Abstract

The multipartite GHZ states are useful resources for quantum information processing. Here we put forward a scalable way to adiabatically prepare the multipartite GHZ states in a chain of Rydberg atoms. Building on the ground-state blockade effect of Rydberg atoms and the stimulated Raman adiabatic passage (STIRAP), we suppress the adverse effect of the atomic spontaneous emission, and obtain a high fidelity of the multipartite GHZ states without requirements on the operational time. After investigating the feasibility of the proposal, we show a 3-qubit GHZ state can be generated in a wide range of relevant parameters and a fidelity above $98\%$ is achievable with the current experimental technologies.

© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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2019 (2)

P. Contreras-Tejada, C. Palazuelos, and J. I. de Vicente, “Resource theory of entanglement with a unique multipartite maximally entangled state,” Phys. Rev. Lett. 122(12), 120503 (2019).
[Crossref]

G. K. Naik, R. Singh, and S. K. Mishra, “Controlled generation of genuine multipartite entanglement in floquet ising spin models,” Phys. Rev. A 99(3), 032321 (2019).
[Crossref]

2018 (7)

D. Sauerwein, N. R. Wallach, G. Gour, and B. Kraus, “Transformations among pure multipartite entangled states via local operations are almost never possible,” Phys. Rev. X 8(3), 031020 (2018).
[Crossref]

C.-P. Yang and Z.-F. Zheng, “Deterministic generation of greenberger-horne-zeilinger entangled states of cat-state qubits in circuit qed,” Opt. Lett. 43(20), 5126–5129 (2018).
[Crossref]

X.-F. Shi, “Deutsch, toffoli, and cnot gates via rydberg blockade of neutral atoms,” Phys. Rev. Appl. 9(5), 051001 (2018).
[Crossref]

S. L. Su, H. Z. Shen, E. Liang, and S. Zhang, “One-step construction of the multiple-qubit rydberg controlled-phase gate,” Phys. Rev. A 98(3), 032306 (2018).
[Crossref]

I. I. Beterov, G. N. Hamzina, E. A. Yakshina, D. B. Tretyakov, V. M. Entin, and I. I. Ryabtsev, “Adiabatic passage of radio-frequency-assisted förster resonances in rydberg atoms for two-qubit gates and the generation of bell states,” Phys. Rev. A 97(3), 032701 (2018).
[Crossref]

D.-X. Li, X.-Q. Shao, J.-H. Wu, and X. X. Yi, “Dissipation-induced w state in a rydberg-atom-cavity system,” Opt. Lett. 43(8), 1639–1642 (2018).
[Crossref]

D. W. Schönleber, C. D. B. Bentley, and A. Eisfeld, “Engineering thermal reservoirs for ultracold dipole-dipole-interacting rydberg atoms,” New J. Phys. 20(1), 013011 (2018).
[Crossref]

2017 (12)

X. Q. Shao, D. X. Li, Y. Q. Ji, J. H. Wu, and X. X. Yi, “Ground-state blockade of rydberg atoms and application in entanglement generation,” Phys. Rev. A 96(1), 012328 (2017).
[Crossref]

M. Ostmann, J. Minář, M. Marcuzzi, E. Levi, and I. Lesanovsky, “Non-adiabatic quantum state preparation and quantum state transport in chains of rydberg atoms,” New J. Phys. 19(12), 123015 (2017).
[Crossref]

S.-L. Su, Y. Tian, H. Z. Shen, H. Zang, E. Liang, and S. Zhang, “Applications of the modified rydberg antiblockade regime with simultaneous driving,” Phys. Rev. A 96(4), 042335 (2017).
[Crossref]

J. Song, C. Li, Z.-J. Zhang, Y.-Y. Jiang, and Y. Xia, “Implementing stabilizer codes in noisy environments,” Phys. Rev. A 96(3), 032336 (2017).
[Crossref]

X. Q. Shao, J. H. Wu, X. X. Yi, and G.-L. Long, “Dissipative preparation of steady greenberger-horne-zeilinger states for rydberg atoms with quantum zeno dynamics,” Phys. Rev. A 96(6), 062315 (2017).
[Crossref]

X.-F. Shi, “Rydberg quantum gates free from blockade error,” Phys. Rev. Appl. 7(6), 064017 (2017).
[Crossref]

S.-L. Su, Y. Gao, E. Liang, and S. Zhang, “Fast rydberg antiblockade regime and its applications in quantum logic gates,” Phys. Rev. A 95(2), 022319 (2017).
[Crossref]

C. Song, K. Xu, W. Liu, C.-p. Yang, S.-B. Zheng, H. Deng, Q. Xie, K. Huang, Q. Guo, L. Zhang, P. Zhang, D. Xu, D. Zheng, X. Zhu, H. Wang, Y.-A. Chen, C.-Y. Lu, S. Han, and J.-W. Pan, “10-qubit entanglement and parallel logic operations with a superconducting circuit,” Phys. Rev. Lett. 119(18), 180511 (2017).
[Crossref]

