Rydberg quantum computation with nuclear spins in two-electron neutral atoms

Abstract

Alkaline-earth-like (AEL) atoms with two valence electrons and a nonzero nuclear spin can be excited to Rydberg state for quantum computing. Typical AEL ground states possess no hyperfine splitting, but unfortunately a GHz-scale splitting seems necessary for Rydberg excitation. Though strong magnetic fields can induce a GHz-scale splitting, weak fields are desirable to avoid noise in experiments. Here, we provide two solutions to this outstanding challenge with realistic data of well-studied AEL isotopes. In the first theory, the two nuclear spin qubit states |0〉 and |1〉 are excited to Rydberg states |r〉 with detuning Δ and 0, respectively, where a MHz-scale detuning Δ arises from a weak magnetic field on the order of 1 G. With a proper ratio between Δ and Ω, the qubit state |1〉 can be fully excited to the Rydberg state while |0〉 remains there. In the second theory, we show that by choosing appropriate intermediate states a two-photon Rydberg excitation can proceed with only one nuclear spin qubit state. The second theory is applicable whatever the magnitude of the magnetic field is. These theories bring a versatile means for quantum computation by combining the broad applicability of Rydberg blockade and the incomparable advantages of nuclear-spin quantum memory in two-electron neutral atoms.

Keywords

alkaline-earth atom / Rydberg state / quantum computation / neutral atom

References

[1] M. A. Nielsen and I. L. Chuang, Quantum Computa-tion and Quantum Information, Cambridge University Press, Cambridge, 2000

[2] T. D. Ladd, F. Jelezko, R. Laflamme, Y. Nakamura, C. Monroe, and J. L. O’Brien, Quantum computers, Nature(London) 464, 45 (2010)

[3] R. Blatt and D. Wineland, Entangled states of trapped atomic ions, Nature 453, 1008 (2008)

[4] J. Q. You and F. Nori, Superconducting circuits and quantum information, Phys. Today 58, 42 (2005)

[5] J. Q. You and F. Nori, Atomic physics and quantum optics using superconducting circuits, Nature 474, 589 (2011)

[6] D. D. Awschalom, L. C. Bassett, A. S. Dzurak, E. L.Hu, and J. R. Petta, Quantum Spintronics: Engineering and manipulating atom-like spins in semiconductors, Science 339, 1174 (2013)

[7] M. H. Devoret and R. J. Schoelkopf, Superconductingcircuits for quantum information: An outlook, Science 339, 1169 (2013)

[8] D. Jaksch, J. I. Cirac, P. Zoller, S. L. Rolston, R. Côté, and M. D. Lukin, Fast quantum gates for neutral atoms, Phys. Rev. Lett. 85, 2208 (2000)

[9] M. D. Lukin, M. Fleischhauer, R. Cote, L. M. Duan, D. Jaksch, J. I. Cirac, and P. Zoller, Dipole blockade and quantum information processing in mesoscopic atomic ensembles, Phys. Rev. Lett. 87, 037901 (2001)

[10] M. Saffman, T. G. Walker, and K. Mølmer, Quantum information with Rydberg atoms, Rev. Mod. Phys. 82, 2313 (2010)

[11] M. Saffman, Quantum computing with atomic qubits and Rydberg interactions: Progress and challenges, J.Phys. B 49, 202001 (2016)

[12] D. S. Weiss and M. Saffman, Quantum computing withneutral atoms, Phys. Today 70, 44 (2017)

[13] C. S. Adams, J. D. Pritchard, and J. P. Shaffer, Rydberg atom quantum technologies, J. Phys. B: At. Mol.Opt. Phys. 53, 012002 (2020)

[14] T. Wilk, A. Gaëtan, C. Evellin, J. Wolters, Y. Miroshnychenko, P. Grangier, and A. Browaeys, Entanglement of two individual neutral atoms using Rydberg blockade, Phys. Rev. Lett. 104, 010502 (2010)

[15] L. Isenhower, E. Urban, X. L. Zhang, A. T.Gill, T. Henage, T. A. Johnson, T. G. Walker, and M. Saffman, Demonstration of a neutral atom controlled-NOT quantum gate, Phys. Rev. Lett. 104, 010503 (2010)

