Training Schrödinger’s cat: quantum optimal control

Strategic report on current status, visions and goals for research in Europe
  • Steffen J. Glaser
  • Ugo Boscain
  • Tommaso Calarco
  • Christiane P. Koch
  • Walter Köckenberger
  • Ronnie Kosloff
  • Ilya Kuprov
  • Burkhard Luy
  • Sophie Schirmer
  • Thomas Schulte-Herbrüggen
  • Dominique Sugny
  • Frank K. Wilhelm
Open Access
Regular Article

Abstract

It is control that turns scientific knowledge into useful technology: in physics and engineering it provides a systematic way for driving a dynamical system from a given initial state into a desired target state with minimized expenditure of energy and resources. As one of the cornerstones for enabling quantum technologies, optimal quantum control keeps evolving and expanding into areas as diverse as quantum-enhanced sensing, manipulation of single spins, photons, or atoms, optical spectroscopy, photochemistry, magnetic resonance (spectroscopy as well as medical imaging), quantum information processing and quantum simulation. In this communication, state-of-the-art quantum control techniques are reviewed and put into perspective by a consortium of experts in optimal control theory and applications to spectroscopy, imaging, as well as quantum dynamics of closed and open systems. We address key challenges and sketch a roadmap for future developments.

Keywords

Quantum Information 

References

  1. 1.
    The QUAINT website, www.quantumcontrol.eu (2015)
  2. 2.
    J.P. Dowling, G. Milburn, Phil. Trans. R. Soc. Lond. A 361, 1655 (2003) ADSMathSciNetCrossRefGoogle Scholar
  3. 3.
    M. Devoret, Quantum Machines: Measurement and Control of Engineered Quantum Systems, École de Physique des Houches 2011 (Oxford University Press, Oxford, 2014)Google Scholar
  4. 4.
    L.S. Pontryagin, V.G. Bol’tanskii, R.S. Gamkrelidze, E.F. Mischenko, The Mathematical Theory of Optimal Processes (Pergamon Press, New York, 1964)Google Scholar
  5. 5.
    E.B. Lee, L. Markus, Foundations of Optimal Control Theory (Wiley, New York, 1967)Google Scholar
  6. 6.
    A.E. Bryson, Y.C. Ho, Applied Optimal Control: Optimization, Estimation, and Control (Taylor and Francis, 1975) Google Scholar
  7. 7.
    R. Kalman, P.L. Falb, M.A. Arbib, Topics in Mathematical System Theory (McGraw-Hill, New York, 1969)Google Scholar
  8. 8.
    E. Sontag, Mathematical Control Theory (Springer, New York, 1998)Google Scholar
  9. 9.
    D.E. Kirk, Optimal Control Theory: An introduction (Dover Publications, New York, 2004)Google Scholar
  10. 10.
    J.M. Coron, Control and Nonlinearity (Am. Math. Soc., Providence RI, 2007)Google Scholar
  11. 11.
    A.A. Agrachev, Y.L. Sachkov, Control theory from the geometric viewpoint (Springer-Verlag, Berlin, 2004), Vol. 87Google Scholar
  12. 12.
    V. Jurdjevic, Geometric Control Theory (Cambridge University Press, Cambridge, 1997)Google Scholar
  13. 13.
    A. Bressan, B. Piccoli, Introduction to the mathematical theory of control, AIMS Series on Applied Mathematics (American Institute of Mathematical Sciences, Springfield, MO, 2007), Vol. 2Google Scholar
  14. 14.
    D. D’Alessandro, Introduction to Quantum Control and Dynamics, Applied Mathematics & Nonlinear Science (Chapman and Hall, Boca Raton, 2008)Google Scholar
  15. 15.
    H.M. Wiseman, G.J. Milburn, Quantum Measurement and Control (Cambridge University Press, Cambridge, 2010) Google Scholar
  16. 16.
    S. Cong, Control of Quantum Systems: Theory and Methods (Wiley & Sons, Singapore, 2014)Google Scholar
  17. 17.
    C. Brif, R. Chakrabarti, H. Rabitz, New J. Phys. 12, 075008 (2010) ADSCrossRefGoogle Scholar
  18. 18.
    G. Dirr, U. Helmke, GAMM-Mitt. 31, 59 (2008)MathSciNetMATHCrossRefGoogle Scholar
  19. 19.
    D. Dong, I.A. Petersen, IET Control Theory A. 4, 2651 (2010)MathSciNetCrossRefGoogle Scholar
  20. 20.
    R. Zeier, T. Schulte-Herbrüggen, J. Math. Phys. 52, 113510 (2011) ADSMathSciNetCrossRefGoogle Scholar
  21. 21.
    C. Altafini, F. Ticozzi, IEEE Trans. Automat. Control 57, 1898 (2012) MathSciNetCrossRefGoogle Scholar
  22. 22.
    A. Borzi, Nanoscale Syst. Math. Model. Theor. Appl. 1, 93 (2012)Google Scholar
  23. 23.
    B. Bonnard, D. Sugny, Optimal Control with Applications in Space and Quantum Dynamics, AIMS on Applied Mathematics (American Institute of Mathematical Sciences, Springfield, 2012), Vol. 5Google Scholar
  24. 24.
    A.G. Butkovskiy, Y.I. Samoilenko, Control of Quantum-Mechanical Processes and Systems (Kluwer Academic Publishers, Dordrecht, The Netherlands, 1990), (see also the translations from Russian originals: A.G. Butkovskiy and Yu. I. Samoilenko, Control of Quantum Systems, Part I and II, Autom. Remote Control (USSR) 40, pp. 485–502 and pp. 629–645 (1979), as well as: A. G. Butkovskiy and Yu. I. Samoilenko, Controllability of Quantum Objects, Dokl. Akad. Nauk. USSR 250, pp. 22–24 (1980).)Google Scholar
  25. 25.
    V. Jurdjevic, H. Sussmann, J. Differ. Eq. 12, 313 (1972)ADSMathSciNetMATHCrossRefGoogle Scholar
  26. 26.
    H. Sussmann, V. Jurdjevic, J. Differ. Eq. 12, 95 (1972)ADSMathSciNetMATHCrossRefGoogle Scholar
  27. 27.
    R.W. Brockett, SIAM J. Control 10, 265 (1972)MathSciNetMATHCrossRefGoogle Scholar
  28. 28.
    R.W. Brockett, SIAM J. Appl. Math. 25, 213 (1973)MathSciNetMATHCrossRefGoogle Scholar
  29. 29.
    D. Elliott, Bilinear Control Systems: Matrices in Action (Springer, London, 2009)Google Scholar
  30. 30.
    F. Albertini, D. D’Alessandro, IEEE Trans. Automat. Control 48, 1399 (2003)MathSciNetCrossRefGoogle Scholar
  31. 31.
    I. Kurniawan, G. Dirr, U. Helmke, IEEE Trans. Automat. Contr. 57, 1984 (2012) MathSciNetCrossRefGoogle Scholar
  32. 32.
    U. Boscain, M. Caponigro, T. Chambrion, M. Sigalotti, Commun. Math. Phys. 311, 423 (2012) ADSMathSciNetMATHCrossRefGoogle Scholar
  33. 33.
    G. Turinici, in Mathematical Models and Methods for Ab Initio Quantum Chemistry (Springer Berlin Heidelberg, 2000), Lecture Notes in Chemistry, Vol. 74, pp. 75–92Google Scholar
  34. 34.
    S.G. Schirmer, H. Fu, A.I. Solomon, Phys. Rev. A 63, 063410 (2001) ADSCrossRefGoogle Scholar
  35. 35.
    C. Altafini, J. Math. Phys. 43, 2051 (2002) ADSMathSciNetMATHCrossRefGoogle Scholar
  36. 36.
    M. Mirrahimi, P. Rouchon, IEEE Trans. Automat. Control 49, 745 (2004)MathSciNetCrossRefGoogle Scholar
  37. 37.
    J.M. Ball, J.E. Marsden, M. Slemrod, SIAM J. Control Optim. 20, 575 (1982)MathSciNetMATHCrossRefGoogle Scholar
  38. 38.
    K. Beauchard, J. Math. Pures Appl. 84, 851 (2005)MathSciNetMATHCrossRefGoogle Scholar
  39. 39.
    K. Beauchard, J. Coron, J. Funct. Anal. 232, 328 (2006) MathSciNetMATHCrossRefGoogle Scholar
  40. 40.
    K. Beauchard, C. Laurent, J. Math. Pures Appl. 94, 520 (2010)MathSciNetMATHCrossRefGoogle Scholar
  41. 41.
