Abstract
We consider a platform for quantum technology based on Rydberg atoms in optical lattices where each atom encodes one qubit of information and external lasers can manipulate their state. We demonstrate how optimal control theory enables the functioning of two specific building blocks on this platform: We engineer an optimal protocol to perform a two-qubit phase gate and to transfer the information within the lattice among specific sites. These two elementary operations allow to design very general operations like storage of atoms and entanglement purification as, for example, needed for quantum repeaters.
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H.-J. Briegel, W. Dür, J.I. Cirac, P. Zoller, Phys. Rev. Lett. 81, 5932 (1998)
L.-M. Duan, M.D. Lukin, J.I. Cirac, P. Zoller, Nature 414, 413 (2001)
B. Zhao, M. Müller, K. Hammerer, P. Zoller, Phys. Rev. A 81, 052329 (2010)
Y. Han, B. He, K. Heshami, C.-Z. Li, C. Simon, Phys. Rev. A 81, 052311 (2010)
E. Brion, F. Carlier, V.M. Akulin, K. Mølmer, Phys. Rev. A 85, 042324 (2012)
H. Wu, Z.-B. Yang, L.-T. Shen, S.-B. Zheng, J. Phys. B At. Mol. Opt. Phys. 46, 185502 (2013)
L. Li, Y.O. Dudin, A. Kuzmich, Nature 498, 466 (2013)
M. Müller, I. Lesanovsky, H. Weimer, H.P. Büchler, P. Zoller, Phys. Rev. Lett. 102, 170502 (2009)
M. Saffman, T.G. Walker, Phys. Rev. A 66, 065403 (2002)
Y.O. Dudin, A. Kuzmich, Science 336, 887 (2012)
R. Heidemann, U. Raitzsch, V. Bendkowsky, B. Butscher, R. Löw, L. Santos, T. Pfau, Phys. Rev. Lett. 99, 163601 (2007)
M. Saffman, T.G. Walker, K. Mølmer, Rev. Mod. Phys. 82, 2313 (2010)
L.H. Pedersen, K. Mølmer, Phys. Rev. A 79, 012320 (2009)
M.M. Müller, A. Kölle, R. Löw, T. Pfau, T. Calarco, S. Montangero, Phys. Rev. A 87, 053412 (2013)
Y. Miroshnychenko, U.V. Poulsen, K. Mølmer, Phys. Rev. A 87, 023821 (2013)
M.M. Müller, H.R. Haakh, T. Calarco, C.P. Koch, C. Henkel, Quant. Inf. Proc. 10, 771–792 (2011)
M.M. Müller, M. Murphy, S. Montangero, T. Calarco, P. Grangier, A. Browaeys, Phys. Rev. A 89, 032334 (2014)
F. Caruso, V. Giovannetti, C. Lupo, S. Mancini, Rev. Mod. Phys. 86, 1203 (2014)
P. Schauß, M. Cheneau, M. Endres, T. Fukuhara, S. Hild, A. Omran, T. Pohl, C. Gross, S. Kuhr, I. Bloch, Nature 491, 87–91 (2012)
P. Schauß, J. Zeiher, T. Fukuhara, S. Hild, M. Cheneau, T. Macrì, T. Pohl, I. Bloch, C. Gross, Science 347, 6229 (2015)
Yao Weimer, C.R. Laumann, M.D. Lukin, Phys. Rev. Lett. 108, 100501 (2012)
C. Brif, R. Chakrabarti, H. Rabitz, New J. Phys. 12, 075008 (2010)
D. Jaksch, J.I. Cirac, P. Zoller, S.L. Rolston, R. Côté, M.D. Lukin, Phys. Rev. Lett. 85, 2208 (2000)
A. Gaëtan, Y. Miroshnychenko, T. Wilk, A. Chotia, M. Vitaeu, D. Comparat, P. Pillet, A. Browaeys, P. Grangier, Nat. Phys. 5, 115 (2009)
L. Isenhower, E. Urban, X.L. Zhang, A.T. Gill, T. Henage, T.A. Johnson, T.G. Walker, M. Saffman, Phys. Rev. Lett. 104, 010503 (2010)