[16] X. L. Zhang, L. Isenhower, A. T. Gill, T. G. Walker, and M. Saffman, Deterministic entanglement of two neutral atoms via Rydberg blockade, Phys. Rev. A 82, 030306(R) (2010)

[17] K. M. Maller, M. T. Lichtman, T. Xia, Y. Sun, M. J.Piotrowicz, A. W. Carr, L. Isenhower, and M. Saffman, Rydberg-blockade controlled-NOT gate and entanglement in a two-dimensional array of neutral-atom qubits, Phys.Rev. A 92, 022336 (2015)

[18] Y.-Y. Jau, A. M. Hankin, T. Keating, I. H. Deutsch, and G. W. Biedermann, Entangling atomic spins with a Rydberg-dressed spin-flip blockade, Nat. Phys. 12, 71(2016)

[19] Y. Zeng, P. Xu, X. He, Y. Liu, M. Liu, J. Wang, D. J. Papoular, G. V. Shlyapnikov, and M. Zhan, Entangling two individual atoms of different isotopes via Rydberg blockade, Phys. Rev. Lett. 119, 160502 (2017)

[20] H. Levine, A. Keesling, A. Omran, H. Bernien, S. Schwartz, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, High-fidelity control and entanglement of Rydberg atom qubits, Phys. Rev. Lett. 121, 123603 (2018)

[21] C. J. Picken, R. Legaie, K. McDonnell, and J. D. Pritchard, Entanglement of neutral-atom qubits with long ground-Rydberg coherence times, Quant. Sci. Technol. 4, 015011 (2019)

[22] H. Levine, A. Keesling, G. Semeghini, A. Omran, T. T. Wang, S. Ebadi, H. Bernien, M. Greiner, V. Vuletić, H. Pichler, and M. D. Lukin, Parallel implementation of high-fidelity multi-qubit gates with neutral atoms, Phys. Rev. Lett. 123, 170503 (2019)

[23] T. M. Graham, M. Kwon, B. Grinkemeyer, Z. Marra, X. Jiang, M. T. Lichtman, Y. Sun, M. Ebert, and M. Saffman, Rydberg mediated entanglement in a twodimensional neutral atom qubit array, Phys. Rev. Lett. 123, 230501 (2019)

[24] H. Jo, Y. Song, M. Kim, and J. Ahn, Rydberg atom entanglements in the weak coupling regime, Phys. Rev. Lett. 124, 33603 (2019)

[25] I. S. Madjarov, J. P. Covey, A. L. Shaw, J. Choi, A. Kale, A. Cooper, H. Pichler, V. Schkolnik, J. R. Williams, and M. Endres, High-fidelity entanglement and detection of alkaline-earth Rydberg atoms, Nat. Phys. 16, 857 (2020)

[26] D. Crow, R. Joynt, and M. Saffman, Improved error thresholds for measurement-free error correction, Phys. Rev. Lett. 117, 130503 (2016)

[27] R. Yamamoto, J. Kobayashi, T. Kuno, K. Kato, and Y. Takahashi, An ytterbium quantum gas microscope with narrow-line laser cooling, New J. Phys. 18, 023016 (2016)

[28] S. Saskin, J. T. Wilson, B. Grinkemeyer, and J. D. Thompson, Narrow-line cooling and imaging of Ytterbium atoms in an optical tweezer array, Phys. Rev. Lett. 122, 143002 (2019)

[29] A. Cooper, J. P. Covey, I. S. Madjarov, S. G. Porsev, M. S. Safronova, and M. Endres, Alkaline-earth atoms in optical tweezers, Phys. Rev. X 8, 41055 (2018)

[30] J. P. Covey, I. S. Madjarov, A. Cooper, and M. Endres, 2000-times repeated imaging of strontium atoms in clockmagic tweezer arrays, Phys. Rev. Lett. 122, 173201 (2019)

[31] M. A. Norcia, A. W. Young, and A. M. Kaufman, Microscopic control and detection of ultracold strontium in optical-tweezer arrays, Phys. Rev. X 8, 041054 (2018)

