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Currently, differential protocols with uncorrelated particles and mode-separable settings reach a sensitivity bounded by the standard quantum limit (SQL). Here we show that differential interferometry can be understood as a distributed multiparameter estimation problem and can benefit from both mode and particle entanglement. Our protocol uses a single spin-squeezed state that is mode-swapped among common interferometric modes. The mode swapping is optimized to estimate the differential phase shift with sub-SQL sensitivity. Numerical calculations are supported by analytical approximations that guide the optimization of the protocol. The scheme is also tested with simulation of noise in atomic clocks and interferometers.<\/jats:p>","DOI":"10.22331\/q-2023-03-30-965","type":"journal-article","created":{"date-parts":[[2023,3,30]],"date-time":"2023-03-30T11:05:37Z","timestamp":1680174337000},"page":"965","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":9,"title":["Quantum-enhanced differential atom interferometers and clocks with spin-squeezing swapping"],"prefix":"10.22331","volume":"7","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6846-9249","authenticated-orcid":false,"given":"Robin","family":"Corgier","sequence":"first","affiliation":[{"name":"QSTAR, INO-CNR and LENS, Largo Enrico Fermi 2, 50125 Firenze, Italy."},{"name":"LNE-SYRTE, Observatoire de Paris, Universit\u00e9 PSL, CNRS, Sorbonne Universit\u00e9 61 avenue de l\u2019Observatoire, 75014 Paris, France"}]},{"given":"Marco","family":"Malitesta","sequence":"additional","affiliation":[{"name":"QSTAR, INO-CNR and LENS, Largo Enrico Fermi 2, 50125 Firenze, Italy."}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4967-6939","authenticated-orcid":false,"given":"Augusto","family":"Smerzi","sequence":"additional","affiliation":[{"name":"QSTAR, INO-CNR and LENS, Largo Enrico Fermi 2, 50125 Firenze, Italy."}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0325-9555","authenticated-orcid":false,"given":"Luca","family":"Pezz\u00e8","sequence":"additional","affiliation":[{"name":"QSTAR, INO-CNR and LENS, Largo Enrico Fermi 2, 50125 Firenze, Italy."}]}],"member":"9598","published-online":{"date-parts":[[2023,3,30]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"P. 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Kolkowitz, Differential clock comparisons with a multiplexed optical lattice clock, Nature 602, 425 (2022). DOI: https:\/\/doi.org\/10.1038\/s41586-021-04344-y.","DOI":"10.1038\/s41586-021-04344-y"},{"key":"36","doi-asserted-by":"publisher","unstructured":"M. Gessner, L. Pezz\u00e8 and A. Smerzi, Sensitivity bounds for multiparameter quantum metrology Phys. Rev. Lett. 121, 130503 (2018). DOI: https:\/\/doi.org\/10.1103\/PhysRevLett.121.130503.","DOI":"10.1103\/PhysRevLett.121.130503"},{"key":"37","doi-asserted-by":"publisher","unstructured":"L.-Z. Liu, et al. Distributed quantum phase estimation with entangled photons, Nat. Phot. 15, 137\u2013142 (2021). DOI: https:\/\/doi.org\/10.1038\/s41566-020-00718-2.","DOI":"10.1038\/s41566-020-00718-2"},{"key":"38","doi-asserted-by":"publisher","unstructured":"A. Gauguet, B. Canuel, T. L\u00e9v\u00e8que, W. Chaibi and A. Landragin, Characterization and limits of a cold-atom Sagnac interferometer, Phys. Rev. A 80, 063604 (2009). DOI: https:\/\/doi.org\/10.1103\/PhysRevA.80.063604.","DOI":"10.1103\/PhysRevA.80.063604"},{"key":"39","doi-asserted-by":"publisher","unstructured":"C. Janvier, V. M\u00e9noret, B. Desruelle, S. Merlet, A. Landragin and F. Pereira dos Santos, Compact differential gravimeter at the quantum projection-noise limit, Phys. Rev. A 105, 022801 (2022). DOI: https:\/\/doi.org\/10.1103\/PhysRevA.105.022801.","DOI":"10.1103\/PhysRevA.105.022801"},{"key":"40","unstructured":"This bound is obtained considering the relation $\\Delta^2 (\\theta_A - \\theta_B) = \\Delta^2 \\theta_A + \\Delta^2 \\theta_B$, valid for independent interferometers, and taking coherent spin states of $N_A$ and $N_B$ particles, respectively, such that $\\Delta^2 \\theta_{A,B}=1\/N_{A,B}$, independently from the value of $\\theta_{A,B}$. Finally, the optimal separable configuration is obtained for $N_A=N_B=N\/2$, giving $\\Delta^2 (\\theta_A - \\theta_B)_{\\rm SQL}=4\/N$."},{"key":"41","doi-asserted-by":"publisher","unstructured":"L. Pezz\u00e8, A. Smerzi, M. K. Oberthaler, R. Schmied and P. Treutlein, Quantum metrology with nonclassical states of atomic ensembles, Rev. Mod. Phys. 90, 035005 (2018). DOI: https:\/\/doi.org\/10.1103\/RevModPhys.90.035005.","DOI":"10.1103\/RevModPhys.90.035005"},{"key":"42","doi-asserted-by":"publisher","unstructured":"S.S. Szigeti, O. Hosten and S.A. Haine, Improving cold-atom sensors with quantum entanglement: Prospects and challenges, Appl. Phys. Lett. 118, 140501 (2021). DOI: https:\/\/doi.org\/10.1063\/5.0050235.","DOI":"10.1063\/5.0050235"},{"key":"43","doi-asserted-by":"publisher","unstructured":"S. S. Szigeti, S. P. Nolan, J. D. Close and S. A. Haine, High-Precision Quantum-Enhanced Gravimetry with a Bose-Einstein Condensate, Phys. Rev. Lett. 125, 100402 (2020). 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