L. Pezzè, M. Gabbrielli, L. Lepori, and A. Smerzi, “Multipartite entanglement in topological quantum phases,” Phys. Rev. Lett. 119(25), 250401 (2017).
[Crossref]

Q.-P. Su, H.-H. Zhu, L. Yu, Y. Zhang, S.-J. Xiong, J.-M. Liu, and C.-P. Yang, “Generating double noon states of photons in circuit qed,” Phys. Rev. A 95(2), 022339 (2017).
[Crossref]

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(1), 015006 (2017).
[Crossref]

X. Q. Shao, J. H. Wu, and X. X. Yi, “Dissipative stabilization of quantum-feedback-based multipartite entanglement with rydberg atoms,” Phys. Rev. A 95(2), 022317 (2017).
[Crossref]

2016 (5)

F. Reiter, D. Reeb, and A. S. Sørensen, “Scalable dissipative preparation of many-body entanglement,” Phys. Rev. Lett. 117(4), 040501 (2016).
[Crossref]

C.-P. Yang, Q.-P. Su, S.-B. Zheng, and F. Nori, “Entangling superconducting qubits in a multi-cavity system,” New J. Phys. 18(1), 013025 (2016).
[Crossref]

S.-L. Su, E. Liang, S. Zhang, J.-J. Wen, L.-L. Sun, Z. Jin, and A.-D. Zhu, “One-step implementation of the rydberg-rydberg-interaction gate,” Phys. Rev. A 93(1), 012306 (2016).
[Crossref]

D. Barredo, S. de Léséleuc, V. Lienhard, T. Lahaye, and A. Browaeys, “An atom-by-atom assembler of defect-free arbitrary two-dimensional atomic arrays,” Science 354(6315), 1021–1023 (2016).
[Crossref]

M. Endres, H. Bernien, A. Keesling, H. Levine, E. R. Anschuetz, A. Krajenbrink, C. Senko, V. Vuletic, M. Greiner, and M. D. Lukin, “Atom-by-atom assembly of defect-free one-dimensional cold atom arrays,” Science 354(6315), 1024–1027 (2016).
[Crossref]

2015 (2)

S.-L. Su, Q. Guo, H.-F. Wang, and S. Zhang, “Simplified scheme for entanglement preparation with rydberg pumping via dissipation,” Phys. Rev. A 92(2), 022328 (2015).
[Crossref]

D. W. Schönleber, A. Eisfeld, M. Genkin, S. Whitlock, and S. Wüster, “Quantum simulation of energy transport with embedded rydberg aggregates,” Phys. Rev. Lett. 114(12), 123005 (2015).
[Crossref]

2014 (7)

A. Grankin, E. Brion, E. Bimbard, R. Boddeda, I. Usmani, A. Ourjoumtsev, and P. Grangier, “Quantum statistics of light transmitted through an intracavity rydberg medium,” New J. Phys. 16(4), 043020 (2014).
[Crossref]

F. Nogrette, H. Labuhn, S. Ravets, D. Barredo, L. Béguin, A. Vernier, T. Lahaye, and A. Browaeys, “Single-atom trapping in holographic 2d arrays of microtraps with arbitrary geometries,” Phys. Rev. X 4(2), 021034 (2014).
[Crossref]

D. Barredo, S. Ravets, H. Labuhn, L. Béguin, A. Vernier, F. Nogrette, T. Lahaye, and A. Browaeys, “Demonstration of a strong rydberg blockade in three-atom systems with anisotropic interactions,” Phys. Rev. Lett. 112(18), 183002 (2014).
[Crossref]

D. Petrosyan and K. Mølmer, “Binding potentials and interaction gates between microwave-dressed rydberg atoms,” Phys. Rev. Lett. 113(12), 123003 (2014).
[Crossref]

D. D. B. Rao and K. Mølmer, “Robust rydberg-interaction gates with adiabatic passage,” Phys. Rev. A 89(3), 030301 (2014).
[Crossref]

M. Hofmann, A. Osterloh, and O. Gühne, “Scaling of genuine multiparticle entanglement close to a quantum phase transition,” Phys. Rev. B 89(13), 134101 (2014).
[Crossref]

J. Stasińska, B. Rogers, M. Paternostro, G. De Chiara, and A. Sanpera, “Long-range multipartite entanglement close to a first-order quantum phase transition,” Phys. Rev. A 89(3), 032330 (2014).
[Crossref]

2013 (4)

D. D. B. Rao and K. Mølmer, “Dark entangled steady states of interacting rydberg atoms,” Phys. Rev. Lett. 111(3), 033606 (2013).
[Crossref]

A. W. Carr and M. Saffman, “Preparation of entangled and antiferromagnetic states by dissipative rydberg pumping,” Phys. Rev. Lett. 111(3), 033607 (2013).
[Crossref]

S. Möbius, M. Genkin, A. Eisfeld, S. Wüster, and J. M. Rost, “Entangling distant atom clouds through rydberg dressing,” Phys. Rev. A 87(5), 051602 (2013).
[Crossref]

X.-F. Zhang, Q. Sun, Y.-C. Wen, W.-M. Liu, S. Eggert, and A.-C. Ji, “Rydberg polaritons in a cavity: A superradiant solid,” Phys. Rev. Lett. 110(9), 090402 (2013).
[Crossref]

