lett., Volume 72 (1994) no. 22, pp. 3439-3443 | DOI

[43] Yun Li; Yvan Castin; Alice Sinatra Optimum Spin Squeezing in Bose–Einstein Condensates with Particle Losses, Phys. Rev. Lett., Volume 100 (2008) no. 21, 210401, 4 pages | DOI

[44] Alice Sinatra; E. Witkowska; Jean-Christophe Dornstetter; Yun Li; Yvan Castin Spin Squeezing in Finite-Temperature Bose–Einstein Condensates, Phys. Rev. Lett., Volume 107 (2011) no. 6, 060404, 5 pages | DOI

[45] Klaus Mølmer; Anders Sørensen Multiparticle Entanglement of Hot Trapped Ions, Phys. Rev. Lett., Volume 82 (1999) no. 9, pp. 1835-1838 | DOI

[46] B. P. Lanyon; P. Jurcevic; C. Hempel; Manuel Gessner; V. Vedral; R. Blatt; C. F. Roos Experimental Generation of Quantum Discord via Noisy Processes, Phys. Rev. Lett., Volume 111 (2013) no. 10, 100504, 5 pages | DOI

[47] Edoardo G. Carnio; Andreas Buchleitner; Manuel Gessner Robust Asymptotic Entanglement under Multipartite Collective Dephasing, Phys. Rev. Lett., Volume 115 (2015) no. 1, 010404, 5 pages | DOI

[48] Ian D. Leroux; Monika H. Schleier-Smith; Hao Zhang; Vladan Vuletić Unitary cavity spin squeezing by quantum erasure, Phys. Rev. A, Volume 85 (2012) no. 1, 013803, 9 pages | DOI

[49] Krzystof Pawłowski; Jérôme Estève; Jakob Reichel; Alice Sinatra Limits of atomic entanglement by cavity feedback: From weak to strong coupling, Eur. Phys. Lett., Volume 113 (2016) no. 3, 34005 | DOI

[50] Claude Cohen-Tannoudji; Jacques Dupont-Roc; Gilbert Grynberg Atom—Photon Interactions. Basic Process and Applications, John Wiley & Sons, 1998 | DOI

[51] Breuer Heinz-Peter; Francesco Petruccione The Theory of Open Quantum Systems, Oxford University Press, 2007 | DOI | Zbl

[52] Monika H. Schleier-Smith; Ian D. Leroux; Vladan Vuletić Squeezing the collective spin of a dilute atomic ensemble by cavity feedback, Phys. Rev. A, Volume 81 (2010) no. 2, 021804, 4 pages | DOI

[53] Alice Sinatra; Yvan Castin Phase dynamics of Bose–Einstein condensates: Losses versus revivals, Eur. Phys. J. D, Volume 4 (1998), pp. 247-260 | DOI

[54] Klaus Mølmer; Yvan Castin; Jean Dalibard Monte-Carlo wave function method in quantum optics, J. Opt. Soc. Am. B., Volume 10 (1993) no. 3, pp. 524-538 | DOI

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