    T. Chambrion, P. Mason, M. Sigalotti, U. Boscain, Ann. Inst. Henri Poincaré 26, 329 (2009)ADSMathSciNetMATHCrossRefGoogle Scholar
  42. 42.
    T. Chambrion, Automatica 48, 2040 (2012) MathSciNetMATHCrossRefGoogle Scholar
  43. 43.
    N. Boussaid, M. Caponigro, T. Chambrion, IEEE Trans. Automat. Control 58, 2205 (2013) MathSciNetCrossRefGoogle Scholar
  44. 44.
    U. Boscain, M. Caponigro, M. Sigalotti, J. Differ. Eq. 256, 3524 (2014) ADSMathSciNetMATHCrossRefGoogle Scholar
  45. 45.
    M. Keyl, R. Zeier, T. Schulte-Herbrüggen, New J. Phys. 16, 065010 (2014) ADSCrossRefGoogle Scholar
  46. 46.
    U. Boscain, P. Mason, G. Panati, M. Sigalotti, J. Math. Phys. 56, 092101 (2015) ADSMathSciNetCrossRefGoogle Scholar
  47. 47.
    K. Beauchard, J.M. Coron, P. Rouchon, Commun. Math. Phys. 296, 525 (2010) ADSMathSciNetMATHCrossRefGoogle Scholar
  48. 48.
    J. Li, N. Khaneja, Phys. Rev. A 73, 030302 (2006) ADSCrossRefGoogle Scholar
  49. 49.
    J.S. Li, N. Khaneja, IEEE Trans. Automat. Control 54, 528 (2009)MathSciNetCrossRefGoogle Scholar
  50. 50.
    Z. Leghtas, A. Sarlette, P. Rouchon, J. Phys. B 44, 154017 (2011) ADSCrossRefGoogle Scholar
  51. 51.
    G. Turinici, H. Rabitz, Phys. Rev. A 70, 063412 (2004) ADSCrossRefGoogle Scholar
  52. 52.
    K. Kobzar, T.E. Skinner, N. Khaneja, S. Glaser, B. Luy, J. Magn. Reson. 170, 236 (2004) ADSCrossRefGoogle Scholar
  53. 53.
    K. Kobzar, T.E. Skinner, N. Khaneja, S.J. Glaser, B. Luy, J. Magn. Reson. 194, 58 (2008)ADSCrossRefGoogle Scholar
  54. 54.
    T.E. Skinner, M. Braun, K. Woelk, N.I. Gershenzon, S.J. Glaser, J. Magn. Reson. 209, 282 (2011) ADSCrossRefGoogle Scholar
  55. 55.
    K. Kobzar, S. Ehni, T.E. Skinner, S.J. Glaser, B. Luy, J. Magn. Reson. 225, 142 (2012) ADSCrossRefGoogle Scholar
  56. 56.
    M. Goerz, E. Halperin, J.M. Aytac, C.P. Koch, K.B. Whaley, Phys. Rev. A 90, 032329 (2014) ADSCrossRefGoogle Scholar
  57. 57.
    C. Altafini, J. Math. Phys. 44, 2357 (2003) ADSMathSciNetMATHCrossRefGoogle Scholar
  58. 58.
    G. Dirr, U. Helmke, I. Kurniawan, T. Schulte-Herbrüggen, Rep. Math. Phys. 64, 93 (2009)ADSMathSciNetMATHCrossRefGoogle Scholar
  59. 59.
    C. O’Meara, G. Dirr, T. Schulte-Herbrüggen, IEEE Trans. Automat. Contr. (IEEE-TAC) 57, 2050 (2012) CrossRefGoogle Scholar
  60. 60.
    D. Reich, N. Katz, C. Koch, Sci. Rep. 5, 12430 (2015) ADSCrossRefGoogle Scholar
  61. 61.
    H.P. Breuer, E.M. Laine, J. Piilo, Phys. Rev. Lett. 103, 210401 (2009) ADSMathSciNetCrossRefGoogle Scholar
  62. 62.
    S. Lloyd, L. Viola, Phys. Rev. A 65, 010101 (2001) MathSciNetCrossRefGoogle Scholar
  63. 63.
    V. Bergholm, T. Schulte-Herbrüggen, arXiv:1206.4945 (2012)
  64. 64.
    Z. Zimborás, R. Zeier, T. Schulte-Herbrüggen, D. Burgarth, Phys. Rev. A 92, 042309 (2015) ADSCrossRefGoogle Scholar
  65. 65.
    D. Burgarth, K. Maruyama, M. Murphy, S. Montangero, T. Calarco, F. Nori, M. Plenio, Phys. Rev. A 81, 040303 (2010) ADSCrossRefGoogle Scholar
  66. 66.
    D.K. Burgarth, P. Facchi, V. Giovanetti, H. Nakazato, S. Pascazio, K. Yuasa, Nat. Commun. 5, 5173 (2014)ADSCrossRefGoogle Scholar
  67. 67.
    R.E. Kalman, J. Basic Eng. 82, 35 (1960)CrossRefGoogle Scholar
  68. 68.
    B. Bonnard, M. Chyba, Singular trajectories and their role in control theory, Mathematics and Applications (Springer-Verlag, Berlin, 2003), Vol. 40Google Scholar
  69. 69.
    U. Boscain, B. Piccoli, Optimal Synthesis for Control Systems on 2-D Manifolds, smai(Springer, 2004), Vol. 43 Google Scholar
  70. 70.
    B. Piccoli, H. Sussmann, SIAM J. Control Optim. 39, 359 (2000)MathSciNetMATHCrossRefGoogle Scholar
  71. 71.
    N. Khaneja, S. Glaser, R. Brockett, Phys. Rev. A 65, 032301 (2002) ADSMathSciNetCrossRefGoogle Scholar
  72. 72.
    U. Boscain, P. Mason, J. Math. Phys. 47, 062101 (2006) ADSMathSciNetCrossRefGoogle Scholar
  73. 73.
    D. D’Alessandro, M. Dahled, IEEE Trans. Automat. Control 46, 866 (2001)MathSciNetMATHCrossRefGoogle Scholar
  74. 74.
    U. Boscain, G. Charlot, J.P. Gauthier, S. Guérin, H.R. Jauslin, J. Math. Phys. 43, 2107 (2002) ADSMathSciNetMATHCrossRefGoogle Scholar
  75. 75.
    A. Garon, S.J. Glaser, D. Sugny, Phys. Rev. A 88, 043422 (2013) ADSCrossRefGoogle Scholar
  76. 76.
    B. Bonnard, M. Chyba, D. Sugny, IEEE Trans. Automat. Control 54, 2598 (2009) MathSciNetCrossRefGoogle Scholar
  77. 77.
    M. Lapert, Y. Zhang, M. Braun, S.J. Glaser, D. Sugny, Phys. Rev. Lett. 104, 083001 (2010) ADSCrossRefGoogle Scholar
  78. 78.
    N. Khaneja, B. Luy, S.J. Glaser, Proc. Natl. Acad. Sci. USA 100, 13162 (2003) ADSMathSciNetMATHCrossRefGoogle Scholar
  79. 79.
    N. Khaneja, J.S. Li, C. Kehlet, B. Luy, S. Glaser, Proc. Natl. Acad. Sci. USA 101, 14742 (2004) ADSCrossRefGoogle Scholar
  80. 80.
    D. Sugny, C. Kontz, H.R. Jauslin, Phys. Rev. A 76, 023419 (2007) ADSCrossRefGoogle Scholar
  81. 81.
    H. Yuan, C.P. Koch, P. Salamon, D. Tannor, Phys. Rev. A 85, 033417 (2012) ADSCrossRefGoogle Scholar
  82. 82.
    N. Khaneja, T. Reiss, B. Luy, S.J. Glaser, J. Magn. Reson. 162, 311 (2003) ADSCrossRefGoogle Scholar
  83. 83.
    T.O. Reiss, N. Khaneja, S.J. Glaser, J. Magn. Reson. 154, 192 (2002) ADSCrossRefGoogle Scholar
  84. 84.
    R.B. Wu, R. Long, J. Dominy, T.S. Ho, H. Rabitz, Phys. Rev. A 86, 013405 (2012) ADSCrossRefGoogle Scholar
  85. 85.
    H. Yuan, N. Khaneja, Phys. Rev. A 72, 040301 (2005) ADSCrossRefGoogle Scholar
  86. 86.
    H. Yuan, S.J. Glaser, N. Khaneja, Phys. Rev. A 76, 012316 (2007) ADSCrossRefGoogle Scholar
  87. 87.
    H. Yuan, N. Khaneja, Phys. Rev. A 84, 062301 (2011) ADSCrossRefGoogle Scholar
  88. 88.