[32] I. Reichenbach and I. H. Deutsch, Sideband cooling while preserving coherences in the nuclear spin state in group- II-like atoms, Phys. Rev. Lett. 99, 123001 (2007)

[33] J. Wilson, S. Saskin, Y. Meng, S. Ma, R. Dilip, A. Burgers, and J. Thompson, Trapped arrays of alkaline earth Rydberg atoms in optical tweezers, arXiv: 1912.08754 [quant-ph] (2019)

[34] X.-F. Shi, Rydberg quantum gates free from blockade error, Phys. Rev. Appl. 7, 064017 (2017)

[35] K. Bergmann, H. Theuer, and B. W. Shore, Coherent population transfer among quantum states of atoms and molecules, Rev. Mod. Phys. 70, 1003 (1998)

[36] P. Král, I. Thanopulos, and M. Shapiro, Coherently controlled adiabatic passage, Rev. Mod. Phys. 79, 53 (2007)

[37] N. V. Vitanov, A. A. Rangelov, B. W. Shore, and K. Bergmann, Stimulated Raman adiabatic passage in physics, chemistry, and beyond, Rev. Mod. Phys. 89, 015006 (2017)

[38] D. Møller, L. B. Madsen, and K. Mølmer, Quantum gates and multiparticle entanglement by Rydberg excitation blockade and adiabatic passage, Phys. Rev. Lett. 100, 170504 (2008)

[39] M. Müller, I. Lesanovsky, H. Weimer, H. P. Büchler, and P. Zoller, Mesoscopic Rydberg gate based on electromagnetically induced transparency, Phys. Rev. Lett.102, 170502 (2009)

[40] M. H. Goerz, T. Calarco, and C. P. Koch, The quantumspeed limit of optimal controlled phase gates for trappedneutral atoms, J. Phys. B44 (2011)

[41] I. I. Beterov, D. B. Tretyakov, V. M. Entin, E. A. Yakshina, I. I. Ryabtsev, C. MacCormick, and S. Bergamini, Deterministic single-atom excitation via adiabatic passage and Rydberg blockade, Phy. Rev. A 84, 023413 (2011)

[42] M. M. Müller, H. R. Haakh, T. Calarco, C. P. Koch, and C. Henkel, Prospects for fast Rydberg gates on anatom chip, Quant. Inf. Proc. 10, 771 (2011)

[43] T. Keating, K. Goyal, Y.-Y. Jau, G. W. Biedermann, A. J. Landahl, and I. H. Deutsch, Adiabatic quantum computation with Rydberg-dressed atoms, Phy. Rev. A 87, 052314 (2013)

[44] D. Petrosyan and K. Mølmer, Stimulated adiabaticpassage in a dissipative ensemble ofatoms with strong Rydberg-state interactions, Phys. Rev. A 87, 033416 (2013)

[45] I. I. Beterov, M. Saffman, E. a. Yakshina, V. P. Zhukov, D. B. Tretyakov, V. M. Entin, I. I. Ryabtsev, C. W. Mansell, C. MacCormick, S. Bergamini, and M. P. Fedoruk, Quantum gates in mesoscopic atomic ensemblesbased on adiabatic passage and Rydberg blockade, Phys. Rev. A 88, 010303(R) (2013)

[46] M. M. Müller, M. Murphy, S. Montangero, T. Calarco, P. Grangier, and A. Browaeys, Implementation of an experimentally feasible controlled-phase gate on two blockaded Rydberg atoms, Phys. Rev. A 89, 032334 (2014)

[47] M. H. Goerz, E. J. Halperin, J. M. Aytac, C. P. Koch, and K. B. Whaley, Robustness of high-fidelity Rydberg gates with single-site addressability, Phys. Rev. A 90, 032329 (2014)

[48] I. I. Beterov, M. Saffman, V. P. Zhukov, D. B.Tretyakov, V. M. Entin, E. A. Yakshina, I. I. Ryabtsev, C. W. Mansell, C. Maccormick, S. Bergamini, and M. P. Fedoruk, Coherent control of mesoscopic atomic ensembles for quantum information, Laser Phys. 24, 074013 (2014)

