Fast nuclear-spin gates and electrons−nuclei entanglement of neutral atoms in weak magnetic fields
Xiao-Feng Shi
Fast nuclear-spin gates and electrons−nuclei entanglement of neutral atoms in weak magnetic fields
We present a novel class of Rydberg-mediated nuclear-spin entanglement in divalent atoms with global laser pulses. First, we show a fast nuclear-spin controlled phase gate of an arbitrary phase realizable either with two laser pulses when assisted by Stark shifts, or with three pulses. Second, we propose to create an electrons−nuclei-entangled state, which is named a super bell state (SBS) for it mimics a large Bell state incorporating three small Bell states. Third, we show a protocol to create a three-atom electrons-nuclei entangled state which contains the three-body W and Greenberger−Horne−Zeilinger (GHZ) states simultaneously. These protocols possess high intrinsic fidelities, do not require single-site Rydberg addressing, and can be executed with large Rydberg Rabi frequencies in a weak, Gauss-scale magnetic field. The latter two protocols can enable measurement-based preparation of Bell, hyperentangled, and GHZ states, and, specifically, SBS can enable quantum dense coding where one can share three classical bits of information by sending one particle.
nuclear-spin qubit / electrons−nuclei entanglement / super Bell state / Greenberger−Horne−Zeilinger state / Rydberg-mediated entanglement / quantum dense coding
[1] |
D. Jaksch, J. I. Cirac, P. Zoller, S. L. Rolston, R. Cote, M. D. Lukin. Fast quantum gates for neutral atoms. Phys. Rev. Lett., 2000, 85(10): 2208
CrossRef
ADS
Google scholar
|
[2] |
M. D. Lukin, M. Fleischhauer, R. Cote, L. M. Duan, D. Jaksch, J. I. Cirac, P. Zoller. Dipole blockade and quantum information processing in mesoscopic atomic ensembles. Phys. Rev. Lett., 2001, 87(3): 037901
CrossRef
ADS
Google scholar
|
[3] |
T. Wilk, A. Gaetan, C. Evellin, J. Wolters, Y. Miroshnychenko, P. Grangier, A. Browaeys. Entanglement of two individual neutral atoms using Rydberg blockade. Phys. Rev. Lett., 2010, 104(1): 010502
CrossRef
ADS
Google scholar
|
[4] |
L. Isenhower, E. Urban, X. L. Zhang, A. T. Gill, T. Henage, T. A. Johnson, T. G. Walker, M. Saffman. Demonstration of a neutral atom controlled-NOT quantum gate. Phys. Rev. Lett., 2010, 104(1): 010503
CrossRef
ADS
Google scholar
|
[5] |
X. L. Zhang, L. Isenhower, A. T. Gill, T. G. Walker, M. Saffman. Deterministic entanglement of two neutral atoms via Rydberg blockade. Phys. Rev. A, 2010, 82: 030306(R)
CrossRef
ADS
Google scholar
|
[6] |
K. M. Maller, M. T. Lichtman, T. Xia, Y. Sun, M. J. Piotrowicz, A. W. Carr, L. Isenhower, M. Saffman. Rydberg-blockade controlled-not gate and entanglement in a two-dimensional array of neutral-atom qubits. Phys. Rev. A, 2015, 92(2): 022336
CrossRef
ADS
Google scholar
|
[7] |
Y. Y. Jau, A. M. Hankin, T. Keating, I. H. Deutsch, G. W. Biedermann. Entangling atomic spins with a Rydberg-dressed spin-flip blockade. Nat. Phys., 2016, 12(1): 71
CrossRef
ADS
Google scholar
|
[8] |
Y. Zeng, P. Xu, X. He, Y. Liu, M. Liu, J. Wang, D. J. Papoular, G. V. Shlyapnikov, M. Zhan. Entangling two individual atoms of different isotopes via Rydberg blockade. Phys. Rev. Lett., 2017, 119(16): 160502