Y. Miroshnychenko, A. Gaëtan, C. Evellin, P. Grangier, D. Comparat, P. Pillet, T. Wilk, A. Browaeys, Phys. Rev. A 82, 013405 (2010)
T. Wilk, A. Gaëtan, C. Evellin, J. Wolters, Y. Miroshnychenko, P. Grangier, A. Browaeys, Phys. Rev. Lett. 104, 010502 (2010)
X.L. Zhang, A.T. Gill, L. Isenhower, T.G. Walker, M. Saffman, Phys. Rev. A 85, 042310 (2012)
M. Saffman, T.G. Walker, Phys. Rev. A 72, 042302 (2005)
L. Isenhower, M. Saffman, K. Mülmer, Quant. Inf. Proc. 10, 755 (2011)
H.-Z. Wu, Z.-B. Yang, S.-B. Zheng, Phys. Rev. A 82, 034307 (2010)
D.D.B. Rao, K. Mülmer, Phys. Rev. A 89, 030301 (2014). (R)
Y. Liang, Q.-C. Wu, S.-L. Su, X. Ji, S. Zhang, Phys. Rev. A 91, 032304 (2015)
J. Zhang, J. Vala, S. Sastry, K.B. Whaley, Phys. Rev. Lett. 91, 027903 (2003)
T. Calarco, J.I. Cirac, P. Zoller, Phys. Rev. A 63, 062304 (2008)
J. Reichel, V. Vuletić (eds.), Atom Chips (Wiley-VCH, Germany, 2011)
I. Bloch, Nature 453, 1016–1022 (2008)
R. Löw, H. Weimer, J. Nipper, J.B. Balewski, B. Butscher, H.P. Büchler, T. Pfau, J. Phys. B. At. Mol. Opt. Phys. 45, 113001 (2012)
E. Brion, L.H. Pedersen, K. M(ø)lmer, J. Phys. A 40, 1033 (2007)
J.A. Nelder, R. Mead, Comput. J. 7, 308 (1965)
A.I. Konnov and V.F. Krotov. Automation and Remote Control, Vol. 60, No. 10 (1999)
S. Sklarz, D. Tannor, Phys. Rev. A 66, 053619 (2002)
J.P. Palao, R. Kosloff, Phys. Rev. A 68, 062308 (2003)
S. White, Phys. Rev. Lett. 69, 2863 (1992)
U. Schollwöck, Rev. Mod. Phys. 77, 259 (2005)
P. Doria, T. Calarco, S. Montangero, Phys. Rev. Lett. 106, 190501 (2011)
T. Caneva, T. Calarco, S. Montangero, Phys. Rev. A 84, 022326 (2011)
N. Rach, M.M.Müller, T. Calarco, and S. Montangero, arXiv:1506.04601 (2015)
S. Lloyd, S. Montangero, Phys. Rev. Lett. 113, 010502 (2014)
T. Caneva, M. Murphy, T. Calarco, R. Fazio, S. Montangero, V. Giovannetti, G.E. Santoro, Phys. Rev. Lett. 103, 240501 (2009)
D. A. Steck, “Rubidium 87 D Line Data,” available online at http://steck.us/alkalidata (revision 2.1.4, 23 December 2010)
This work was performed on the computational resource bwUniCluster funded by the Ministry of Science, Research and Arts and the Universities of the State of Baden-Württemberg, Germany, within the framework program bwHPC
Acknowledgments
The authors acknowledge support from SFB/TRR21, Q.com, the EU project RYSQ, and we thank the bwUniCluster [52] for the computational resources.
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This paper is part of the topical collection “Quantum Repeaters: From Components to Strategies” guest edited by Manfred Bayer, Christoph Becher and Peter van Loock.
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Müller, M.M., Pichler, T., Montangero, S. et al. Optimal control for Rydberg quantum technology building blocks. Appl. Phys. B 122, 104 (2016). https://doi.org/10.1007/s00340-016-6383-2
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DOI: https://doi.org/10.1007/s00340-016-6383-2