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NMR Hamiltonian as an effective Hamiltonian to generate Schrödinger’s cat states. (English) Zbl 1508.81433

Summary: This report experimentally demonstrates that the theoretical background of the atom-field scenario points out that the NMR quadrupolar Hamiltonian works as an effective Hamiltonian to generate Schrödinger’s cat states in a \(2I+1\) low-dimensional Hilbert space. The versatility of this nuclear spin setup is verified by monitoring the \(^{23}\mathrm{Na}\) nucleus of a lyotropic liquid crystal sample at the nematic phase. The quantum state tomography and the Wigner quasiprobability distribution function are performed to characterize the accuracy of the experimental implementation.

MSC:

81P68 Quantum computation
81V35 Nuclear physics

References:

[1] Buek, V.; Knight, PL, Quantum interference, superposition states of light, and nonclassical effects, Prog. Opt., 34, 1-158 (1995)
[2] Monroe, C.; Meekhof, DM; King, BE; Wineland, DJ, A “schrödinger cat” superposition state of an atom, Science., 272, 1131-1136 (1996) · Zbl 1226.81011
[3] Bouwmeester, D.; Jian-Wei, P.; Mattle, K.; Eibl, M.; Weinfurter, H.; Zeilinger, A., Experimental quantum teleportation, Nature., 390, 575-579 (1997) · Zbl 1369.81006
[4] Leibfried, D.; Knill, E.; Seidelin, S.; Britton, J.; Blakestad, RB; Chiaverini, J.; Dume, DB; Itano, WM; Jost, JD; Langer, C.; Ozeri, R.; Reichle, R.; Wineland, DJ, Creation of a six-atom schrödinger cat state, Nature., 438, 639-642 (2005)
[5] Delglise, S.; Dotsenko, I.; Sayrin, C.; Bernu, J.; Brune, M.; Raimond, J.-M, Reconstruction of non-classical cavity field states with snapshots of their decoherence, Nature., 455, 510-514 (2008)
[6] Vlastakis, B.; Kirchmair, G.; Leghtas, Z.; Nigg, SE; Frunzio, L.; Girvin, SM; Mirrahimi, M.; Devoret, MH; Schoelkopf, RJ, Deterministically encoding quantum information using 100-photon schrödinger cat states, Science., 342, 607-610 (2013) · Zbl 1355.81054
[7] Leek, PJ, Storing quantum information in schrödinger’s cats, Science., 342, 568-569 (2013)
[8] Barreiro, JT; Mller, M.; Schindler, P.; Nigg, D.; Monz, T.; Chwalla, M.; Hennrich, M.; Roos, CF; Zoller, P.; Blatt, R., An open-system quantum simulator with trapped ions, Nature., 470, 486-491 (2011)
[9] Tiecke, TG; Thompson, JD; de Leon, NP; Liu, LR; Vuleti, V.; Lukin, MD, Nanophotonic quantum phase switch with a single atom, Nature., 508, 241-244 (2014)
[10] Agarwal, GS; Puri, RR; Singh, RP, Atomic schrödinger cat states, Phys. Rev. A., 56, 3, 2249-2254 (1997)
[11] Zheng, S., One-step synthesis of multiatom greenberger-horne-zeilinger states, Phys. Rev. Lett., 87, 230404 (2001)
[12] Klimov, AB; Saavedra, C., The dicke model dynamics in a high detuning limit, Phys. Lett. A., 247, 14-20 (1998)
[13] Klimov, AB; Romero, JL; Delgado, J.; Sánchez-Soto, LL, Master equations for effective hamiltonians, J. Opt. B Quantum Semiclassical Opt., 5, 34-39 (2002)