CrossRef
ADS
Google scholar
|
[9] |
H. Levine, A. Keesling, A. Omran, H. Bernien, S. Schwartz, A. S. Zibrov, M. Endres, M. Greiner, V. Vuletíc, M. D. Lukin. High-fidelity control and entanglement of Rydberg atom qubits. Phys. Rev. Lett., 2018, 121(12): 123603
CrossRef
ADS
Google scholar
|
[10] |
C. J. Picken, R. Legaie, K. McDonnell, J. D. Pritchard. Entanglement of neutral-atom qubits with long ground-Rydberg coherence times. Quantum Sci. Technol., 2018, 4(1): 015011
CrossRef
ADS
Google scholar
|
[11] |
H. Levine, A. Keesling, G. Semeghini, A. Omran, T. T. Wang, S. Ebadi, H. Bernien, M. Greiner, V. Vuletíc, H. Pichler, M. D. Lukin. Parallel implementation of high-fidelity multi-qubit gates with neutral atoms. Phys. Rev. Lett., 2019, 123(17): 170503
CrossRef
ADS
Google scholar
|
[12] |
T. M. Graham, M. Kwon, B. Grinkemeyer, Z. Marra, X. Jiang, M. T. Lichtman, Y. Sun, M. Ebert, M. Saffman. Rydberg mediated entanglement in a two-dimensional neutral atom qubit array. Phys. Rev. Lett., 2019, 123(23): 230501
CrossRef
ADS
Google scholar
|
[13] |
H. Jo, Y. Song, M. Kim, J. Ahn. Rydberg atom entanglements in the weak coupling regime. Phys. Rev. Lett., 2020, 124(3): 033603
CrossRef
ADS
Google scholar
|
[14] |
Z. Fu, P. Xu, Y. Sun, Y. Y. Liu, X. D. He, X. Li, M. Liu, R. B. Li, J. Wang, L. Liu, M. S. Zhan. High-fidelity entanglement of neutral atoms via a Rydberg-mediated single-modulated-pulse controlled-PHASE gate. Phys. Rev. A, 2022, 105(4): 042430
CrossRef
ADS
Google scholar
|
[15] |
K. McDonnell, L. F. Keary, J. D. Pritchard. Demonstration of a quantum gate using electromagnetically induced transparency. Phys. Rev. Lett., 2022, 129(20): 200501
CrossRef
ADS
Google scholar
|
[16] |
D. Bluvstein, H. Levine, G. Semeghini, T. T. Wang, S. Ebadi, M. Kalinowski, A. Keesling, N. Maskara, H. Pichler, M. Greiner, V. Vuleti’c, M. D. Lukin. A quantum processor based on coherent transport of entangled atom arrays. Nature, 2022, 604(7906): 451
CrossRef
ADS
Google scholar
|
[17] |
T. M. Graham, Y. Song, J. Scott, C. Poole, L. Phuttitarn, K. Jooya, P. Eichler, X. Jiang, A. Marra, B. Grinkemeyer, M. Kwon, M. Ebert, J. Cherek, M. T. Lichtman, M. Gillette, J. Gilbert, D. Bowman, T. Ballance, C. Campbell, E. D. Dahl, O. Crawford, N. S. Blunt, B. Rogers, T. Noel, M. Saffman. Multi-qubit entanglement and algorithms on a neutral-atom quantum computer. Nature, 2022, 604(7906): 457
CrossRef
ADS
Google scholar
|
[18] |
S.J. EveredD. BluvsteinM.KalinowskiS.EbadiT.Manovitz H.ZhouS. H. LiA.A. GeimT.T. WangN.Maskara H.LevineG. SemeghiniM.GreinerV.VuleticM.D. Lukin, High-fidelity parallel entangling gates on a neutral atom quantum computer, arXiv: 2304.05420v1 (2023)
|
[19] |
I. S. Madjarov, J. P. Covey, A. L. Shaw, J. Choi, A. Kale, A. Cooper, H. Pichler, V. Schkolnik, J. R. Williams, M. Endres. High-fidelity entanglement and detection of alkaline-earth Rydberg atoms. Nat. Phys., 2020, 16(8): 857
CrossRef
ADS
Google scholar
|
[20] |
S. Ma, A. P. Burgers, G. Liu, J. Wilson, B. Zhang, J. D. Thompson. Universal gate operations on nuclear spin qubits in an optical tweezer array of 171Yb atoms. Phys. Rev. X, 2022, 12(2): 021028