2011 (2)

A.-X. Chen, “Implementation of deutsch-jozsa algorithm and determination of value of function via rydberg blockade,” Opt. Express 19(3), 2037–2045 (2011).
[Crossref]

C.-P. Yang, “Preparation of $n$n-qubit greenberger-horne-zeilinger entangled states in cavity qed: An approach with tolerance to nonidentical qubit-cavity coupling constants,” Phys. Rev. A 83(6), 062302 (2011).
[Crossref]

2010 (7)

M. Saffman, T. G. Walker, and K. Mølmer, “Quantum information with rydberg atoms,” Rev. Mod. Phys. 82(3), 2313–2363 (2010).
[Crossref]

H. Weimer, M. Muller, I. Lesanovsky, P. Zoller, and H. P. Buchler, “A rydberg quantum simulator,” Nat. Phys. 6(5), 382–388 (2010).
[Crossref]

Y. Han, B. He, K. Heshami, C.-Z. Li, and C. Simon, “Quantum repeaters based on rydberg-blockade-coupled atomic ensembles,” Phys. Rev. A 81(5), 052311 (2010).
[Crossref]

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(3), 030306 (2010).
[Crossref]

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(1), 010502 (2010).
[Crossref]

T. Amthor, C. Giese, C. S. Hofmann, and M. Weidemüller, “Evidence of antiblockade in an ultracold rydberg gas,” Phys. Rev. Lett. 104(1), 013001 (2010).
[Crossref]

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(1), 010503 (2010).
[Crossref]

2009 (5)

M. Saffman and K. Mølmer, “Efficient multiparticle entanglement via asymmetric rydberg blockade,” Phys. Rev. Lett. 102(24), 240502 (2009).
[Crossref]

A. Gaëtan, Y. Miroshnychenko, T. Wilk, A. Chotia, M. Viteau, D. Comparat, P. Pillet, A. Browaeys, and P. Grangier, “Observation of collective excitation of two individual atoms in the rydberg blockade regime,” Nat. Phys. 5(2), 115–118 (2009).
[Crossref]

O. Gühne and G. Tóth, “Entanglement detection,” Phys. Rep. 474(1-6), 1–75 (2009).
[Crossref]

M. Müller, I. Lesanovsky, H. Weimer, H. P. Büchler, and P. Zoller, “Mesoscopic rydberg gate based on electromagnetically induced transparency,” Phys. Rev. Lett. 102(17), 170502 (2009).
[Crossref]

R. Horodecki, P. Horodecki, M. Horodecki, and K. Horodecki, “Quantum entanglement,” Rev. Mod. Phys. 81(2), 865–942 (2009).
[Crossref]

2008 (2)

T. G. Walker and M. Saffman, “Consequences of zeeman degeneracy for the van der waals blockade between rydberg atoms,” Phys. Rev. A 77(3), 032723 (2008).
[Crossref]

D. Møller, L. B. Madsen, and K. Mølmer, “Quantum gates and multiparticle entanglement by rydberg excitation blockade and adiabatic passage,” Phys. Rev. Lett. 100(17), 170504 (2008).
[Crossref]

2007 (2)

C. Ates, T. Pohl, T. Pattard, and J. M. Rost, “Antiblockade in rydberg excitation of an ultracold lattice gas,” Phys. Rev. Lett. 98(2), 023002 (2007).
[Crossref]

F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. Köhl, and T. Esslinger, “Cavity qed with a bose-einstein condensate,” Nature 450(7167), 268–271 (2007).
[Crossref]

2006 (1)

M. Mohseni and D. A. Lidar, “Direct characterization of quantum dynamics,” Phys. Rev. Lett. 97(17), 170501 (2006).
[Crossref]

2005 (3)

O. Gühne, G. Tóth, and H. J. Briegel, “Multipartite entanglement in spin chains,” New J. Phys. 7, 229 (2005).
[Crossref]

R. T. Horn, S. A. Babichev, K.-P. Marzlin, A. I. Lvovsky, and B. C. Sanders, “Single-qubit optical quantum fingerprinting,” Phys. Rev. Lett. 95(15), 150502 (2005).
[Crossref]

S.-B. Zheng, “Nongeometric conditional phase shift via adiabatic evolution of dark eigenstates: A new approach to quantum computation,” Phys. Rev. Lett. 95(8), 080502 (2005).
[Crossref]

2004 (2)

V. Giovannetti, S. Lloyd, and L. Maccone, “Quantum-enhanced measurements: Beating the standard quantum limit,” Science 306(5700), 1330–1336 (2004).
[Crossref]

C.-P. Yang and S. Han, “Preparation of greenberger-horne-zeilinger entangled states with multiple superconducting quantum-interference device qubits or atoms in cavity qed,” Phys. Rev. A 70(6), 062323 (2004).
[Crossref]

2002 (1)

Z. Kis and F. Renzoni, “Qubit rotation by stimulated raman adiabatic passage,” Phys. Rev. A 65(3), 032318 (2002).
[Crossref]