[14] James, DFV, Quantum computation with hot and cold ions: an assessment of proposed schemes, Fortschr. Phys., 48, 823-837 (2000)
[15] Prado, FO; Luiz, FS; Villas-Bôas, M.; Alcalde, AM; Duzzioni, EI; Sanz, L., Atom-mediated effective interactions between modes of a bimodal cavity, Phys. Rev. A., 84, 053839 (2011)
[16] Auccaise, R.; Araujo-Ferreira, AG; Sarthour, RS; Oliveira, IS; Bonagamba, TJ; Roditi, I., Spin squeezing in a quadrupolar nuclei nmr system, Phys. Rev. Lett., 114, 043604 (2015)
[17] Gao, W.; Lu, C-Y; Yao, X-C; Xu, P.; Gühne, O.; Goebel, A.; Chen, Y-A; Peng, C-Z; Chen, Z-B; Pan, J-W, Experimental demonstration of a hyper-entangled ten-qubit schrödinger cat state, Nature Phys., 6, 331-335 (2010)
[18] Song, C.; Xu, K.; Liu, W.; Yang, C-P; Zheng, S-B; Deng, H.; Xie, Q.; Huang, K.; Guo, Q.; Zhang, L.; Zhang, P.; Xu, D.; Zheng, D.; Zhu, X.; Wang, H.; Chen, Y-A; Lu, C-Y; Han, S.; Pan, J-W, 10-Qubit entanglement and parallel logic operations with a superconducting circuit, Phys. Rev. Lett., 119, 180511 (2017)
[19] Cappellaro, P.; Emerson, J.; Boulant, N.; Ramanathan, C.; Lloyd, S.; Cory, DG, Entanglement assisted metrology, Phys. Rev. Lett., 94, 020502 (2005)
[20] Cohen-Tannoudji, C.; Bernard, D.; Laloë, F., Quantum mechanics (1977), New York: Wiley, New York · Zbl 1440.81003
[21] Slichter, C. P.: Principles of magnetic resonance, Springer International (1992)
[22] Wasylishen, R.E., Ashbrook, S.E., Wimperis S.: NMR of quadrupolar nuclei in solid materials, John Wiley & Sons Ltd (2012)
[23] Auccaise, R.; Teles, J.; Bonagamba, TJ; Oliveira, IS; deAzevedo, ER; Sarthour, RS, NMR quadrupolar system described as Bose-Einstein-condensate-like system, J. Chem. Phys., 130, 144501 (2009)
[24] Estrada, RA; deAzevedo, ER; Duzzioni, EI; Bonagamba, TJ; Moussa, MHY, Spin coherent states in nmr quadrupolar system: experimental and theoretical applications, Eur. Phys. J. D., 67, 127 (2013)
[25] Araujo-Ferreira, AG; Auccaise, R.; Sarthour, RS; Oliveira, IS; Bonagamba, TJ; Roditi, I., Classical bifurcation in a quadrupolar nmr system, Phys. Rev. A., 87, 053605 (2013)
[26] Nie, X.; Li, J.; Cui, J.; Luo, Z.; Huang, J.; Chen, H.; Lee, C.; Peng, X.; Du, J-F, Quantum simulation of interaction blockade in a two-site BoseHubbard system with solid quadrupolar crystal, New J. Phys., 17, 053028 (2015)
[27] Teles, J.; Auccaise, R.; Rivera-Ascona, C.; Araujo-Ferreira, AG; Andreeta, JP; Bonagamba, TJ, Spin coherent states phenomena probed by quantum state tomography in Zeeman perturbed nuclear quadrupole resonance, Quantum Inf. Process., 17, 177 (2018) · Zbl 1448.81086
[28] Perelomov, A.: Generalized coherent states and their applications, text and monographs in physics, Springer-Verlag (1985)
[29] Agarwal, GS, Relation between atomic coherent-state representation, state multipoles, and generalized phase-space distributions, Phys. Rev. A., 24, 2889-2896 (1981)
[30] Benedict, MG; Czirják, A., Wigner functions, squeezing properties, and slow decoherence of a mesoscopic superposition of two-level atoms, Phys. Rev. A., 60, 4034-4044 (1999)