CrossRef
ADS
Google scholar
|
[21] |
N. Schine, A. W. Young, W. J. Eckner, M. J. Martin, A. M. Kaufman. Long-lived Bell states in an array of optical clock qubits. Nat. Phys., 2022, 18(9): 1067
CrossRef
ADS
Google scholar
|
[22] |
P.SchollA. L. ShawR.B. S. TsaiR.FinkelsteinJ.Choi M.Endres, Erasure conversion in a high-fidelity Rydberg quantum simulator, arXiv: 2305.03406v1 (2023)
|
[23] |
S.MaG.Liu P.PengB. ZhangS.JanduraA.P. BurgersG.Pupillo S.PuriJ. D. Thompson, High-fidelity gates with mid-circuit erasure conversion in a metastable neutral atom qubit, arXiv: 2305.05493v1 (2023)
|
[24] |
R. Yamamoto, J. Kobayashi, T. Kuno, K. Kato, Y. Takahashi. An ytterbium quantum gas microscope with narrow-line laser cooling. New J. Phys., 2016, 18(2): 023016
CrossRef
ADS
Google scholar
|
[25] |
S. Saskin, J. T. Wilson, B. Grinkemeyer, J. D. Thompson. Narrow-line cooling and imaging of ytterbium atoms in an optical tweezer array. Phys. Rev. Lett., 2019, 122(14): 143002
CrossRef
ADS
Google scholar
|
[26] |
A. Cooper, J. P. Covey, I. S. Madjarov, S. G. Porsev, M. S. Safronova, M. Endres. Alkaline-earth atoms in optical tweezers. Phys. Rev. X, 2018, 8(4): 041055
CrossRef
ADS
Google scholar
|
[27] |
M. A. Norcia, A. W. Young, A. M. Kaufman. Microscopic control and detection of ultracold strontium in optical-tweezer arrays. Phys. Rev. X, 2018, 8(4): 041054
CrossRef
ADS
Google scholar
|
[28] |
J. P. Covey, I. S. Madjarov, A. Cooper, M. Endres. 2000-times repeated imaging of strontium atoms in clock-magic tweezer arrays. Phys. Rev. Lett., 2019, 122(17): 173201
CrossRef
ADS
Google scholar
|
[29] |
J. T. Wilson, S. Saskin, Y. Meng, S. Ma, R. Dilip, A. P. Burgers, J. D. Thompson. Trapping alkaline earth Rydberg atoms optical tweezer arrays. Phys. Rev. Lett., 2022, 128(3): 033201
CrossRef
ADS
Google scholar
|
[30] |
A. J. Daley, M. M. Boyd, J. Ye, P. Zoller. Quantum computing with alkaline-earth-metal atoms. Phys. Rev. Lett., 2008, 101(17): 170504
CrossRef
ADS
Google scholar
|
[31] |
A. V. Gorshkov, A. M. Rey, A. J. Daley, M. M. Boyd, J. Ye, P. Zoller, M. D. Lukin. Alkaline-earth-metal atoms as few-qubit quantum registers. Phys. Rev. Lett., 2009, 102(11): 110503
CrossRef
ADS
Google scholar
|
[32] |
I. Reichenbach, I. H. Deutsch. Sideband cooling while preserving coherences in the nuclear spin state in group-II-like atoms. Phys. Rev. Lett., 2007, 99(12): 123001
CrossRef
ADS
Google scholar
|
[33] |
X. F. Shi. Coherence-preserving cooling of nuclear-spin qubits in a weak magnetic field. Phys. Rev. A, 2023, 107(2): 023102
CrossRef
ADS
Google scholar
|
[34] |
S. Omanakuttan, A. Mitra, M. J. Martin, I. H. Deutsch. Quantum optimal control of ten-level nuclear spin qudits in 87Sr. Phys. Rev. A, 2021, 104(6): L060401
CrossRef
ADS
Google scholar
|
[35] |
N. Chen, L. Li, W. Huie, M. Zhao, I. Vetter, C. H. Greene, J. P. Covey. Analyzing the Rydberg-based optical-metastable-ground architecture for 171Yb nuclear spins. Phys. Rev. A, 2022, 105(5): 052438
CrossRef
ADS
Google scholar
|
[36] |
M. M. Boyd, T. Zelevinsky, A. D. Ludlow, S. Blatt, T. Zanon-Willette, S. M. Foreman, J. Ye. Nuclear spin effects in optical lattice clocks. Phys. Rev. A, 2007, 76(2): 022510