2001 (1)

H. Buhrman, R. Cleve, J. Watrous, and R. de Wolf, “Quantum fingerprinting,” Phys. Rev. Lett. 87(16), 167902 (2001).
[Crossref]

2000 (1)

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(10), 2208–2211 (2000).
[Crossref]

1998 (2)

K. Bergmann, H. Theuer, and B. W. Shore, “Coherent population transfer among quantum states of atoms and molecules,” Rev. Mod. Phys. 70(3), 1003–1025 (1998).
[Crossref]

D. Boschi, S. Branca, F. De Martini, L. Hardy, and S. Popescu, “Experimental realization of teleporting an unknown pure quantum state via dual classical and einstein-podolsky-rosen channels,” Phys. Rev. Lett. 80(6), 1121–1125 (1998).
[Crossref]

1997 (1)

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390(6660), 575–579 (1997).
[Crossref]

1996 (1)

K. Mattle, H. Weinfurter, P. G. Kwiat, and A. Zeilinger, “Dense coding in experimental quantum communication,” Phys. Rev. Lett. 76(25), 4656–4659 (1996).
[Crossref]

1993 (1)

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and einstein-podolsky-rosen channels,” Phys. Rev. Lett. 70(13), 1895–1899 (1993).
[Crossref]

1992 (1)

C. H. Bennett and S. J. Wiesner, “Communication via one- and two-particle operators on einstein-podolsky-rosen states,” Phys. Rev. Lett. 69(20), 2881–2884 (1992).
[Crossref]

1990 (1)

U. Gaubatz, P. Rudecki, S. Schiemann, and K. Bergmann, “Population transfer between molecular vibrational levels by stimulated raman scattering with partially overlapping laser fields. a new concept and experimental results,” J. Chem. Phys. 92(9), 5363–5376 (1990).
[Crossref]

1989 (1)

J. R. Kuklinski, U. Gaubatz, F. T. Hioe, and K. Bergmann, “Adiabatic population transfer in a three-level system driven by delayed laser pulses,” Phys. Rev. A 40(11), 6741–6744 (1989).
[Crossref]

1935 (1)

A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev. 47(10), 777–780 (1935).
[Crossref]

Amthor, T.

T. Amthor, C. Giese, C. S. Hofmann, and M. Weidemüller, “Evidence of antiblockade in an ultracold rydberg gas,” Phys. Rev. Lett. 104(1), 013001 (2010).
[Crossref]

Anschuetz, E. R.

M. Endres, H. Bernien, A. Keesling, H. Levine, E. R. Anschuetz, A. Krajenbrink, C. Senko, V. Vuletic, M. Greiner, and M. D. Lukin, “Atom-by-atom assembly of defect-free one-dimensional cold atom arrays,” Science 354(6315), 1024–1027 (2016).
[Crossref]

Ates, C.

C. Ates, T. Pohl, T. Pattard, and J. M. Rost, “Antiblockade in rydberg excitation of an ultracold lattice gas,” Phys. Rev. Lett. 98(2), 023002 (2007).
[Crossref]

Babichev, S. A.

R. T. Horn, S. A. Babichev, K.-P. Marzlin, A. I. Lvovsky, and B. C. Sanders, “Single-qubit optical quantum fingerprinting,” Phys. Rev. Lett. 95(15), 150502 (2005).
[Crossref]

Barredo, D.

D. Barredo, S. de Léséleuc, V. Lienhard, T. Lahaye, and A. Browaeys, “An atom-by-atom assembler of defect-free arbitrary two-dimensional atomic arrays,” Science 354(6315), 1021–1023 (2016).
[Crossref]

F. Nogrette, H. Labuhn, S. Ravets, D. Barredo, L. Béguin, A. Vernier, T. Lahaye, and A. Browaeys, “Single-atom trapping in holographic 2d arrays of microtraps with arbitrary geometries,” Phys. Rev. X 4(2), 021034 (2014).
[Crossref]

D. Barredo, S. Ravets, H. Labuhn, L. Béguin, A. Vernier, F. Nogrette, T. Lahaye, and A. Browaeys, “Demonstration of a strong rydberg blockade in three-atom systems with anisotropic interactions,” Phys. Rev. Lett. 112(18), 183002 (2014).
[Crossref]

Béguin, L.

D. Barredo, S. Ravets, H. Labuhn, L. Béguin, A. Vernier, F. Nogrette, T. Lahaye, and A. Browaeys, “Demonstration of a strong rydberg blockade in three-atom systems with anisotropic interactions,” Phys. Rev. Lett. 112(18), 183002 (2014).
[Crossref]

F. Nogrette, H. Labuhn, S. Ravets, D. Barredo, L. Béguin, A. Vernier, T. Lahaye, and A. Browaeys, “Single-atom trapping in holographic 2d arrays of microtraps with arbitrary geometries,” Phys. Rev. X 4(2), 021034 (2014).
[Crossref]

Bell, J. S.

J. S. Bell, Speakable and Unspeakable in Quantum Mechanics (Cambridge University, 1988).

Bennett, C. H.