[49] T. Keating, R. L. Cook, A. M. Hankin, Y.-Y. Jau, G. W. Biedermann, and I. H. Deutsch, Robust quantum logicin neutral atoms via adiabatic Rydberg dressing, Phys. Rev. A 91, 012337 (2015)

[50] I. I. Beterov, M. Saffman, E. A. Yakshina, D. B. Tretyakov, V. M. Entin, G. N. Hamzina, and I. I. Ryabtsev, Simulated quantum process tomography of quantum gates with Rydberg superatoms, J. Phys. B 49, 114007 (2016)

[51] L. S. Theis, F. Motzoi, F. K. Wilhelm, and M. Saffman, High-fidelity Rydberg-blockade entangling gate usingshaped, analytic pulses, Phys. Rev. A 94, 032306 (2016)

[52] H. Wu, X. R. Huang, C. S. Hu, Z. B. Yang, and S. B. Zheng, Rydberg-interaction gates via adiabatic passage and phase control of driving fields, Phy. Rev. A 96, 022321 (2017)

[53] D. Petrosyan, F. Motzoi, M. Saffman, and K. Mølmer, High-fidelity Rydberg quantum gate via a two-atom dark state, Phys. Rev. A 96, 042306 (2017)

[54] Y.-H. Kang, Y.-H. Chen, Z.-C. Shi, B.-H. Huang, J. Song, and Y. Xia, Nonadiabatic holonomic quantum computation using Rydberg blockade, Phys. Rev. A 97, 042336 (2018)

[55] A. Omran, H. Levine, A. Keesling, G. Semeghini, T. T.16Wang, S. Ebadi, H. Bernien, A. S. Zibrov, H. Pichler, S. Choi, J. Cui, M. Rossignolo, P. Rembold, S. Montangero, T. Calarco, M. Endres, M. Greiner, V. Vuletić, and M. D. Lukin, Generation and manipulation of Schrödinger cat states in Rydberg atom arrays, Science 365, 570 (2019)

[56] K.-Y. Liao, X.-H. Lu, Z. Li, and Y.-X. Du, Geometric Rydberg quantum gate with shortcuts to adiabaticity, Opt. Lett. 44, 4801 (2019)

[57] Y. Sun, P. Xu, P.-X. Chen, and L. Liu, Controlled phase gate protocol for neutral atoms via off-resonant, Phys. Rev. Appl. 13, 024059 (2020)

[58] X.-F. Shi, Single-site Rydberg addressing in 3D atomicarrays for quantum computing with neutral atoms, J. Phys. B 53, 054002 (2020)

[59] A. Mitra, M. J. Martin, G. W. Biedermann, A. M. Marino, P. M. Poggi, and I. H. Deutsch, Robust Molmer–Sorenson gate for neutralatoms using rapid adiabatic Rydberg dressing, Phys. Rev. A 101, 030301(R) (2020)

[60] I. I. Beterov, D. B. Tretyakov, V. M. Entin, E. A. Yakshina, I. I. Ryabtsev, M. Saffman, and S. Bergamini, Application of adiabatic passage in Rydberg atomic ensembles for quantum information processing, J. Phys. B 53, 182001 (2020)

[61] M. Saffman, I. I. Beterov, A. Dalal, E. J. Paez, and B. C. Sanders, Symmetric Rydberg controlled-Z gates with adiabatic pulses control target, Phys. Rev. A 101, 62309 (2020)

[62] Y.-H. Kang, Z.-C. Shi, J. Song, and Y. Xia, Heralded atomic nonadiabatic holonomic quantum computation with Rydberg blockade, Phys. Rev. A 102, 022617 (2020)

[63] C.-Y. Guo, L. L. Yan, S. Zhang, S.-L. Su, and W. Li, Optimized geometric quantum computation with mesoscopic ensemble of Rydberg atoms, Phys. Rev. A 102, 042607 (2020)