CrossRef
ADS
Google scholar
|
[37] |
X. F. Shi. Rydberg quantum computation with nuclear spins in two-electron neutral atoms. Front. Phys., 2021, 16(5): 52501
CrossRef
ADS
Google scholar
|
[38] |
X. F. Shi. Fast, accurate, and realizable two-qubit entangling gates by quantum interference in detuned Rabi cycles of Rydberg atoms. Phys. Rev. Appl., 2019, 11(4): 044035
CrossRef
ADS
Google scholar
|
[39] |
K. Barnes, P. Battaglino, B. J. Bloom, K. Cassella, N. Coxe, N. Crisosto, J. P. King, S. S. Kondov, K. Kotru, S. C. Larsen, J. Lauigan, B. J. Lester, M. McDonald, E. Megidish, S. Narayanaswami, C. Nishiguchi, R. Notermans, L. S. Peng, A. Ryou, T. Y. Wu, M. Yarwood. Assembly and coherent control of a register of nuclear spin qubits. Nat. Commun., 2022, 13(1): 2779
CrossRef
ADS
Google scholar
|
[40] |
A. Jenkins, J. W. Lis, A. Senoo, W. F. McGrew, A. M. Kaufman. Ytterbium nuclear-spin qubits in an optical tweezer array. Phys. Rev. X, 2022, 12(2): 021027
CrossRef
ADS
Google scholar
|
[41] |
C. H. Bennett, S. J. Wiesner. Communication via one- and two-particle operators on Einstein−Podolsky−Rosen states. Phys. Rev. Lett., 1992, 69(20): 2881
CrossRef
ADS
Google scholar
|
[42] |
W. Dür, G. Vidal, J. I. Cirac. Three qubits can be entangled in two inequivalent ways. Phys. Rev. A, 2000, 62(6): 062314
CrossRef
ADS
Google scholar
|
[43] |
B. Fang, M. Menotti, M. Liscidini, J. E. Sipe, V. O. Lorenz. Three-photon discrete-energy-entangled W state in an optical fiber. Phys. Rev. Lett., 2019, 123(7): 070508
CrossRef
ADS
Google scholar
|
[44] |
D.M. GreenbergerM.HorneA.Zeilinger, Bell’s Theorem, Quantum Theory, and Conceptions of the Universe, edited by M. Kafatos, Kluwer, Dordrecht, 1989
|
[45] |
X. F. Shi. Hyperentanglement of divalent neutral atoms by Rydberg blockade. Phys. Rev. A, 2021, 104(4): 042422
CrossRef
ADS
Google scholar
|
[46] |
M. Saffman, T. G. Walker, K. Mølmer. Quantum information with Rydberg atoms. Rev. Mod. Phys., 2010, 82(3): 2313
CrossRef
ADS
Google scholar
|
[47] |
X. F. Shi. Quantum logic and entanglement by neutral Rydberg atoms: Methods and fidelity. Quantum Sci. Technol., 2022, 7(2): 023002
CrossRef
ADS
Google scholar
|
[48] |
A. P. Burgers, S. Ma, S. Saskin, J. Wilson, M. A. Alarcón, C. H. Greene, J. D. Thompson. Controlling Rydberg excitations using ion core transitions in alkaline earth atom tweezer arrays. PRX Quantum, 2022, 3(2): 020326
CrossRef
ADS
Google scholar
|
[49] |
R. Ding, J. D. Whalen, S. K. Kanungo, T. C. Killian, F. B. Dunning, S. Yoshida, J. Burgdörfer. Spectroscopy of 87Sr triplet Rydberg states. Phys. Rev. A, 2018, 98(4): 042505
CrossRef
ADS
Google scholar
|
[50] |
A. Lurio, M. Mandel, R. Novick. Second-order hyperfine and Zeeman corrections for an (sl) configuration. Phys. Rev., 1962, 126(5): 1758
CrossRef
ADS
Google scholar
|
[51] |
X. F. Shi. Rydberg quantum gates free from blockade error. Phys. Rev. Appl., 2017, 7(6): 064017
CrossRef
ADS
Google scholar
|
[52] |
X. F. Shi. Accurate quantum logic gates by spin echo in Rydberg atoms. Phys. Rev. Appl., 2018, 10(3): 034006
CrossRef
ADS
Google scholar
|
[53] |
C.P. Williams, Explorations in Quantum Computing, 2nd Ed., edited by D. Gries and F. B. Schneider, Texts in Computer Science, Springer-Verlag, London, 2011