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and einstein-podolsky-rosen channels,” Phys. Rev. Lett. 70(13), 1895–1899 (1993).
[Crossref]

C. H. Bennett and S. J. Wiesner, “Communication via one- and two-particle operators on einstein-podolsky-rosen states,” Phys. Rev. Lett. 69(20), 2881–2884 (1992).
[Crossref]

Bentley, C. D. B.

D. W. Schönleber, C. D. B. Bentley, and A. Eisfeld, “Engineering thermal reservoirs for ultracold dipole-dipole-interacting rydberg atoms,” New J. Phys. 20(1), 013011 (2018).
[Crossref]

Bergmann, K.

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(1), 015006 (2017).
[Crossref]

K. Bergmann, H. Theuer, and B. W. Shore, “Coherent population transfer among quantum states of atoms and molecules,” Rev. Mod. Phys. 70(3), 1003–1025 (1998).
[Crossref]

U. Gaubatz, P. Rudecki, S. Schiemann, and K. Bergmann, “Population transfer between molecular vibrational levels by stimulated raman scattering with partially overlapping laser fields. a new concept and experimental results,” J. Chem. Phys. 92(9), 5363–5376 (1990).
[Crossref]

J. R. Kuklinski, U. Gaubatz, F. T. Hioe, and K. Bergmann, “Adiabatic population transfer in a three-level system driven by delayed laser pulses,” Phys. Rev. A 40(11), 6741–6744 (1989).
[Crossref]

Bernien, H.

M. Endres, H. Bernien, A. Keesling, H. Levine, E. R. Anschuetz, A. Krajenbrink, C. Senko, V. Vuletic, M. Greiner, and M. D. Lukin, “Atom-by-atom assembly of defect-free one-dimensional cold atom arrays,” Science 354(6315), 1024–1027 (2016).
[Crossref]

Beterov, I. I.

I. I. Beterov, G. N. Hamzina, E. A. Yakshina, D. B. Tretyakov, V. M. Entin, and I. I. Ryabtsev, “Adiabatic passage of radio-frequency-assisted förster resonances in rydberg atoms for two-qubit gates and the generation of bell states,” Phys. Rev. A 97(3), 032701 (2018).
[Crossref]

Bimbard, E.

A. Grankin, E. Brion, E. Bimbard, R. Boddeda, I. Usmani, A. Ourjoumtsev, and P. Grangier, “Quantum statistics of light transmitted through an intracavity rydberg medium,” New J. Phys. 16(4), 043020 (2014).
[Crossref]

Boddeda, R.

A. Grankin, E. Brion, E. Bimbard, R. Boddeda, I. Usmani, A. Ourjoumtsev, and P. Grangier, “Quantum statistics of light transmitted through an intracavity rydberg medium,” New J. Phys. 16(4), 043020 (2014).
[Crossref]

Boschi, D.

D. Boschi, S. Branca, F. De Martini, L. Hardy, and S. Popescu, “Experimental realization of teleporting an unknown pure quantum state via dual classical and einstein-podolsky-rosen channels,” Phys. Rev. Lett. 80(6), 1121–1125 (1998).
[Crossref]

Bourdel, T.

F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. Köhl, and T. Esslinger, “Cavity qed with a bose-einstein condensate,” Nature 450(7167), 268–271 (2007).
[Crossref]

Bouwmeester, D.

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390(6660), 575–579 (1997).
[Crossref]

Branca, S.

D. Boschi, S. Branca, F. De Martini, L. Hardy, and S. Popescu, “Experimental realization of teleporting an unknown pure quantum state via dual classical and einstein-podolsky-rosen channels,” Phys. Rev. Lett. 80(6), 1121–1125 (1998).
[Crossref]

Brassard, G.

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and einstein-podolsky-rosen channels,” Phys. Rev. Lett. 70(13), 1895–1899 (1993).
[Crossref]

Brennecke, F.

F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. Köhl, and T. Esslinger, “Cavity qed with a bose-einstein condensate,” Nature 450(7167), 268–271 (2007).
[Crossref]

Briegel, H. J.

O. Gühne, G. Tóth, and H. J. Briegel, “Multipartite entanglement in spin chains,” New J. Phys. 7, 229 (2005).
[Crossref]

Brion, E.

A. Grankin, E. Brion, E. Bimbard, R. Boddeda, I. Usmani, A. Ourjoumtsev, and P. Grangier, “Quantum statistics of light transmitted through an intracavity rydberg medium,” New J. Phys. 16(4), 043020 (2014).
[Crossref]

Browaeys, A.

