{"status":"public","date_updated":"2026-03-16T09:28:24Z","project":[{"_id":"bdb108fd-d553-11ed-ba76-83dc74a9864f","grant_number":"F07105","name":"QUANTUM INFORMATION SYSTEMS BEYOND CLASSICAL CAPABILITIES / P5- Integration of Superconducting Quantum Circuits"}],"has_accepted_license":"1","volume":25,"scopus_import":"1","publisher":"American Physical Society","PlanS_conform":"1","issue":"3","oa":1,"type":"journal_article","intvolume":"        25","department":[{"_id":"JoFi"},{"_id":"GradSch"}],"day":"01","OA_place":"publisher","arxiv":1,"abstract":[{"lang":"eng","text":"Three-dimensional (3D) crystals offer a route to scaling up trapped-ion systems for quantum sensing and quantum simulation applications; however, engineering coherent spin-motion couplings and effective spin-spin interactions in large crystals poses technical challenges associated with decoherence and prolonged timescales to generate appreciable entanglement. Here, we explore the possibility of speeding up these interactions in 3D crystals via parametric amplification. For this purpose, we derive a general Hamiltonian for the parametric amplification of spin-motion coupling that is broadly applicable to normal modes with motion transverse to or along the spatial extent of the crystal. Unlike in lower-dimensional crystals, we find that the ability to faithfully (uniformly) amplify the spin-spin interactions in 3D crystals depends on the physical implementation of the spin-motion coupling. We consider the light-shift gate, and the so-called phase-insensitive and phase-sensitive Mølmer-Sørensen (MS) gates, and we find that only the phase-sensitive MS gate can be faithfully amplified in general 3D crystals. We discuss a situation where nonuniform amplification can be advantageous. We also reconsider the effect of counter-rotating terms on parametric amplification and find that they are not as detrimental as previous studies suggest."}],"citation":{"chicago":"Hawaldar, Samarth, N. Nikhil, Ana Maria Rey, John J. Bollinger, and Athreya Shankar. “Parametric Amplification of Spin-Motion Coupling in Three-Dimensional Trapped-Ion Crystals.” <i>Physical Review Applied</i>. American Physical Society, 2026. <a href=\"https://doi.org/10.1103/h1m9-h3yw\">https://doi.org/10.1103/h1m9-h3yw</a>.","ista":"Hawaldar S, Nikhil N, Rey AM, Bollinger JJ, Shankar A. 2026. Parametric amplification of spin-motion coupling in three-dimensional trapped-ion crystals. Physical Review Applied. 25(3), 034004.","ama":"Hawaldar S, Nikhil N, Rey AM, Bollinger JJ, Shankar A. Parametric amplification of spin-motion coupling in three-dimensional trapped-ion crystals. <i>Physical Review Applied</i>. 2026;25(3). doi:<a href=\"https://doi.org/10.1103/h1m9-h3yw\">10.1103/h1m9-h3yw</a>","mla":"Hawaldar, Samarth, et al. “Parametric Amplification of Spin-Motion Coupling in Three-Dimensional Trapped-Ion Crystals.” <i>Physical Review Applied</i>, vol. 25, no. 3, 034004, American Physical Society, 2026, doi:<a href=\"https://doi.org/10.1103/h1m9-h3yw\">10.1103/h1m9-h3yw</a>.","ieee":"S. Hawaldar, N. Nikhil, A. M. Rey, J. J. Bollinger, and A. Shankar, “Parametric amplification of spin-motion coupling in three-dimensional trapped-ion crystals,” <i>Physical Review Applied</i>, vol. 25, no. 3. American Physical Society, 2026.","short":"S. Hawaldar, N. Nikhil, A.M. Rey, J.J. Bollinger, A. Shankar, Physical Review Applied 25 (2026).","apa":"Hawaldar, S., Nikhil, N., Rey, A. M., Bollinger, J. J., &#38; Shankar, A. (2026). Parametric amplification of spin-motion coupling in three-dimensional trapped-ion crystals. <i>Physical Review Applied</i>. American Physical Society. <a href=\"https://doi.org/10.1103/h1m9-h3yw\">https://doi.org/10.1103/h1m9-h3yw</a>"},"file_date_updated":"2026-03-16T09:24:53Z","ddc":["530"],"corr_author":"1","article_processing_charge":"Yes (via OA deal)","month":"03","article_type":"original","oa_version":"Published Version","author":[{"id":"221708e1-1ff6-11ee-9fa6-85146607433e","last_name":"Hawaldar","full_name":"Hawaldar, Samarth","orcid":"0000-0002-1965-4309","first_name":"Samarth"},{"full_name":"Nikhil, N.","first_name":"N.","last_name":"Nikhil"},{"last_name":"Rey","first_name":"Ana Maria","full_name":"Rey, Ana Maria"},{"last_name":"Bollinger","full_name":"Bollinger, John J.","first_name":"John J."},{"full_name":"Shankar, Athreya","first_name":"Athreya","last_name":"Shankar"}],"quality_controlled":"1","external_id":{"arxiv":["2507.16741"]},"title":"Parametric amplification of spin-motion coupling in three-dimensional trapped-ion crystals","date_published":"2026-03-01T00:00:00Z","article_number":"034004","publication":"Physical Review Applied","date_created":"2026-03-15T23:01:35Z","file":[{"relation":"main_file","file_id":"21456","file_name":"2026_PhysicalReviewApplied_Hawaldar.pdf","content_type":"application/pdf","date_updated":"2026-03-16T09:24:53Z","checksum":"f0dc6a50222b778fd75cc72a28d38689","date_created":"2026-03-16T09:24:53Z","success":1,"access_level":"open_access","creator":"dernst","file_size":1421954}],"_id":"21449","publication_status":"published","OA_type":"hybrid","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode","image":"/images/cc_by.png"},"publication_identifier":{"eissn":["2331-7019"]},"year":"2026","language":[{"iso":"eng"}],"doi":"10.1103/h1m9-h3yw","acknowledgement":"We thank Wenchao Ge and Allison Carter for feedback on the manuscript. We also thank Wenchao Ge for sharing the numerical simulation data that we have used in Fig. 5 of this paper. N.N. would like to thank Perimeter Institute and Boston University for support during this research. S.H. acknowledges partial support from the Institute of Science and Technology Austria and the Austrian Science Fund (FWF) DOI 10.55776/F71 for the duration of this project. This work was supported by DOE Quantum Systems Accelerator, ARO W911NF24-1-0128, and NSF JILA-PFC PHY-2317149. J.J.B. and A.M.R. acknowledge support through AFOSR Grant No. FA9550-25-1-0080. A.S. acknowledges support by the Department of Science and Technology, Govt. of India through the INSPIRE Faculty Award (DST/INSPIRE/04/2023/001486), by the Anusandhan National Research Foundation (ANRF), Govt. of India through the Prime Minister’s Early Career Research Grant (PMECRG) (ANRF/ECRG/2024/001160/PMS) and by IIT Madras through the New Faculty Initiation Grant (NFIG)."}