[64] M. Khazali and K. Molmer, Fast multiqubit gates by adiabatic evolution in interacting excited-state manifolds of Rydberg atoms and superconducting circuits, Phys. Rev. X 10, 21054 (2020)

[65] A. M. Hankin, Y.-Y. Jau, L. P. Parazzoli, C. W. Chou, D. J. Armstrong, A. J. Landahl, and G. W. Biedermann, Two-atom Rydberg blockade using direct 6S to nP excitation. Phys. Rev. A 89, 033416 (2014)

[66] R. C. Teixeira, A. Larrouy, A. Muni, L. Lachaud, J. M. Raimond, S. Gleyzes, and M. Brune, Preparation of longlived, non-autoionizing circular Rydberg states of strontium, Phys. Rev. Lett. 125, 263001 (2020)

[67] D. Jaksch, H. J. Briegel, J. I. Cirac, C. W. Gardiner, and P. Zoller, Entanglement of atoms via cold controlled collisions, Phys. Rev. Lett. 82, 1975 (1999)

[68] T. Calarco, E. A. Hinds, D. Jaksch, J. Schmiedmayer, J. I. Cirac, and P. Zoller, Quantum gates with neutral atoms: Controlling collisional interactions in time dependent traps, Phys. Rev. A 61, 022304 (2000)

[69] D. Hayes, P. S. Julienne, and I. H. Deutsch, Quantum logic via the exchange blockade in ultracold collisions, Phys. Rev. Lett. 98, 070501 (2007)

[70] J. P. Covey, A. Sipahigil, S. Szoke, N. Sinclair, M. Endres, and O. Painter, Telecom-band quantum optics with ytterbium atoms and silicon nanophotonics, Phys. Rev. Appl. 11, 034044 (2019)

[71] A. J. Daley, M. M. Boyd, J. Ye, and P. Zoller, Quantum computing with alkaline-earth-metal atoms, Phys. Rev. Lett. 101, 170504 (2008)

[72] G. Cappellini, M. Mancini, G. Pagano, P. Lombardi, L. Livi, M. Siciliani de Cumis, P. Cancio, M. Pizzocaro, D. Calonico, F. Levi, C. Sias, J. Catani, M. Inguscio, and L. Fallani, Direct observation of coherent interorbital spinexchange dynamics, Phys. Rev. Lett. 113, 120402 (2014)

[73] F. Scazza, C. Hofrichter, M. Höfer, P. C. De Groot, I. Bloch, and S. Fölling, Observation of two-orbital spinexchange interactions with ultracold SU(N)-symmetric fermions, Nat. Phys. 10, 779 (2014)

[74] A. M. Kaufman, B. J. Lester, M. Foss-Feig, M. L.Wall, A. M. Rey, and C. A. Regal, Entangling two transportable neutral atoms via local spin exchange, Nature 527, 208 (2015)

[75] A. V. Gorshkov, A. M. Rey, A. J. Daley, M. M.Boyd, J. Ye, P. Zoller, and M. D. Lukin, Alkaline earth-metal atoms as few-qubit quantum registers, Phys. Rev. Lett. 102, 110503 (2009)

[76] A. J. Daley, J. Ye, and P. Zoller, State-dependent lattices for quantum computing with alkaline-earth-metal atoms, Eur. Phys. J. D 65, 207 (2011)

[77] A. J. Daley, Quantum computing and quantum simulation with group-II atoms, Quant. Inf. Proc. 10, 865 (2011)

[78] G. Pagano, F. Scazza, and M. FossFeig, Fast and scalable quantum information processing with two electron atoms in optical tweezer arrays, Adv. Quant. Technol. 2, 1970021 (2019)

[79] J. H. M. Jensen, J. J. Sørensen, K. Mølmer, and J. F. Sherson, Time-optimal control of collisional SWAP gates in ultracold atomic systems, Phys. Rev. A 100, 052314 (2019)

[80] R. Stock, N. S. Babcock, M. G. Raizen, and B. C. Sanders, Entanglement of group-II-like atoms with fast measurement for quantum information processing, Phys. Rev. 78, 022301 (2008)