D. Barredo, S. de Léséleuc, V. Lienhard, T. Lahaye, and A. Browaeys, “An atom-by-atom assembler of defect-free arbitrary two-dimensional atomic arrays,” Science 354(6315), 1021–1023 (2016).
[Crossref]

F. Nogrette, H. Labuhn, S. Ravets, D. Barredo, L. Béguin, A. Vernier, T. Lahaye, and A. Browaeys, “Single-atom trapping in holographic 2d arrays of microtraps with arbitrary geometries,” Phys. Rev. X 4(2), 021034 (2014).
[Crossref]

D. Barredo, S. Ravets, H. Labuhn, L. Béguin, A. Vernier, F. Nogrette, T. Lahaye, and A. Browaeys, “Demonstration of a strong rydberg blockade in three-atom systems with anisotropic interactions,” Phys. Rev. Lett. 112(18), 183002 (2014).
[Crossref]

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(1), 010502 (2010).
[Crossref]

A. Gaëtan, Y. Miroshnychenko, T. Wilk, A. Chotia, M. Viteau, D. Comparat, P. Pillet, A. Browaeys, and P. Grangier, “Observation of collective excitation of two individual atoms in the rydberg blockade regime,” Nat. Phys. 5(2), 115–118 (2009).
[Crossref]

Buchler, H. P.

H. Weimer, M. Muller, I. Lesanovsky, P. Zoller, and H. P. Buchler, “A rydberg quantum simulator,” Nat. Phys. 6(5), 382–388 (2010).
[Crossref]

Büchler, H. P.

M. Müller, I. Lesanovsky, H. Weimer, H. P. Büchler, and P. Zoller, “Mesoscopic rydberg gate based on electromagnetically induced transparency,” Phys. Rev. Lett. 102(17), 170502 (2009).
[Crossref]

Buhrman, H.

H. Buhrman, R. Cleve, J. Watrous, and R. de Wolf, “Quantum fingerprinting,” Phys. Rev. Lett. 87(16), 167902 (2001).
[Crossref]

Carr, A. W.

A. W. Carr and M. Saffman, “Preparation of entangled and antiferromagnetic states by dissipative rydberg pumping,” Phys. Rev. Lett. 111(3), 033607 (2013).
[Crossref]

Chen, A.-X.

Chen, Y.-A.

C. Song, K. Xu, W. Liu, C.-p. Yang, S.-B. Zheng, H. Deng, Q. Xie, K. Huang, Q. Guo, L. Zhang, P. Zhang, D. Xu, D. Zheng, X. Zhu, H. Wang, Y.-A. Chen, C.-Y. Lu, S. Han, and J.-W. Pan, “10-qubit entanglement and parallel logic operations with a superconducting circuit,” Phys. Rev. Lett. 119(18), 180511 (2017).
[Crossref]

Chotia, A.

A. Gaëtan, Y. Miroshnychenko, T. Wilk, A. Chotia, M. Viteau, D. Comparat, P. Pillet, A. Browaeys, and P. Grangier, “Observation of collective excitation of two individual atoms in the rydberg blockade regime,” Nat. Phys. 5(2), 115–118 (2009).
[Crossref]

Chuang, I. L.

M. A. Nielsen and I. L. Chuang, Quantum Computation and Quantum Information (Cambridge University, 2000).

Cirac, J. I.

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(10), 2208–2211 (2000).
[Crossref]

Cleve, R.

H. Buhrman, R. Cleve, J. Watrous, and R. de Wolf, “Quantum fingerprinting,” Phys. Rev. Lett. 87(16), 167902 (2001).
[Crossref]

Comparat, D.

A. Gaëtan, Y. Miroshnychenko, T. Wilk, A. Chotia, M. Viteau, D. Comparat, P. Pillet, A. Browaeys, and P. Grangier, “Observation of collective excitation of two individual atoms in the rydberg blockade regime,” Nat. Phys. 5(2), 115–118 (2009).
[Crossref]

Contreras-Tejada, P.

P. Contreras-Tejada, C. Palazuelos, and J. I. de Vicente, “Resource theory of entanglement with a unique multipartite maximally entangled state,” Phys. Rev. Lett. 122(12), 120503 (2019).
[Crossref]

Côté, R.

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(10), 2208–2211 (2000).
[Crossref]

Crépeau, C.

C. H. Bennett, G. Brassard, C. Crépeau, R. Jozsa, A. Peres, and W. K. Wootters, “Teleporting an unknown quantum state via dual classical and einstein-podolsky-rosen channels,” Phys. Rev. Lett. 70(13), 1895–1899 (1993).
[Crossref]

De Chiara, G.

J. Stasińska, B. Rogers, M. Paternostro, G. De Chiara, and A. Sanpera, “Long-range multipartite entanglement close to a first-order quantum phase transition,” Phys. Rev. A 89(3), 032330 (2014).
[Crossref]

de Léséleuc, S.

D. Barredo, S. de Léséleuc, V. Lienhard, T. Lahaye, and A. Browaeys, “An atom-by-atom assembler of defect-free arbitrary two-dimensional atomic arrays,” Science 354(6315), 1021–1023 (2016).
[Crossref]

De Martini, F.

D. Boschi, S. Branca, F. De Martini, L. Hardy, and S. Popescu, “Experimental realization of teleporting an unknown pure quantum state via dual classical and einstein-podolsky-rosen channels,” Phys. Rev. Lett. 80(6), 1121–1125 (1998).
[Crossref]

de Vicente, J. I.

P. Contreras-Tejada, C. Palazuelos, and J. I. de Vicente, “Resource theory of entanglement with a unique multipartite maximally entangled state,” Phys. Rev. Lett. 122(12), 120503 (2019).
[Crossref]

de Wolf, R.