    M. Lapert, Y. Zhang, M. Janich, S.J. Glaser, D. Sugny, Sci. Rep. 2, 589 (2012)ADSCrossRefGoogle Scholar
  89. 89.
    N. Khaneja, R. Brockett, S. Glaser, Phys. Rev. A 63, 032308 (2001) ADSCrossRefGoogle Scholar
  90. 90.
    N. Khaneja, S.J. Glaser, Chem. Phys. 267, 11 (2001)ADSCrossRefGoogle Scholar
  91. 91.
    U. Boscain, T. Chambrion, J.P. Gauthier, J. Dynam. Control Syst. 8, 547 (2002)MathSciNetMATHCrossRefGoogle Scholar
  92. 92.
    N. Khaneja, T. Reiss, C. Kehlet, T. Schulte-Herbrüggen, S. Glaser, J. Magn. Reson. 172, 296 (2005) ADSCrossRefGoogle Scholar
  93. 93.
    P. de Fouquieres, S.G. Schirmer, S.J. Glaser, I. Kuprov, J. Magn. Reson. 212, 412 (2011) ADSCrossRefGoogle Scholar
  94. 94.
    S. Machnes, U. Sander, S.J. Glaser, P. de Fouquières, A. Gruslys, S. Schirmer, T. Schulte-Herbrüggen, Phys. Rev. A 84, 022305 (2011) ADSCrossRefGoogle Scholar
  95. 95.
    G. Ciaramella, A. Borzì, G. Dirr, D. Wachsmuth, SIAM J. Sci. Comput. 37, A319 (2015) CrossRefGoogle Scholar
  96. 96.
    V.F. Krotov, Global Methods in Optimal Control (Marcel Dekker, New York, 1996)Google Scholar
  97. 97.
    Y. Maday, G. Turinici, J. Chem. Phys. 118, 8191 (2003) ADSCrossRefGoogle Scholar
  98. 98.
    D. Reich, M. Ndong, C. Koch, J. Chem. Phys. 136, 104103 (2012) ADSCrossRefGoogle Scholar
  99. 99.
    R. Eitan, M. Mundt, D. Tannor, Phys. Rev. A 83, 053426 (2011) ADSCrossRefGoogle Scholar
  100. 100.
    Z. Tošner, T. Vosegaard, C. Kehlet, N. Khaneja, S.J. Glaser, N. Nielsen, J. Magn. Reson. 197, 120 (2009) ADSCrossRefGoogle Scholar
  101. 101.
    H.J. Hogben, M. Krzystyniak, G.T.P. Charnock, P.J. Hore, I. Kuprov, J. Magn. Reson. 208, 179 (2011) ADSCrossRefGoogle Scholar
  102. 102.
    J.R. Johansson, P.D. Nation, F. Nori, Comput. Phys. Commun. 184, 1234 (2013) ADSCrossRefGoogle Scholar
  103. 103.
    J. Werschnik, E.K.U. Gross, J. Phys. B 40, 175 (2007)ADSMathSciNetCrossRefGoogle Scholar
  104. 104.
    T.E. Skinner, T.O. Reiss, B. Luy, N. Khaneja, S.J. Glaser, J. Magn. Reson. 167, 68 (2004)ADSCrossRefGoogle Scholar
  105. 105.
    A. Walther, B. Julsgaard, L. Rippe, Y. Ying, S. Kröll, R. Fisher, S. Glaser, Phys. Scr. T 137, 014009 (2009) ADSCrossRefGoogle Scholar
  106. 106.
    M. Janich, R. Schulte, M.M. Schwaiger, S. Glaser, J. Magn. Reson. 213, 126 (2011) ADSGoogle Scholar
  107. 107.
    F. Motzoi, J.M. Gambetta, S.T. Merkel, F.K. Wilhelm, Phys. Rev. A 84, 022307 (2011) ADSCrossRefGoogle Scholar
  108. 108.
    P.E. Spindler, Y. Zhang, B. Endeward, N. Gershernzon, T.E. Skinner, S. Glaser, T.F. Prisner, J. Magn. Reson. 218, 49 (2012)ADSCrossRefGoogle Scholar
  109. 109.
    D. Reich, J. Palao, C. Koch, J. Mod. Opt. 61, 822 (2014)ADSMathSciNetCrossRefGoogle Scholar
  110. 110.
    I.N. Hincks, C.E. Granade, T.W. Borneman, D.G. Cory, Phys. Rev. Appl. 4, 024012 (2015) ADSCrossRefGoogle Scholar
  111. 111.
    M. Lapert, R. Tehini, G. Turinici, D. Sugny, Phys. Rev. A 79, 063411 (2009) ADSCrossRefGoogle Scholar
  112. 112.
    A. Bartana, R. Kosloff, D.J. Tannor, J. Chem. Phys. 106, 1435 (1997) ADSCrossRefGoogle Scholar
  113. 113.
    S. Kallush, R. Kosloff, Phys. Rev. A 73, 032324 (2006) ADSCrossRefGoogle Scholar
  114. 114.
    T. Schulte-Herbrüggen, A. Spörl, N. Khaneja, S.J. Glaser, J. Phys. B 44, 154013 (2011) ADSCrossRefGoogle Scholar
  115. 115.
    R. Schmidt, A. Negretti, J. Ankerhold, T. Calarco, J.T. Stockburger, Phys. Rev. Lett. 107, 130404 (2011) ADSCrossRefGoogle Scholar
  116. 116.
    F. Floether, P. de Fouquieres, S. Schirmer, New J. Phys. 14, 073023 (2012) ADSCrossRefGoogle Scholar
  117. 117.
    M. Goerz, D. Reich, C. Koch, New J. Phys. 16, 055012 (2014) ADSMathSciNetCrossRefGoogle Scholar
  118. 118.
    T.E. Skinner, N.I. Gershenzon, J. Magn. Reson. 204, 248 (2010) ADSCrossRefGoogle Scholar
  119. 119.
    S. Meister, J.T. Stockburger, R. Schmidt, J. Ankerhold, J. Phys. A 47, 495002 (2014) MathSciNetCrossRefGoogle Scholar
  120. 120.
    S. Machnes, D.J. Tannor, F.K. Wilhelm, E. Assémat, arXiv:1507.04261 (2015)
  121. 121.
    D.V. Savostyanov, S.V. Dolgov, J.M. Werner, I. Kuprov, Phys. Rev. B 90, 085139 (2014) ADSCrossRefGoogle Scholar
  122. 122.
    P. Doria, T. Calarco, S. Montangero, Phys. Rev. Lett. 106, 190501 (2011) ADSCrossRefGoogle Scholar
  123. 123.
    T. Caneva, T. Calarco, S. Montangero, Phys. Rev. A 84, 022326 (2011) ADSCrossRefGoogle Scholar
  124. 124.
    V. Engel, C. Meier, D. Tannor, Local Control Theory: Recent Applications to Energy and Particle Transfer Processes in Molecules (John Wiley & Sons, Inc., 2009), Vol. 141, pp. 29–101 Google Scholar
  125. 125.
    M. Sugawara, J. Chem. Phys. 118, 6784 (2003) ADSCrossRefGoogle Scholar
  126. 126.
    X. Wang, S.G. Schirmer, IEEE Trans. Automat. Control 55, 2259 (2010) MathSciNetCrossRefGoogle Scholar
  127. 127.
    A. Peirce, M. Dahleh, H. Rabitz, Phys. Rev. A 37, 4950 (1987) ADSMathSciNetCrossRefGoogle Scholar
  128. 128.
    S. Lloyd, S. Montangero, Phys. Rev. Lett. 113, 010502 (2014) ADSCrossRefGoogle Scholar
  129. 129.
    R. Chakrabarti, H. Rabitz, Int. Rev. Phys. Chem. 26, 671 (2007)CrossRefGoogle Scholar
  130. 130.
    P. de Fouquieres, S.G. Schirmer, Infin. Dimens. Anal. Qu. 16, 1350021 (2013) CrossRefGoogle Scholar
  131. 131.
    A.N. Pechen, D.J. Tannor, Phys. Rev. Lett. 106, 120402 (2011) ADSCrossRefGoogle Scholar
  132. 132.
    H. Rabitz, T.S. Ho, R. Long, R. Wu, C. Brif, Phys. Rev. Lett. 108, 198901 (2012) ADSCrossRefGoogle Scholar
  133. 133.
    A.N. Pechen, D.J. Tannor, Phys. Rev. Lett. 108, 198902 (2012) ADSCrossRefGoogle Scholar
  134. 134.
    G. Riviello, K. Moore Tibbetts, C. Brif, R. Long, R.B. Wu, T.S. Ho, H. Rabitz, Phys. Rev. A 91, 043401 (2015) ADSCrossRefGoogle Scholar
  135. 135.