[81] M. Saffman and T. G. Walker, Analysis of a quantum logic device based on dipole-dipole interactions of opticallytrapped Rydberg atoms, Phys. Rev. A 72, 022347(2005)

[82] M. Saffman, X. L. Zhang, A. T. Gill, L. Isenhower, and T. G. Walker, Rydberg state mediated quantum gates and entanglement of pairs of neutral atoms, J. Phys.: Conf. Ser. 264, 012023 (2011)

[83] S. G. Porsev, A. Derevianko, and E. N. Fortson, Possibility of an optical clock using the 6¹S₀ → 6³Po₀ transition in 171,173Yb atoms held in an optical lattice, Phys. Rev. A 69, 021403(R) (2004)

[84] B. Budick and J. Snir, Hyperfine structure of the 6s6p¹P₁ level of the stable ytterbium isotopes, Phys. Rev. 178, 18 (1969)

[85] R. W. Berends and L. Maleki, Hyperfine structure andisotope shifts of transitions in neutral and singly ionized ytterbium, J. Opt. Soc. Am. B 9, 332 (1992)

[86] K. Deilamian, J. D. Gillaspy, and D. E. Kelleher, Isotopeshifts and hyperfine splittings of the 3988-nm Yb I line, J. Opt. Soc. Am. B 10, 789 (1993)

[87] R. Zinkstok, E. J. Van Duijn, S. Witte, and W. Hogervorst, Hyperfine structure and isotope shift of transitions in Yb I using UV and deep-UV cw laser light and the angular distribution of fluorescence radiation, J. Phys. B 35, 2693 (2002)

[88] P. E. Atkinson, J. S. Schelfhout, and J. J. McFerran, Hyperfine constants and line separationsfor the ¹S₀ → ³P₁ intercombination linein neutral ytterbium with sub- Doppler resolution, Phys. Rev. A 100, 042505 (2019)

[89] A.-M. Mårtensson-Pendrill, D. S. Gough, and P. Hannaford, Isotope shifts and hyperfine structure in the 369.4-nm 6s–6p_1/2 resonance line of singly ionized ytterbium, Phys. Rev. A 49, 3351 (1994)

[90] K. B. Blagoev and V. A. Komarovskii, Lifetimes of levels of neutral and singly ionized lanthanide atoms, At. Data Nucl. Data Tables 56, 1 (1994)

[91] M. M. Boyd, T. Zelevinsky, A. D. Ludlow, S. Blatt, T. Zanon-Willette, S. M. Foreman, and J. Ye, Nuclear spin effects in optical lattice clocks, Phys. Rev. A76(2007)

[92] B. Budick and J. Snir, Hyperfine-structure anomalies of stable ytterbium isotopes, Phys. Rev. A 1, 545 (1970)

[93] K. Pandey, A. K. Singh, P. V. Kumar, M. V. Suryanarayana, and V. Natarajan, Isotope shifts and hyperfine structure in the 555.8-nm ¹S₀ → ³P₁ line of Yb, Phys. Rev. A 80, 022518 (2009)

[94] H. Lehec, X. Hua, P. Pillet, and P. Cheinet, Isolated core excitation of high-orbital quantum-number Rydberg states of ytterbium, Phys. Rev. A 103, 022806 (2021)

[95] G. Higgins, W. Li, F. Pokorny, C. Zhang, F. Kress, C. Maier, J. Haag, Q. Bodart, I. Lesanovsky, and M. Hennrich, A single strontium Rydberg ion confinedin a Paul trap, Phys. Rev. X 7, 021038 (2017)

[96] G. Higgins, F. Pokorny, C. Zhang, Q. Bodart, and M. Hennrich, Coherent control of a single trapped Rydbergion, Phys. Rev. Lett. 119, 220501 (2017)

[97] C. Zhang, F. Pokorny, W. Li, G. Higgins, A. Pöschl, I. Lesanovsky, and M. Hennrich, Submicrosecond entangling gate between trapped ions via Rydberg interaction, Nature 580, 345 (2020)

[98] X.-F. Shi, Fast, Accurate, and realizable two-qubit entangling gates by quantum interference in detuned Rabi cycles of Rydberg atoms, Phys. Rev. Appl. 11, 044035 (2019)