H. Buhrman, R. Cleve, J. Watrous, and R. de Wolf, “Quantum fingerprinting,” Phys. Rev. Lett. 87(16), 167902 (2001).
[Crossref]

Deng, H.

C. Song, K. Xu, W. Liu, C.-p. Yang, S.-B. Zheng, H. Deng, Q. Xie, K. Huang, Q. Guo, L. Zhang, P. Zhang, D. Xu, D. Zheng, X. Zhu, H. Wang, Y.-A. Chen, C.-Y. Lu, S. Han, and J.-W. Pan, “10-qubit entanglement and parallel logic operations with a superconducting circuit,” Phys. Rev. Lett. 119(18), 180511 (2017).
[Crossref]

Donner, T.

F. Brennecke, T. Donner, S. Ritter, T. Bourdel, M. Köhl, and T. Esslinger, “Cavity qed with a bose-einstein condensate,” Nature 450(7167), 268–271 (2007).
[Crossref]

Eggert, S.

X.-F. Zhang, Q. Sun, Y.-C. Wen, W.-M. Liu, S. Eggert, and A.-C. Ji, “Rydberg polaritons in a cavity: A superradiant solid,” Phys. Rev. Lett. 110(9), 090402 (2013).
[Crossref]

Eibl, M.

D. Bouwmeester, J. W. Pan, K. Mattle, M. Eibl, H. Weinfurter, and A. Zeilinger, “Experimental quantum teleportation,” Nature 390(6660), 575–579 (1997).
[Crossref]

Einstein, A.

A. Einstein, B. Podolsky, and N. Rosen, “Can quantum-mechanical description of physical reality be considered complete?” Phys. Rev. 47(10), 777–780 (1935).
[Crossref]

Eisfeld, A.

D. W. Schönleber, C. D. B. Bentley, and A. Eisfeld, “Engineering thermal reservoirs for ultracold dipole-dipole-interacting rydberg atoms,” New J. Phys. 20(1), 013011 (2018).
[Crossref]

D. W. Schönleber, A. Eisfeld, M. Genkin, S. Whitlock, and S. Wüster, “Quantum simulation of energy transport with embedded rydberg aggregates,” Phys. Rev. Lett. 114(12), 123005 (2015).
[Crossref]

S. Möbius, M. Genkin, A. Eisfeld, S. Wüster, and J. M. Rost, “Entangling distant atom clouds through rydberg dressing,” Phys. Rev. A 87(5), 051602 (2013).
[Crossref]

Endres, M.

M. Endres, H. Bernien, A. Keesling, H. Levine, E. R. Anschuetz, A. Krajenbrink, C. Senko, V. Vuletic, M. Greiner, and M. D. Lukin, “Atom-by-atom assembly of defect-free one-dimensional cold atom arrays,” Science 354(6315), 1024–1027 (2016).
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Figures (5)

Fig. 1.
Fig. 1. The total scheme preparing the $N$-qubit GHZ state composes of $N-1$ steps, which can be divided into two groups: Step 1 and Step $n~(n=2,3,\ldots ,N-1)$. For the Step 1, only the first two atoms will be addressed individually by three lasers, respectively. As for the Step $n$, we only coupled the $n$-th atom to one laser and the $(n+1)$-th atom to three lasers, respectively.
Fig. 2.
Fig. 2. (a) The shapes of pulses to prepare the 3-qubit GHZ state. For Step 1 ($\Omega _c t\in [0,6000]$), we set $t_c=6000/\Omega _c$. For Step 2 ($\Omega _c t\in (6000,14000]$), we set $t_c=8000/\Omega _c$. (b) The shapes of pulses to prepare the 4-qubit GHZ state. For Step 1 ($\Omega _c t\in [0,6000]$), we set $t_c=6000/\Omega _c$. For Steps 2 and 3 ($\Omega _c t\in (6000,14000]$ and $(14000,22000]$), we set $t_c=8000/\Omega _c$. (c) and (d) are the fidelity of the $3$- and $4$-qubit states governed by the original Hamiltonian and the effective Hamiltonian, where the fidelity of state $\rho _i=|i\rangle \langle i|$ is defined as $F=\textrm {Tr}\sqrt {\rho _i^{1/2}\rho (t)\rho _i^{1/2}}$ and $\rho (t)$ is the density matrix of system at time $t$. The other relevant parameters are all chosen as: $\Omega _a=\Omega _b=\sqrt {0.05}\Omega _c$, $\Delta _p=20\Omega _c$, $\Delta _r=20\Omega _c$, $T=0.15t_c$, and $\tau =0.1t_c$.
Fig. 3.
Fig. 3. The dynamical evolution of the fidelity for the 3-qubit GHZ state with different $\delta$. For the Step 1 and Step 2, we set $t_c=6000/\Omega _c$ and $t_c=8000/\Omega _c$, respectively. The other relevant parameters are $\Omega _{a}=\Omega _b=\sqrt {2}\Omega _c$, $\Delta _p=800\Omega _c$, $\Delta _r=20\Omega _c$, $T=0.15t_c$, and $\tau =0.1t_c$.
Fig. 4.
Fig. 4. The dynamical evolution of the fidelity for the 3-qubit GHZ state with different $\Delta _r$. For the Step 1 and Step 2, we set $t_c=6000/\Omega _c$ and $t_c=8000/\Omega _c$, respectively. The other relevant parameters are $\Omega _{a}=\Omega _b=\sqrt {2}\Omega _c$, $\Delta _p=800\Omega _c$, $\delta =0$, $T=0.15t_c$, and $\tau =0.1t_c$.
Fig. 5.
Fig. 5. The fidelity of the $3$-qubit GHZ state governed by the original master equation. The decay rates are $\gamma _p=3\Omega _c$ and $\gamma =0.001\Omega _c$. The other relevant parameters are the same as those of Fig. 2(c).