    K. Moore Tibbetts, H. Rabitz, Phys. Chem. Chem. Phys. 17, 3164 (2015) CrossRefGoogle Scholar
  136. 136.
    K. Bergmann, H. Theuer, B.W. Shore, Rev. Mod. Phys. 70, 1003 (1998) ADSCrossRefGoogle Scholar
  137. 137.
    N.V. Vitanov, T. Halfmann, B.W. Shore, K. Bergmann, Annu. Rev. Phys. Chem. 52, 763 (2001)ADSCrossRefGoogle Scholar
  138. 138.
    S. Guérin, H.R. Jauslin, Control of Quantum Dynamics by Laser Pulses: Adiabatic Floquet Theory (John Wiley & Sons, Inc., 2003), Vol. 125, pp. 147–267Google Scholar
  139. 139.
    S. Teufel, Adiabatic Perturbation Theory in Quantum Dynamics (Springer-Verlag, Berlin, 2003)Google Scholar
  140. 140.
    R. Adami, U. Boscain, Controllability of the Schrödinger Equation via Intersection of Eigenvalues, in 2005 and 2005 European Control Conference. CDC-ECC ’05. 44th IEEE Conference on Decision and Control (2005), pp. 1080–1085Google Scholar
  141. 141.
    U. Boscain, F. Chittaro, P. Mason, M. Sigalotti, IEEE Trans. Automat. Control 57, 1970 (2012) MathSciNetCrossRefGoogle Scholar
  142. 142.
    U. Boscain, J.P. Gauthier, F. Rossi, M. Sigalotti, Commun. Math. Phys. 333, 1225 (2015) ADSMathSciNetMATHCrossRefGoogle Scholar
  143. 143.
    E. Torrontegui, S. Ibná˜ez, S. Martínez-Garaot, M. Modugno, A. del Campo, D. Guéry-Odelin, A. Ruschhaupt, X. Chen, J.G. Muga, in Advances in Atomic, Molecular, and Optical Physics, edited by E. Arimondo, P.R. Berman, C.C. Lin (Academic Press, 2013), Vol. 62, pp. 117–169 Google Scholar
  144. 144.
    A. Ruschhaupt, X. Chen, D. Alonso, J.G. Muga, New J. Phys. 14, 093040 (2012) ADSCrossRefGoogle Scholar
  145. 145.
    X. Chen, I. Lizuain, A. Ruschhaupt, D. Guéry-Odelin, J.G. Muga, Phys. Rev. Lett. 105, 123003 (2010) ADSCrossRefGoogle Scholar
  146. 146.
    D. Daems, A. Ruschhaupt, D. Sugny, S. Guérin, Phys. Rev. Lett. 111, 050404 (2013) ADSCrossRefGoogle Scholar
  147. 147.
    Y. Ban, X. Chen, E.Y. Sherman, J.G. Muga, Phys. Rev. Lett. 109, 206602 (2012) ADSCrossRefGoogle Scholar
  148. 148.
    A. Joye, Commun. Math. Phys. 275, 139 (2007) ADSMathSciNetMATHCrossRefGoogle Scholar
  149. 149.
    M.S. Sarandy, D.A. Lidar, Phys. Rev. Lett. 95, 250503 (2005) ADSCrossRefGoogle Scholar
  150. 150.
    D.J. Egger, F.K. Wilhelm, Phys. Rev. Lett. 112, 240503 (2014) ADSCrossRefGoogle Scholar
  151. 151.
    H.P. Büchler, S. Diehl, A. Kantian, A. Micheli, P. Zoller, Phys. Rev. A 78, 042307 (2008) ADSCrossRefGoogle Scholar
  152. 152.
    F. Verstraete, M.M. Wolf, J.I. Cirac, Nat. Phys. 5, 633 (2009)CrossRefGoogle Scholar
  153. 153.
    H. Krauter, C. Muschik, K. Jensen, W. Wasilewski, J. Petersen, J.I. Cirac, E. Polzik, Phys. Rev. Lett. 107, 080503 (2011) ADSCrossRefGoogle Scholar
  154. 154.
    S.G. Schirmer, X. Wang, Phys. Rev. A 81, 062306 (2010) ADSCrossRefGoogle Scholar
  155. 155.
    A. Pechen, H. Rabitz, J. Math. Sci. 199, 695 (2014) MathSciNetMATHCrossRefGoogle Scholar
  156. 156.
    L. Bouten, R. van Handel, M. James, SIAM J. Control Optim. 46, 2199 (2007) MathSciNetMATHCrossRefGoogle Scholar
  157. 157.
    K.R. Parthasarathy, An introduction to quantum stochastic calculus (Birkhauser, Basel, 1992)Google Scholar
  158. 158.
    M. Annunziato, A. Borzi, Math. Modelling Anal. 15, 393 (2010)MathSciNetMATHCrossRefGoogle Scholar
  159. 159.
    Y. Zhang, M. Lapert, D. Sugny, M. Braun, S.J. Glaser, J. Chem. Phys. 134, 054103 (2011) ADSCrossRefGoogle Scholar
  160. 160.
    A. Doherty, S. Habib, K. Jacobs, H. Mabuchi, S. Tan, Phys. Rev. A 62, 012105 (2000) ADSCrossRefGoogle Scholar
  161. 161.
    R. Judson, H. Rabitz, Phys. Rev. Lett. 68, 1500 (1992) ADSCrossRefGoogle Scholar
  162. 162.
    N. Yamamoto, Phys. Rev. X 4, 041029 (2014) Google Scholar
  163. 163.
    H.M. Wiseman, G.J. Milburn, Phys. Rev. Lett. 70, 548 (1993)ADSCrossRefGoogle Scholar
  164. 164.
    S. Lloyd, Phys. Rev. A 62, 022108 (2000) ADSMathSciNetCrossRefGoogle Scholar
  165. 165.
    L. Bouten, R. van Handel, M. James, SIAM Rev. 51, 239 (2009)ADSMathSciNetMATHCrossRefGoogle Scholar
  166. 166.
    J. Combes, K. Jacobs, Phys. Rev. Lett. 96, 010504 (2006) ADSCrossRefGoogle Scholar
  167. 167.
    J. Combes, H. Wiseman, K. Jacobs, Phys. Rev. Lett. 100, 160503 (2008) ADSCrossRefGoogle Scholar
  168. 168.
    I. Sayrin et al., Nature 477, 73 (2011)ADSCrossRefGoogle Scholar
  169. 169.
    G. Kirchmair, B. Vlastakis, Z. Leghtas, S. Nigg, H. Paik, M. Ginossar, E. Mirrahimi, L. Frunzio, S. Girvin, R. Schoelkopf, Nature 495, 205 (2013) ADSCrossRefGoogle Scholar
  170. 170.
    M.R. James, H.I. Nurdin, I.R. Petersen, IEEE Trans. Automat. Control 53, 1787 (2008) MathSciNetCrossRefGoogle Scholar
  171. 171.
    J.E. Gough, S. Wildfeuer, Phys. Rev. A 80, 042107 (2009) ADSCrossRefGoogle Scholar
  172. 172.
    H. Mabuchi, Phys. Rev. A 78, 032323 (2008) ADSCrossRefGoogle Scholar
  173. 173.
    S. Iida, M. Yukawa, H. Yonezawa, N. Yamamoto, A. Furusawa, IEEE Trans. Automat. Control 57, 2045 (2012) CrossRefGoogle Scholar
  174. 174.
    V. Buzek, M. Hillery, M. Ziman, M. Rosko, Quant. Inf. Proc. 5, 313 (2006)MathSciNetMATHCrossRefGoogle Scholar
  175. 175.
    M. Hillery, V. Buzek, Contemp. Phys. 50, 575 (2009)ADSCrossRefGoogle Scholar
  176. 176.
    J.E. Reiner, W.P. Smith, L.A. Orozco, H.M. Wiseman, J. Gambetta, Phys. Rev. A 70, 023819 (2004) ADSCrossRefGoogle Scholar
  177. 177.
    L. Martin, F. Motzoi, H. Li, M. Sarovar, B. Whaley, arXiv:1506.07888 (2015)
  178. 178.
    D. Ristè, C.C. Bulting, K.W. Lehnert, L. DiCarlo, Phys. Rev. Lett. 109, 240502 (2012) ADSCrossRefGoogle Scholar
  179. 179.
    R. Vijay, C. Macklin, D.H. Slichter, S.J. Weber, K.W. Murch, R. Naik, A.N. Korotkov, I. Siddiqi, Nature 490, 77 (2012)ADSCrossRefGoogle Scholar
  180. 180.