[31] Sánchez-Soto, L. L.; Klimov, A. B.; de la Hoz, P.; Leuchs, G., Quantum versus classical polarization states: when multipoles count, J. Phys. B At. Mol. Opt. Phys., 46, 104011 (2013)
[32] Ourjoumtsev, A.; Tualle-Brouri, R.; Laurat, J.; Grangier, P., Generating optical schrödinger kittens for quantum information processing, Science., 312, 83-86 (2006)
[33] Ourjoumtsev, A.; Jeong, H.; Tualle-Brouri, R.; Grangier, P., Generation of optical schrödinger cats from photon number states, Nature., 448, 784-786 (2007)
[34] Leibfried, D.; Meekhof, DM; King, BE; Monroe, C.; Itano, WM; Wineland, DJ, Experimental determination of the motional quantum state of a trapped atom, Phys. Rev. Lett., 77, 4281-4285 (1996)
[35] Teles, J.; Rivera-Ascona, C.; Polli, RS; Oliveira-Silva, R.; Vidoto, ELG; Andreeta, JP; Bonagamba, TJ, Experimental implementation of quantum information processing by Zeeman-perturbed nuclear quadrupole resonance, Quantum Inf. Process., 14, 1889-1906 (2015) · Zbl 1317.81067
[36] Garon, A.; Zeier, R.; Glaser, SJ, Visualizing operators of coupled spin systems, Phys. Rev. A., 91, 042122 (2015)
[37] Koczor, B.; Zeier, R.; Glaser, S. J., Continuous phase spaces and the time evolution of spins: star products and spin-weighted spherical harmonics, J. Phys. A Math. Theor., 52, 055302 (2019) · Zbl 1422.81123
[38] Koczor, B.; Zeier, R.; Glaser, SJ, Time evolution of coupled spin systems in a generalized Wigner representation, Ann. Phys., 408, 1-50 (2019) · Zbl 1421.81014
[39] Teles, J.; deAzevedo, ER; Auccaise, R.; Sarthour, RS; Oliveira, IS; Bonagamba, TJ, Quantum state tomography for quadrupolar nuclei using global rotations of the spin system, J. Chem. Phys., 126, 154506 (2007)
[40] Varshalovich, D.A., Moskalev, A.N., Khersonskii, V.K.: Quantum theory of angular momentum, World Scientific Publishing Co. Pte. Ltd - A Editora (1988)
[41] Auccaise, R.; Teles, J.; Sarthour, RS; Bonagamba, TJ; Oliveira, IS; deAzevedo, ER, A study of the relaxation dynamics in a quadrupolar nmr system using quantum state tomography, J. Magn. Reson., 192, 17-26 (2008)
[42] Quist, P-O; Halle, B.; Furó, I., Micelle size and order in lyotropic nematic phases from nuclear spin relaxation, J. Chem. Phys., 96, 3875-3891 (1992)
[43] Oliveira, I.S., Bonagamba, T., Sarthour, R., Freitas, J.C., Azevedo, E.: NMR quantum information processing, Elsevier-Amsterdan, E. R. (2007)
[44] Fortunato, EM; Pravia, MA; Boulant, N.; Teklemariam, G.; Havel, TF; Cory, DG, Design of strongly modulating pulses to implement precise effective Hamiltonians for quantum information processing, J. Chem. Phys., 116, 7599-7606 (2002)
[45] Jin, G-R; Kim, SW, Spin squeezing and maximal-squeezing time, Phys. Rev. A., 76, 043621 (2007)
[46] Neergaard-Nielsen, JS; Nielsen, BM; Hettich, C.; Mølmer, K.; Polzik, ES, Generation of a superposition of odd photon number states for quantum information networks, Phys. Rev. Lett., 97, 083604 (2006)