|
[54] |
M. Saffman, T. G. Walker. Analysis of a quantum logic device based on dipole−dipole interactions of optically trapped Rydberg atoms. Phys. Rev. A, 2005, 72(2): 022347
CrossRef
ADS
Google scholar
|
[55] |
L. H. Pedersen, N. M. Møller, K. Mølmer. Fidelity of quantum operations. Phys. Lett. A, 2007, 367(1−2): 47
CrossRef
ADS
Google scholar
|
[56] |
X. F. Shi. Deutsch, Toffoli, and CNOT gates via rydberg blockade of neutral atoms. Phys. Rev. Appl., 2018, 9: 051001(R)
CrossRef
ADS
Google scholar
|
[57] |
X. F. Shi. Transition slow-down by Rydberg interaction of neutral atoms and a fast controlled-NOT quantum gate. Phys. Rev. Appl., 2020, 14(5): 054058
CrossRef
ADS
Google scholar
|
[58] |
J. L. Wu, Y. Wang, J. X. Han, S. L. Su, Y. Xia, Y. Jiang, J. Song. Unselective ground-state blockade of Rydberg atoms for implementing quantum gates. Front. Phys., 2022, 17(2): 22501
CrossRef
ADS
Google scholar
|
[59] |
S. Liu, J. H. Shen, R. H. Zheng, Y. H. Kang, Z. C. Shi, J. Song, Y. Xia. Optimized nonadiabatic holonomic quantum computation based on Förster resonance in Rydberg atoms. Front. Phys., 2022, 17(2): 21502
CrossRef
ADS
Google scholar
|
[60] |
V. M. Stojanović, J. K. Nauth. Interconversion of W and Greenberger−Horne−Zeilinger states for Ising-coupled qubits with transverse global control. Phys. Rev. A, 2022, 106(5): 052613
CrossRef
ADS
Google scholar
|
[61] |
X. Wu, X. Liang, Y. Tian, F. Yang, C. Chen, Y. C. Liu, M. K. Tey, L. You. A concise review of Rydberg atom based quantum computation and quantum simulation. Chin. Phys. B, 2021, 30(2): 020305
CrossRef
ADS
Google scholar
|
[62] |
D. R. Chong, M. Kim, J. Ahn, H. Jeong. Machine learning identification of symmetrized base states of Rydberg atoms. Front. Phys., 2022, 17(1): 12504
CrossRef
ADS
Google scholar
|
[63] |
H. Zhang, J. Wu, M. Artoni, G. C. La Rocca. Single-photon-level light storage with distributed Rydberg excitations in cold atoms. Front. Phys., 2022, 17(2): 22502
CrossRef
ADS
Google scholar
|
[64] |
J. P. Covey, A. Sipahigil, S. Szoke, N. Sinclair, M. Endres, O. Painter. Telecom-band quantum optics with ytterbium atoms and silicon nanophotonics. Phys. Rev. Appl., 2019, 11(3): 034044
CrossRef
ADS
Google scholar
|
[65] |
A. D. Boozer, A. Boca, R. Miller, T. E. Northup, H. J. Kimble. Reversible state transfer between light and a single trapped atom. Phys. Rev. Lett., 2007, 98(19): 193601
CrossRef
ADS
Google scholar
|
[66] |
Y. Wu, S. Kolkowitz, S. Puri, J. D. Thompson. Erasure conversion for fault-tolerant quantum computing in alkaline earth Rydberg atom arrays. Nat. Commun., 2022, 13(1): 4657
CrossRef
ADS
Google scholar
|
[67] |
A. Mitra, M. J. Martin, G. W. Biedermann, A. M. Marino, P. M. Poggi, I. H. Deutsch. Robust Mølmer−Sørensen gate for neutral atoms using rapid adiabatic Rydberg dressing. Phys. Rev. A, 2020, 101: 030301(R)
CrossRef
ADS
Google scholar
|
[68] |
K. L. Pham, T. F. Gallagher, P. Pillet, S. Lepoutre, P. Cheinet. A coherent light shift on alkaline-earth Rydberg atoms from isolated core excitation without auto-ionization. PRX Quantum, 2022, 3(2): 020327
CrossRef
ADS
Google scholar
|
/
〈 | 〉 |