    C. Emary, J. Gough, Phys. Rev. B 90, 205436 (2014) ADSCrossRefGoogle Scholar
  181. 181.
    D.J. Tannor, S.A. Rice, J. Chem. Phys. 83, 5013 (1985) ADSCrossRefGoogle Scholar
  182. 182.
    D. Tannor, R. Kosloff, S. Rice, J. Chem. Phys. 85, 5805 (1986) ADSCrossRefGoogle Scholar
  183. 183.
    R. Kosloff, S.A. Rice, P. Gaspard, S. Tersigni, D.J. Tannor, Chem. Phys. 139, 201 (1989) ADSCrossRefGoogle Scholar
  184. 184.
    S.A. Rice, M. Zhao, Optical control of molecular dynamics (John Wiley & Sons, 2000)Google Scholar
  185. 185.
    P. Brumer, M. Shapiro, Principles and Applications of the Quantum Control of Molecular Processes (Wiley Interscience, 2003)Google Scholar
  186. 186.
    A.M. Weiner, Rev. Sci. Instrum. 71, 1929 (2000) ADSCrossRefGoogle Scholar
  187. 187.
    A. Monmayrant, S. Weber, B. Chatel, J. Phys. B 43, 103001 (2010) ADSCrossRefGoogle Scholar
  188. 188.
    R.J. Gordon, S.A. Rice, Annu. Rev. Phys. Chem. 48, 601 (1997)ADSCrossRefGoogle Scholar
  189. 189.
    H. Rabitz, R. de Vivie Riedle, M. Motzkus, K. Kompa, Science 288, 824 (2000) ADSCrossRefGoogle Scholar
  190. 190.
    R.J. Levis, G.M. Menkir, H. Rabitz, Science 292, 709 (2001) ADSCrossRefGoogle Scholar
  191. 191.
    C. Daniel, J. Full, L. González, C. Lupulescu, J. Manz, A. Merli, S. Vajda, L. Wöste, Science 299, 536 (2003) ADSCrossRefGoogle Scholar
  192. 192.
    T. Brixner, G. Gerber, Chem. Phys. Chem. 4, 418 (2003)Google Scholar
  193. 193.
    M. Dantus, V.V. Lozovoy, Chem. Rev. 104, 1813 (2004) CrossRefGoogle Scholar
  194. 194.
    M. Wollenhaupt, V. Engel, T. Baumert, Ann. Rev. Phys. Chem. 56, 25 (2005)ADSCrossRefGoogle Scholar
  195. 195.
    P. Nuernberger, G. Vogt, T. Brixner, G. Gerber, Phys. Chem. Chem. Phys. 9, 2470 (2007)CrossRefGoogle Scholar
  196. 196.
    Analysis and Control of Ultrafast Photoinduced Reactions, edited by O. Kühn, L. Wöste (Springer, Berlin, 2007)Google Scholar
  197. 197.
    K. Hoki, P. Brumer, Phys. Rev. Lett. 95, 168305 (2005) ADSCrossRefGoogle Scholar
  198. 198.
    M. Spanner, P. Brumer, Phys. Rev. A 73, 023809 (2006) ADSCrossRefGoogle Scholar
  199. 199.
    M. Spanner, P. Brumer, Phys. Rev. A 73, 023810 (2006) ADSCrossRefGoogle Scholar
  200. 200.
    P. Brumer, K. Hoki, M. Spanner, Isr. J. Chem. 47, 111 (2007)CrossRefGoogle Scholar
  201. 201.
    T. Bayer, M. Wollenhaupt, C. Sarpe-Tudoran, T. Baumert, Phys. Rev. Lett. 102, 023004 (2009) ADSCrossRefGoogle Scholar
  202. 202.
    T. Bayer, M. Wollenhaupt, H. Braun, T. Baumert (2014), in Advances in Chemical Physics, 2015, 1–50, https://www.uni-kassel.de/fb10/institute/physik/forschungsgruppen/femtosekundenspektroskopie/veroeffentlichungen.html
  203. 203.
    C. Trallero-Herrero, D. Cardoza, T.C. Weinacht, J.L. Cohen, Phys. Rev. A 71, 013423 (2005) ADSCrossRefGoogle Scholar
  204. 204.
    C. Trallero-Herrero, J.L. Cohen, T. Weinacht, Phys. Rev. Lett. 96, 063603 (2006) ADSCrossRefGoogle Scholar
  205. 205.
    J.G. Underwood, M. Spanner, M.Y. Ivanov, J. Mottershead, B.J. Sussman, A. Stolow, Phys. Rev. Lett. 90, 223001 (2003) ADSCrossRefGoogle Scholar
  206. 206.
    B. Sussman, D. Townsend, M. Ivanov, A. Stolow, Science 314, 278 (2006) ADSCrossRefGoogle Scholar
  207. 207.
    T. Bayer, H. Braun, C. Sarpe, R. Siemering, P. von den Hoff, R. de Vivie-Riedle, T. Baumert, M. Wollenhaupt, Phys. Rev. Lett. 110, 123003 (2013) ADSCrossRefGoogle Scholar
  208. 208.
    D. Meshulach, Y. Silberberg, Nature 396, 239 (1998) ADSCrossRefGoogle Scholar
  209. 209.
    P. Brumer, M. Shapiro, Chem. Phys. 139, 221 (1989) ADSCrossRefGoogle Scholar
  210. 210.
    V.I. Prokhorenko, A.M. Nagy, S. Waschuk, L.S. Brown, R.R. Birge, R.D. Miller, Science 313, 1257 (2006) ADSCrossRefGoogle Scholar
  211. 211.
    P. van der Walle, M.T.W. Milder, L. Kuipers, J.L. Herek, Proc. Natl. Acad. Sci. USA 106, 7714 (2009) ADSCrossRefGoogle Scholar
  212. 212.
    G. Katz, M. Ratner, R. Kosloff, New J. Phys. 12, 015003 (2010) ADSCrossRefGoogle Scholar
  213. 213.
    M. Am-Shallem, R. Kosloff, J. Chem. Phys. 141, 044121 (2014) ADSCrossRefGoogle Scholar
  214. 214.
    U. Marvet, M. Dantus, Chem. Phys. Lett. 245, 393 (1995) ADSCrossRefGoogle Scholar
  215. 215.
    P. Gross, M. Dantus, J. Chem. Phys. 106, 8013 (1997) ADSCrossRefGoogle Scholar
  216. 216.
    W. Salzmann et al., Phys. Rev. Lett. 100, 233003 (2008) ADSCrossRefGoogle Scholar
  217. 217.
    P. Nuernberger, D. Wolpert, H. Weiss, G. Gerber, Proc. Natl. Acad. Sci. USA 107, 10366 (2010) ADSCrossRefGoogle Scholar
  218. 218.
    A. Merli et al., Phys. Rev. A 80, 063417 (2009) ADSCrossRefGoogle Scholar
  219. 219.
    L. Rybak, S. Amaran, M. Levin, L.and Tomza, R. Moszynski, R. Kosloff, C. Koch, Z. Amitay, Phys. Rev. Lett. 107, 273001 (2011) ADSCrossRefGoogle Scholar
  220. 220.
    C. Koch, M. Shapiro, Chem. Rev. 212, 4928 (2012) CrossRefGoogle Scholar
  221. 221.
    S. Amaran, R. Kosloff, M. Tomza, R. Moszynski, L. Rybak, L. Levin, Z. Amitay, J.M. Berglund, D.M. Reich, C.P. Koch, J. Chem. Phys. 139, 164124 (2013) ADSCrossRefGoogle Scholar
  222. 222.
    L. Levin, W. Skomorowski, R. Kosloff, Z. Koch, and C.P. Amitay, Phys. Rev. Lett. 114, 233003 (2015)ADSCrossRefGoogle Scholar
  223. 223.
    H. Stapelfeldt, T. Seideman, Rev. Mod. Phys. 75, 543 (2003)ADSCrossRefGoogle Scholar
  224. 224.
    T. Seideman, E. Hamilton, Adv. At. Mol. Opt. Phys. 52, 289 (2006)ADSCrossRefGoogle Scholar
  225. 225.
    D. Sugny, A. Keller, O. Atabek, D. Daems, C.M. Dion, S. Guérin, H.R. Jauslin, Phys. Rev. A 69, 033402 (2004) ADSCrossRefGoogle Scholar
  226. 226.
    H. Katsuki, H. Chiba, B. Girard, C. Meier, K. Ohmori, Science 311, 1589 (2006) ADSCrossRefGoogle Scholar
  227. 227.
    M. Aeschlimann, M. Bauer, D. Bayer, T. Brixner, F.J. García de Abajo, W. Pfeiffer, M. Rohmer, C. Spindler, F. Steeb, Nature 446, 301 (2007) ADSCrossRefGoogle Scholar
  228. 228.