Equations (19)

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Ω a ( t ) = Ω a exp [ ( t t c / 2 τ ) 2 T 2 ] ,
Ω b ( t ) = Ω b exp [ ( t t c / 2 + τ ) 2 T 2 ] ,
H I 1 ( t ) = j = 1 , 2 Ω a ( t ) | p j 0 | e i Δ p t + Ω b ( t ) | p j 1 | e i Δ p t + Ω c | r j 1 | e i Δ r t + H.c. + α β U α β | r r α β r r | ,
H I 1 ( t ) = j = 1 , 2 Ω a ( t ) | p j 0 | + Ω b ( t ) | p j 1 | + Ω c | r j 1 | + H.c. Δ p | p j p | Δ r | r j r | + k = 1 N 1 U k , k + 1 | r r k , k + 1 r r | .
H I 1 ( t ) = 2 Ω a ( t ) | ψ 1 12 00 | + Ω b ( t ) | ψ 1 12 ψ 0 | + Ω a ( t ) | ψ 2 12 ψ 0 | + 2 Ω b ( t ) | ψ 2 12 11 | + Ω | 11 12 r r | + H.c. Δ p | ψ 1 12 ψ 1 | Δ p | ψ 2 12 ψ 2 | ,
H I 1 ( t ) = 2 Ω a ( t ) | ψ 1 12 00 | + Ω b ( t ) | ψ 1 12 ψ 0 | + Ω a ( t ) | ψ 2 12 ψ 0 | + Ω b ( t ) | ψ 2 12 ( + | + | ) + H.c. + Ω ( | + 12 + | | 12 | ) Δ p | ψ 1 12 ψ 1 | Δ p | ψ 2 12 ψ 2 | ,
H eff 1 ( t ) = 2 Ω a ( t ) | ψ 1 12 00 | + Ω b ( t ) | ψ 1 12 ψ 0 | + H.c. Δ p | ψ 1 12 ψ 1 | .
| Φ 12 = cos [ Θ ( t ) ] | 00 12 sin [ Θ ( t ) ] | ψ 0 12 ,
lim t cos [ Θ ( t ) ] = 1 , lim t + cos [ Θ ( t ) ] = 0.
H I n ( t ) = j = n , n + 1 ( Ω c | r j 1 | + H.c. Δ r | r j r | ) + Ω a ( t ) | p n + 1 0 | + Ω b ( t ) | p n + 1 1 | + H.c. Δ p | p n + 1 p | + U n , n + 1 | r r n , n + 1 r r | ,
H eff n ( t ) = Ω a ( t ) | 0 p n , n + 1 00 | + Ω b ( t ) | 0 p n , n + 1 01 | + H.c. Δ p | 0 p n , n + 1 0 p | .
| Φ n , n + 1 = cos [ Θ ( t ) ] | 00 n , n + 1 sin [ Θ ( t ) ] | 01 n , n + 1 .
H I 1 ( t ) = 2 Ω a ( t ) | ψ 1 12 00 | + Ω b ( t ) | ψ 1 12 ψ 0 | + Ω a ( t ) | ψ 2 12 ψ 0 | + 2 Ω b ( t ) | ψ 2 12 11 | + Ω | 11 12 r r | + H.c. Δ p | ψ 1 12 ψ 1 | Δ p | ψ 2 12 ψ 2 | + δ | r r 12 r r | .
H I 1 ( t ) = 2 Ω a ( t ) | ψ 1 12 00 | + Ω b ( t ) | ψ 1 12 ψ 0 | + Ω a ( t ) | ψ 2 12 ψ 0 | + Ω b ( t ) | ψ 2 12 ( sin θ + ~ | cos θ ~ | ) + H.c. + Ω ~ + | + ~ 12 + ~ | + Ω ~ | ~ 12 ~ | Δ p | ψ 1 12 ψ 1 | Δ p | ψ 2 12 ψ 2 | .
ρ ˙ = i [ H I j ( t ) , ρ ] + L j ρ + L j + 1 ρ ,
L j ρ = k = 1 3 L j k ρ L j k 1 2 ( L j k L j k ρ + ρ L j k L j k ) ,
L j 1 = γ p 2 | 0 j p | ,
L j 2 = γ p 2 | 1 j p | ,
L j 3 = γ | 1 j r | .