[99] X. L. Zhang, A. T. Gill, L. Isenhower, T. G. Walker, and M. Saffman, Fidelity of a Rydberg-blockade quantum gate from simulated quantum process tomography, Phys. Rev. A 85, 042310 (2012)

[100] X.-F. Shi, Accurate quantum logic gates by spin echo in Rydberg atoms, Phys. Rev. Appl. 10, 034006 (2018)

[101] L. H. Pedersen, N. M. Møller, and K. Mølmer, Fidelity of quantum operations, Phys. Lett. A 367, 47 (2007)

[102] E. J. Robertson, N. ŠˇSibalić, R. M. Potvliege, and M. P. A. Jones, ARC 3.0: An expanded Python toolbox for atomic physics, Comp. Phys. Comm. 261, 107814 (2021)

[103] H. Lehec, A. Zuliani, W. Maineult, E. Luc-Koenig, P. Pillet, P. Cheinet, F. Niyaz, and T. F. Gallagher, Laser and microwave spectroscopy of even-parity Rydberg states of neutral ytterbium and multichannel quantum defect theory analysis, Phys. Rev. A 98, 062506 (2018)

[104] B. Kaulakys, Consistent analytical approach for the quasi-classical radial dipole matrix elements, J. Phys. B 28, 4963 (1995)

[105] X.-F. Shi, F. Bariani, and T. A. B. Kennedy, Entanglement of neutral-atom chains by spin-exchange Rydberg interaction, Phys. Rev. A 90, 062327 (2014)

[106] X.-F. Shi, Transition slow-down by Rydberg interactionof neutral atoms and a fast controlled-NOT quantum gate, Phys. Rev. Appl. 14, 054058 (2020)

[107] J. S. Ross and K. Murakawa, Nuclear quadrupole moment of Yb173, Phys. Rev. 128, 1159 (1962)

[108] M. Aymar, Multichannel-quantum-defect theory wavefunctions of Ba tested or improved by laser measurements, J. Opt. Soc. Am. B 1, 239 (1984)

[109] L. Xingye, L. Wanfa, J. Zhankui, and J. Larsson, Test of the multichannel quantum-defect wave function by a Landé-factor (gJ ) investigation in the perturbed 6snp^1,3P₁ sequencesof Yb I, Phys. Rev. A 49, 4443 (1994)

[110] T. Ido and H. Katori, Recoil-free spectroscopy of neutral Sr atoms in the Lamb–Dicke regime, Phys. Rev. Lett. 91, 053001 (2003)

[111] S. Ye, X. Zhang, T. C. Killian, F. B. Dunning, M. Hiller, S. Yoshida, S. Nagele, and J. Burgdörfer, Production of very-high-n strontium Rydberg atoms, Phys. Rev. A 88, 043430 (2013)

[112] C. Gaul, B. J. DeSalvo, J. A. Aman, F. B. Dunning, T. C. Killian, and T. Pohl, Resonant Rydberg dressing of alkaline-earth atoms via electromagnetically induced transparency, Phys. Rev. Lett. 116, 243001 (2016)

[113] M. N. Winchester, M. A. Norcia, J. R. K. Cline, and J. K. Thompson, Magnetically Induced optical transparency on a forbidden transition in strontium for cavityenhanced spectroscopy, Phys. Rev. Lett. 118, 263601 (2017)

[114] R. Ding, J. D. Whalen, S. K. Kanungo, T. C. Killian, F. B. Dunning, S. Yoshida, and J. Burgdörfer, Spectroscopy of Sr⁸⁷ triplet Rydberg states, Phys. Rev. A 98, 042505 (2018)

[115] H. G. C. Werij, C. H. Greene, C. E. Theodosiou, and A. Gallagher, Oscillator strengths and radiative branching ratios in atomic Sr, Phys. Rev. A 46, 1248 (1992)

[116] C. L. Vaillant, M. P. Jones, and R. M. Potvliege, Longrange Rydberg–Rydberg interactions in calcium, strontium and ytterbium, J. Phys. B: At. Mol. Opt. Phys. 45, 135004 (2012)