    W. Pfeiffer, M. Aeschlimann, T. Brixner, Optical Antennas (Cambridge University Press, 2013), pp. 135–156, eds. M. Agio & A. AlúGoogle Scholar
  229. 229.
    A. Bartana, R. Kosloff, D.J. Tannor, Chem. Phys. 267, 195 (2001) ADSCrossRefGoogle Scholar
  230. 230.
    D. Sofikitis, S. Weber, A. Fioretti, R. Horchani, M. Allegrini, B. Chatel, P. Comparat, D. Pillet, New J. Phys. 11, 055037 (2009) ADSCrossRefGoogle Scholar
  231. 231.
    C.Y. Lien, C.M. Seck, Y.W. Lin, J.H.V. Nguyen, D.A. Tabor, B.C. Odom, Nat. Commun. 5, 4783 (2014)ADSCrossRefGoogle Scholar
  232. 232.
    D. Reich, C.P. Koch, New J. Phys. 15, 125028 (2013) ADSCrossRefGoogle Scholar
  233. 233.
    C. Koch, J.P. Palao, R. Kosloff, F. Masnou-Seeuws, Phys. Rev. A 70, 013402 (2004) ADSCrossRefGoogle Scholar
  234. 234.
    M.J. Wright, S.D. Gensemer, J. Vala, R. Kosloff, P.L. Gould, Phys. Rev. Lett. 95, 063001 (2005) ADSCrossRefGoogle Scholar
  235. 235.
    J. Danzl, E. Haller, M. Gustavsson, M. Mark, R. Hart, N. Bouloufa, O. Dulieu, H. Ritsch, H.C. Nägerl, Science 321, 1062 (2008) ADSCrossRefGoogle Scholar
  236. 236.
    K.K. Ni, S. Ospelkaus, M.H.G. de Miranda, A. Pe’er, B. Neyenhuis, J.J. Zirbel, S. Kotochigova, P.S. Julienne, D.S. Jin, J. Ye, Science 322, 231 (2008) ADSCrossRefGoogle Scholar
  237. 237.
    X. Li, C. Menzel-Jones, D. Avisar, M. Shapiro, Phys. Chem. Chem. Phys. 12, 15760 (2010) CrossRefGoogle Scholar
  238. 238.
    D. Avisar, D.J. Tannor, Phys. Rev. Lett. 106, 170405 (2011) ADSCrossRefGoogle Scholar
  239. 239.
    D. Avisar, D.J. Tannor, J. Chem. Phys. 136, 214107 (2012) ADSCrossRefGoogle Scholar
  240. 240.
    J. Herek, M. Wohlleben, X. Cogdell, X. Zeidler, M. Motzkus, Nature 417, 533 (2002) ADSCrossRefGoogle Scholar
  241. 241.
    T. Caruso, S. Montangero, T. Calarco, S. Huelga, M. Plenio, Phys. Rev. A 85, 042331 (2012) ADSCrossRefGoogle Scholar
  242. 242.
    Y. Hover, F. Caruso, S. Montangero, T. Sarovar, T. Calarco, M.B. Plenio, K.B. Whaley, New J. Phys. 16, 045007 (2014) ADSCrossRefGoogle Scholar
  243. 243.
    N. Dudovich, D. Oron, Y. Silberberg, Nature 418, 512 (2002) ADSCrossRefGoogle Scholar
  244. 244.
    P. Hamm, M. Zanni, Concepts and Methods of 2D Infrared Spectroscopy (Cambridge University Press, 2011)Google Scholar
  245. 245.
    A.L. Serrano, J.S. Ghosh, A. Ostrander, M.T. Zanni, Opt. Express 23, 17815 (2015) ADSCrossRefGoogle Scholar
  246. 246.
    H. Frostig, T. Bayer, N. Dudovich, Y.C. Eldar, Y. Silberberg, Nat. Photon. 9, 339 (2015)ADSCrossRefGoogle Scholar
  247. 247.
    I. Pastirk, J. Dela-Cruz, K. Walowicz, V. Lozovoy, M. Dantus, Opt. Express 11, 1695 (2003) ADSCrossRefGoogle Scholar
  248. 248.
    J.M. Dela Cruz, I. Pastirk, M. Comstock, V.V. Lozovoy, M. Dantus, Proc. Natl. Acad. Sci. USA 101, 16996 (2004) ADSCrossRefGoogle Scholar
  249. 249.
    O. Katz, E. Small, Y. Bromberg, Y. Silberberg, Nat. Photon. 5, 372 (2011)ADSCrossRefGoogle Scholar
  250. 250.
    O. Katz, E. Small, Y. Silberberg, Nat. Photon. 6, 549 (2012)ADSCrossRefGoogle Scholar
  251. 251.
    D. Oron, E. Tal, Y. Silberberg, Opt. Express 13, 1468 (2005) ADSCrossRefGoogle Scholar
  252. 252.
    J. Ogilvie, D. Débarre, X. Solinas, J. Martin, E. Beaurepaire, M. Joffre, Opt. Express 14, 759 (2006)ADSCrossRefGoogle Scholar
  253. 253.
    R.S.C. Pillai, C. Boudoux, G. Labroille, N. Olivier, I. Veilleux, E. Farge, M. Joffre, E. Beaurepaire, Opt. Express 17, 12741 (2009) ADSCrossRefGoogle Scholar
  254. 254.
    J. Rehbinder, L. Brückner, A. Wipfler, T. Buckup, M. Motzkus, Opt. Express 22, 28790 (2014) ADSCrossRefGoogle Scholar
  255. 255.
    H. Li, D.A. Harris, B. Xu, P. Wrzesinski, V. Lozovoy, M. Dantus, Opt. Express 16, 5499 (2008) ADSCrossRefGoogle Scholar
  256. 256.
    F. Courvoisier, L. Bonacina, V. Boutou, L. Guyon, C. Bonnet, B. Thuillier, J. Extermann, M. Roth, H. Rabitz, J. Wolf, Farad. Discuss. 137, 37 (2008)ADSCrossRefGoogle Scholar
  257. 257.
    D. Kiselev, L. Bonacina, J. Wolf, Opt. Express 19, 24516 (2011) ADSCrossRefGoogle Scholar
  258. 258.
    A. Steinbacher, P. Nuernberger, T. Brixner, Phys. Chem. Chem. Phys. 17, 6340 (2015) CrossRefGoogle Scholar
  259. 259.
    T. Matthews, I.R. Piletic, M. Selim, M. Simpson, W. Warren, Sci. Transl. Med. 3, 71ra15 (2011)CrossRefGoogle Scholar
  260. 260.
    L. Englert, M. Wollenhaupt, L. Haag, C. Sarpe-Tudoran, B. Rethfeld, T. Baumert, Appl. Phys. A 92, 749 (2008)ADSCrossRefGoogle Scholar
  261. 261.
    T. Bohinski, K. Moore-Tibbetts, M. Tarazkar, D.A. Romanov, S. Matsika, R.J. Levis, J. Phys. Chem. Lett. 5, 4305 (2014)CrossRefGoogle Scholar
  262. 262.
    K. Moore-Tibbetts, M. Tarazkar, T. Bohinski, D.A. Romanov, S. Matsika, R. Levis, J. Phys. B 48, 164002 (2015) ADSCrossRefGoogle Scholar
  263. 263.
    L. Greenman, C. Koch, K.B. Whaley, Phys. Rev. A 92, 013407 (2015) ADSCrossRefGoogle Scholar
  264. 264.
    I. Serban, J. Werschnik, E.K.U. Gross, Phys. Rev. A 71, 053810 (2005) ADSCrossRefGoogle Scholar
  265. 265.
    I. Schaefer, R. Kosloff, Phys. Rev. A 86, 063417 (2012) ADSCrossRefGoogle Scholar
  266. 266.
    D. Tannor, V. Kazakov, V. Orlov, in Time-dependent quantum molecular dynamics, edited by J. Broeckhove, L. Lathouwers (Plenum, 1992), pp. 347–360Google Scholar
  267. 267.
    J. Somlói, V.A. Kazakovski, D.J. Tannor, Chem. Phys. 172, 85 (1993)ADSCrossRefGoogle Scholar
  268. 268.
    P. Gross, D. Neuhauser, H. Rabitz, J. Chem. Phys. 96, 2834 (1992) ADSCrossRefGoogle Scholar
  269. 269.
    W. Zhu, J. Botina, H. Rabitz, J. Chem. Phys. 108, 1953 (1998) ADSCrossRefGoogle Scholar
  270. 270.