[47] Lücke, B.; Peise, J.; Vitagliano, G.; Arlt, J.; Santos, L.; Tóth, G.; Klempt, C., Detecting multiparticle entanglement of Dicke states, Phys. Rev. Lett., 112, 155304 (2014)
[48] Kampermann, H.; Veeman, WS, Characterization of quantum algorithms by quantum process tomography using quadrupolar spins in solid-state nuclear magnetic resonance, J. Chem. Phys., 122, 214108 (2005)
[49] Yusa, G.; Muraki, K.; Takashina, K.; Hashimoto, K.; Hirayama, Y., Controlled multiple quantum coherences of nuclear spins in a nanometre-scale device, Nature., 434, 1001-1005 (2005)
[50] Miranowicz, A.; Özdemir, ŞK; Bajer, J.; Yusa, G.; Imoto, N.; Hirayama, Y.; Nori, F., Quantum state tomography of large nuclear spins in a semiconductor quantum well: Optimal robustness against errors as quantified by condition numbers, Phys. Rev. B., 92, 075312 (2015)
[51] Hendrickx, NW; Lawrie, WIL; Russ, M.; van Riggelen, F.; de Snoo, SL; Schouten, RN; Sammak, A.; Scappucci, G.; Veldhorst, M., A four-qubit germanium quantum processor, Nature., 591, 580-585 (2021)
[52] Glenn, DR; Bucher, DB; Lee, J.; Lukin, MD; Park, H.; Walsworth, RL, High-resolution magnetic resonance spectroscopy using a solid-state spin sensor, Nature., 555, 351-354 (2018)
[53] Dutt, MVG; Childress, L.; Jiang, L.; Togan, E.; Maze, J.; Jelezko, F.; Zibrov, AS; Hemmer, PR; Lukin, MD, Quantum register based on individual electronic and nuclear spin qubits in diamond, Science., 316, 1312-1316 (2007)
[54] Aiello, CD; Hirose, M.; Cappellaro, P., Composite-pulse magnetometry with a solid-state quantum sensor, Nature Commun., 4, 1419 (2013)
[55] Kong, F.; Ju, C.; Liu, Y.; Lei, C.; Wang, M.; Kong, X.; Wang, P-F; Huang, P.; Li, Z.; Shi, F.; Jiang, L.; Du, J-F, Direct measurement of topological numbers with spins in diamond, Phys. Rev. Lett., 117, 060503 (2016)
[56] Rose, BC; Huang, D.; Zhang, Z-H; Stevenson, P.; Tyryshkin, AM; Sangtawesin, S.; Srinivasan, S.; Loudin, L.; Markham, ML; Edmonds, AM; Twitchen, DJ; Lyon, SA; de Leon, NP, Observation of an environmentally insensitive solid-state spin defect in diamond, Science., 361, 60-63 (2018)
[57] Das, R.; Kumar, A., Use of quadrupolar nuclei for quantum-information processing by nuclear magnetic resonance: implementation of a quantum algorithm, Phys. Rev. A., 68, 032304 (2003)
[58] Hacker, B.; Welte, S.; Daiss, S.; Shaukat, A.; Ritter, S.; Li, L.; Rempe, G., Deterministic creation of entangled atom-light schrödinger-cat states, Nature Photonics., 13, 110-115 (2019)
[59] Omran, A.; Levine, H.; Keesling, A.; Semeghini, G.; Wang, TT; Ebadi, S.; Bernien, H.; Zibrov, AS; Pichler, H.; Choi, S.; Cui, J.; Rossignolo, M.; Rembold, P.; Montangero, S.; Calarco, T.; Endres, M.; Greiner, M.; Vuletić, V.; Lukin, MD, Generation and manipulation of schrödinger cat states in Rydberg atom arrays, Science., 365, 570-574 (2019)
[60] Gati, R.; Oberthaler, MK, A bosonic Josephson junction, J. Phys. B., 40, R61-R89 (2007)
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