[117] C. L. Vaillant, M. P. Jones, and R. M. Potvliege, Multichannel quantum defect theory of strontium bound Rydberg states, J. Phys. B: At. Mol. Opt. Phys. 47, 155001 (2014)

[118] F. B. Dunning, T. C. Killian, S. Yoshida, and J. Burgdörfer, Recent advances in Rydberg physics using alkalineearth atoms, J. Phys. B 49, 112003 (2016)

[119] F. Robicheaux, Calculations of long range interactions for ⁸⁷Sr Rydberg states, J. Phys. B 52, 244001 (2019)

[120] R. Mukherjee, J. Millen, R. Nath, M. P. Jones, and T. Pohl, Many-body physics with alkaline-earth Rydberg lattices, J. Phys. B 44, 184010 (2011)

[121] X. Zhang, F. B. Dunning, S. Yoshida, and J. Burgdörfer, Rydberg blockade effects at n∼ 300 instrontium, Phys. Rev. A 92, 051402(R) (2015)

[122] B. J. DeSalvo, J. A. Aman, C. Gaul, T. Pohl, S. Yoshida, J. Burgdörfer, K. R. A. Hazzard, F. B. Dunning, and T. C. Killian, Rydberg–blockade effectsin Autler–Townes spectra of ultracold strontium, Phys. Rev. A 93, 022709 (2016)

[123] S. Yoshida, J. Burgdörfer, X. Zhang, and F. B. Dunning, Rydberg blockade in a hot atomic beam, Phy. Rev. A 95, 042705 (2017)

[124] J. E. Sansonetti and G. Nave, Wavelengths, transition probabilities, and energy levels for the spectrum of neutral strontium (Sr I), J. Phys. Chem. Ref. Data 39, 033103 (2010)

[125] R. J. Fonck, F. L. Roesler, D. H. Tracy, K. T. Lu, F. S. Tomkins, and W. R. S. Garton, Atomic diamagnetism and diamagnetically induced configuration mixing in laser-excited barium, Phys. Rev. Lett. 39, 1513 (1977)

[126] C. Ates, T. Pohl, T. Pattard, and J. M. Rost, Antiblockade in Rydberg excitation of an ultracold lattice gas, Phys. Rev. Lett. 98, 023002 (2007)

[127] T. Amthor, C. Giese, C. S. Hofmann, and M. Weidemüller, Evidence of antiblockade in an ultracold Rydberg gas, Phys. Rev. Lett. 104, 013001 (2010)

[128] S.-L. Su, F.-Q. Guo, J.-L. Wu, Z. Jin, X. Q. Shao, and S. Zhang, Rydberg antiblockade regimes: Dynamics and applications, EPL 131, 53001 (2020)

[129] A. Lurio, M. Mandel, and R. Novick, Second-order hyperfineand Zeeman corrections for an (sl) configuration, Phys. Rev. 126, 1758 (1962)

[130] D. W. Fang, W. J. Xie, Y. Zhang, X. Hu, and Y. Y. Liu, Radiative lifetimes of Rydberg state of ytterbium, J. Quant. Spectrosc. Ra. 69, 469 (2001)

[131] J. P. Covey, A. Sipahigil, and M. Saffman, Microwavetooptical conversion via four-wave mixing in a cold ytterbium ensemble, Phys. Rev. A 100, 012307 (2019)

[132] D. A. Steck, Quantum and Atom Optics,

[133] T. G. Walker and M. Saffman, Consequences of Zeemandegeneracy for the van der Waals blockade between Rydberg atoms, Phys. Rev. A 77, 032723 (2008)

[134] T. Zelevinsky, M. M. Boyd, A. D. Ludlow, T. Ido, J. Ye, R. Ciury lo, P. Naidon, and P. S. Julienne, Narrow line photo association in an optical lattice, Phys. Rev. Lett. 96, 203201 (2006)

[135] J. Millen, G. Lochead, and M. P. A. Jones, Two electron excitation of an interacting cold Rydberg gas, Phys. Rev. Lett. 105, 213004 (2010)

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