    Y.J. Yan, R.E. Gillilan, R.M. Whitnell, K.R. Wilson, S. Mukamel, J. Phys. Chem. 97, 2320 (1993) CrossRefGoogle Scholar
  271. 271.
    J. Salomon, C. Dion, G. Turinici, J. Chem. Phys. 123, 144310 (2005) ADSCrossRefGoogle Scholar
  272. 272.
    M. Lapert, D. Sugny, Phys. Rev. A 85, 063418 (2012) ADSCrossRefGoogle Scholar
  273. 273.
    S. Ramakrishna, T. Seideman, Phys. Rev. Lett. 95, 113001 (2005) ADSCrossRefGoogle Scholar
  274. 274.
    M.Z. Hoque, M. Lapert, E. Hertz, F. Billard, D. Sugny, B. Lavorel, O. Faucher, Phys. Rev. A 84, 013409 (2011) ADSCrossRefGoogle Scholar
  275. 275.
    C. Gollub, M. Kowalewski, R. de Vivie Riedle, Phys. Rev. Lett. 101, 073002 (2008)ADSCrossRefGoogle Scholar
  276. 276.
    M. Schröder, A. Brown, New J. Phys. 11, 105031 (2009) CrossRefGoogle Scholar
  277. 277.
    J. Palao, D.M. Reich, C.P. Koch, Phys. Rev. A 88, 053409 (2013) ADSCrossRefGoogle Scholar
  278. 278.
    A. Hansen, M. Sørensen, P. Staanum, M. Drewsen, Angew. Chem. Int. Ed. 51, 7960 (2012) CrossRefGoogle Scholar
  279. 279.
    R. Rugango, J.E. Goeders, T.H. Dixon, J. Gray, N. Khanyile, G. Shu, R. Clark, K. Brown, New J. Phys. 17, 035009 (2015) ADSCrossRefGoogle Scholar
  280. 280.
    R. Ernst, G. Bodenhausen, A. Wokaun, Principles of Nuclear Magnetic Resonance in One and Two Dimensions (Clarendon Press Oxford, 1987)Google Scholar
  281. 281.
    A. Abragam, The Principles of Nuclear Magnetism (Oxford University Press, Oxford, 1961)Google Scholar
  282. 282.
    M.H. Levitt, Spin Dynamics: Basics of Nuclear Magnetic Resonance (Wiley, 2001)Google Scholar
  283. 283.
    A. Schweiger, G. Jeschke, Principles of Pulse Electron Paramagnetic Resonance (Oxford University Press, 2001) Google Scholar
  284. 284.
    M.A. Bernstein, K.F. King, Zhou, Handbook of MRI Pulse Sequences (Elsevier, Burlington-San Diego-London, 2004) Google Scholar
  285. 285.
    R. Ernst, Angew. Chem. Internat Ed. 31, 805 (1992)CrossRefGoogle Scholar
  286. 286.
    K. Wüthrich, Angew. Chem. Int. Ed. 42, 3340 (2003) CrossRefGoogle Scholar
  287. 287.
    P. Mansfield, Angew. Chem. Int. Ed. 43, 5456 (2004) CrossRefGoogle Scholar
  288. 288.
    T. Kaufmann, J.M. Franck, T.J. Keller, R.P. Barnes, S.J. Glaser, J.M. Martinis, S. Han, J. Magn. Reson. 235, 95 (2013)ADSCrossRefGoogle Scholar
  289. 289.
    K. Kobzar, B. Luy, N. Khaneja, S.J. Glaser, J. Magn. Reson. 173, 229 (2005) ADSCrossRefGoogle Scholar
  290. 290.
    L.M.K. Vandersypen, I.L. Chuang, Rev. Mod. Phys. 76, 1037 (2005) ADSCrossRefGoogle Scholar
  291. 291.
    C.A. Ryan, C. Negrevergne, M. Laforest, E. Knill, R. Laflamme, Phys. Rev. A 78, 012328 (2008) ADSCrossRefGoogle Scholar
  292. 292.
    J.A. Jones, Prog. Nucl. Magn. Reson. Spectrosc. 59, 91 (2011)CrossRefGoogle Scholar
  293. 293.
    N.A. Kurnit, I.D. Abella, S.R. Hartmann, Phys. Rev. Lett. 13, 567 (1964)ADSCrossRefGoogle Scholar
  294. 294.
    F. Jelezko, J. Wrachtrup, Phys. Status Solidi A 203, 3207 (2006) ADSCrossRefGoogle Scholar
  295. 295.
    T. Häberle, D. Schmid-Lorch, K. Karrai, F. Reinhard, J. Wrachtrup, Phys. Rev. Lett. 111, 170801 (2013) CrossRefGoogle Scholar
  296. 296.
    F. Dolde et al., Nat. Commun. 5, 3371 (2014)ADSCrossRefGoogle Scholar
  297. 297.
    A. Viale, S. Aime, Curr. Opin. Chem. Biol. 14, 90 (2010)CrossRefGoogle Scholar
  298. 298.
    S.B. Duckett, R.E. Mewis, Acc. Chem. Res. 45, 1247 (2012) CrossRefGoogle Scholar
  299. 299.
    L.T. Kuhn, Hyperpolarization Methods in NMR Spectroscopy (Springer, 2013)Google Scholar
  300. 300.
    A.W. Overhauser, Phys. Rev. 92, 411 (1953)ADSMATHCrossRefGoogle Scholar
  301. 301.
    Q.Z. Ni, E. Daviso, T. Can, E. Markhasin, S. Jawla, T. Swager, R. Temkin, J. Herzfeld, R. Griffin, Acc. Chem. Res. 46, 1933 (2013) CrossRefGoogle Scholar
  302. 302.
    C. Griesinger, M. Bennati, H.M. Vieth, C. Luchinat, G. Parigi, P. Höfer, F. Engelke, S.J. Glaser, V. Denysenkov, T.F. Prisner, Prog. Nucl. Magn. Reson. Spectrosc. 64, 4 (2012)CrossRefGoogle Scholar
  303. 303.
    C.R. Bowers, D.P. Weitekamp, Phys. Rev. Lett. 57, 2645 (1986) ADSCrossRefGoogle Scholar
  304. 304.
    F. Jelezko, T. Gaebel, I. Popa, M. Domhan, A. Gruber, J. Wrachtrup, Phys. Rev. Lett. 93, 130501 (2004) ADSCrossRefGoogle Scholar
  305. 305.
    C. Müller et al., Nat. Commun. 5, 4703 (2014)CrossRefGoogle Scholar
  306. 306.
    D.D. Awschalom, L.C. Bassett, A.S. Dzurak, E.L. Hu, J.R. Petta, Science 339, 1174 (2013) ADSCrossRefGoogle Scholar
  307. 307.
    J.J. Pla, K.Y. Tan, J.P. Dehollain, W.H. Lim, J.J.L. Morton, F.A. Zwanenburg, D.N. Jamieson, A.S. Dzurak, A. Morello, Nature 496, 334 (2013) ADSCrossRefGoogle Scholar
  308. 308.
    E.L. Hahn, Phys. Rev. 80, 580 (1950)ADSMATHCrossRefGoogle Scholar
  309. 309.
    U. Haeberlen, The Principles of Nuclear Magnetism (Academic Press, New York, 1976)Google Scholar
  310. 310.
    M.H. Levitt, Prog. Nucl. Magn. Reson. Spectrosc. 18, 61 (1986)ADSCrossRefGoogle Scholar
  311. 311.
    M.H. Levitt, Composite pulses (Wiley, 1996)Google Scholar
  312. 312.
    R. Freeman, Prog. Nucl. Magn. Reson. Spectrosc. 32, 59 (1998)CrossRefGoogle Scholar
  313. 313.
    T.O. Reiss, N. Khaneja, S.J. Glaser, J. Magn. Reson. 165, 95 (2003)ADSCrossRefGoogle Scholar
  314. 314.
    N. Khaneja, B. Heitmann, A. Spörl, H. Yuan, T. Schulte-Herbrüggen, S.J. Glaser, Phys. Rev. A 75, 012322 (2007) ADSCrossRefGoogle Scholar
  315. 315.
    D. Stefanatos, N. Khaneja, S.J. Glaser, Phys. Rev. A 69, 022319 (2004) ADSCrossRefGoogle Scholar
  316. 316.
    M. Lapert, E. Assémat, S.J. Glaser, D. Sugny, Phys. Rev. A 90, 023411 (2014) ADSCrossRefGoogle Scholar
  317. 317.
    M. Lapert, E. Assémat, S.J. Glaser, D. Sugny, J. Chem. Phys. 142, 044202 (2015) ADSCrossRefGoogle Scholar
  318. 318.
    J.B. Murdoch, A.H. Lent, M.R. Kritzer, J. Magn. Reson. 74, 226 (1987)ADSGoogle Scholar
  319. 319.
    S.J. Glaser, G. Drobny, Chem. Phys. Lett. 164, 456 (1989) ADSCrossRefGoogle Scholar
  320. 320.
    H. Liu, S.J. Glaser, G. Drobny, J. Chem. Phys. 93, 7543 (1990) ADSCrossRefGoogle Scholar
  321. 321.
    R. Freeman, X. Wu, J. Magn. Reson. 75, 184 (1987)ADSGoogle Scholar
  322. 322.
    R. Freeman, Chem. Rev. 91, 1397 (1991) CrossRefGoogle Scholar
  323. 323.
    T. Untidt, T. Schulte-Herbrüggen, B. Luy, S. Glaser, C. Griesinger, O. Sorensen, N. Nielsen, Mol. Phys. 95, 787 (1998)ADSCrossRefGoogle Scholar
  324. 324.
    S. Conolly, D. Nishimura, A. Macovski, IEEE Trans. Med. Imag. MI-5, 106 (1986)CrossRefGoogle Scholar
  325. 325.
    J. Mao, T.H. Mareci, K.N. Scott, E.R. Andrew, J. Magn. Reson. 70, 310 (1986)ADSGoogle Scholar
  326. 326.
    D. Rosenfeld, Y. Zur, Magn. Reson. Med. 36, 401 (1996)CrossRefGoogle Scholar
  327. 327.
    J.S. Li, J. Ruths, T.Y. Yu, H. Arthanari, G. Wagner, Proc. Natl. Acad. Sci. USA 108, 1879 (2011) ADSCrossRefGoogle Scholar
  328. 328.
    L.J. Edwards, D.V. Savostyanov, Z.T. Welderufael, D. Lee, I. Kuprov, J. Magn. Reson. 243, 107 (2014) ADSCrossRefGoogle Scholar
  329. 329.
    G. Matson, Magn. Reson. Imag. 12, 1205 (1994) CrossRefGoogle Scholar
  330. 330.
    H. Liu, G. Matson, Magn. Reson. Med. 66, 1254 (2011) CrossRefGoogle Scholar
  331. 331.
    S.J. Glaser, G.P. Drobny, Adv. Magn. Opt. Reson. 14, 35 (1990)CrossRefGoogle Scholar
  332. 332.
    K. Kobzar, Ph.D. thesis, Technische Universität München (TUM), 2007Google Scholar
  333. 333.
    S. Ehni, Ph.D. thesis, Karlsruhe Institute of Technology, 2013Google Scholar
  334. 334.
    S.A. Smith, T.O. Levante, B.H. Meier, R.R. Ernst, J. Magn. Reson. 106, 75 (1994)ADSCrossRefGoogle Scholar
  335. 335.
    M. Veshtort, R.G. Griffin, J. Magn. Reson. 178, 248 (2006) ADSCrossRefGoogle Scholar
  336. 336.
    D.J. Tannor, A. Bartana, J. Phys. Chem. A 103, 10359 (1999) CrossRefGoogle Scholar
  337. 337.
    U. Boscain, T. Chambrion, G. Charlot, Discrete Contin. Dyn. Syst. Ser. B 5, 957 (2005)MathSciNetMATHCrossRefGoogle Scholar
  338. 338.
    M. Lapert, Y. Zhang, S.J. Glaser, D. Sugny, J. Phys. B 44, 154014 (2011) ADSCrossRefGoogle Scholar
  339. 339.
    A.D. Boozer, Phys. Rev. A 85, 013409 (2012) CrossRefGoogle Scholar
  340. 340.
    V. Mukherjee, A. Carlini, A. Mari, T. Caneva, M. S. T. Carlarco, R. Fazio, V. Giovannetti, Phys. Rev. A 88, 062326 (2013) ADSCrossRefGoogle Scholar
  341. 341.
    M. Lapert, E. Assémat, S.J. Glaser, D. Sugny, Phys. Rev. A 88, 033407 (2013) ADSCrossRefGoogle Scholar
  342. 342.
    F. Albertini, D. D’Alessandro, J. Math. Phys. 56, 012106 (2015)ADSMathSciNetCrossRefGoogle Scholar
  343. 343.
    T.E. Skinner, N.I. Gershenzon, M. Nimbalkar, W. Bermel, B. Luy, S.J. Glaser, J. Magn. Reson. 216, 78 (2012)ADSCrossRefGoogle Scholar
  344. 344.
    N.I. Gershenzon, T.E. Skinner, B. Brutscher, N. Khaneja, M. Nimbalkar, B. Luy, S. Glaser, J. Magn. Reson. 192, 235 (2008) ADSCrossRefGoogle Scholar
  345. 345.
    N.I. Gershenzon, K. Kobzar, B. Luy, S. Glaser, T. Skinner, J. Magn. Reson. 188, 330 (2007) ADSCrossRefGoogle Scholar
  346. 346.
    T.E. Skinner, K. Kobzar, B. Luy, M.R. Bendall, W. Bermel, N. Khaneja, S.J. Glaser, J. Magn. Reson. 179, 241 (2006) ADSCrossRefGoogle Scholar
  347. 347.
    T.E. Skinner, T.O. Reiss, B. Luy, N. Khaneja, S.J. Glaser, J. Magn. Reson. 172, 17 (2005)ADSCrossRefGoogle Scholar
  348. 348.
    T.E. Skinner, T. Reiss, B. Luy, N. Khaneja, S.J. Glaser, J. Magn. Reson. 163, 8 (2003)ADSCrossRefGoogle Scholar
  349. 349.
    E. Assémat, M. Lapert, Y. Zhang, M. Braun, S.J. Glaser, D. Sugny, Phys. Rev. A 82, 013415 (2010) ADSCrossRefGoogle Scholar
  350. 350.
    E. Assémat, L. Attar, M.J. Penouilh, M. Picquet, A. Tabard, Y. Zhang, S.J. Glaser, D. Sugny, Chem. Phys. 405, 71 (2012)ADSCrossRefGoogle Scholar
  351. 351.
    C.H. Bennett, I. Cirac, M.S. Leifer, D.W. Leung, N. Linden, S. Popescu, G. Vidal, Phys. Rev. A 66, 012305 (2002) ADSMathSciNetCrossRefGoogle Scholar
  352. 352.
    G. Vidal, K. Hammerer, J.I. Cirac, Phys. Rev. Lett. 88, 237902 (2002) ADSCrossRefGoogle Scholar
  353. 353.
    K. Hammerer, G. Vidal, J.I. Cirac, Phys. Rev. A 66, 062321 (2002) ADSCrossRefGoogle Scholar
  354. 354.
    N. Khaneja, F. Kramer, S.J. Glaser, J. Magn. Reson. 173, 116 (2005) ADSCrossRefGoogle Scholar
  355. 355.
    S. Ehni, B. Luy, J. Magn. Reson. 232, 7 (2013)ADSCrossRefGoogle Scholar
  356. 356.
    N. Khaneja, S.J. Glaser, Phys. Rev. A 66, 060301 (2002) ADSMathSciNetCrossRefGoogle Scholar
  357. 357.
    S. Bose, Phys. Rev. Lett. 91, 207901 (2003) ADSCrossRefGoogle Scholar
  358. 358.
    R. Zeier, M. Grassl, T. Beth, Phys. Rev. A 70, 032319 (2004) ADSCrossRefGoogle Scholar
  359. 359.
    D. Stefanatos, N. Khaneja, S.J. Glaser, Phys. Rev. A 72, 062320 (2005) ADSCrossRefGoogle Scholar
  360. 360.
    T. Schulte-Herbrüggen, A.K. Spörl, N. Khaneja, S.J. Glaser, Phys. Rev. A 72, 042331 (2005) ADSCrossRefGoogle Scholar
  361. 361.
    A. Carlini, A. Hosoya, T. Koike, Y. Okudaira, Phys. Rev. Lett. 96, 060503 (2006) ADSCrossRefGoogle Scholar
  362. 362.
    H. Yuan, R. Zeier, N. Khaneja, Phys. Rev. A 77, 032340 (2008) ADSCrossRefGoogle Scholar
  363. 363.
    S.G. Schirmer, P.J. Pemberton-Ross, Phys. Rev. A 80, 030301 (2009) ADSCrossRefGoogle Scholar
  364. 364.
    X. Wang, A. Bayat, S. Bose, S. Schirmer, Phys. Rev. A 82, 012330 (2010) ADSCrossRefGoogle Scholar
  365. 365.
    X. Wang, A. Bayat, S.G. Schirmer, S. Bose, Phys. Rev. A 81, 032312 (2010) ADSCrossRefGoogle Scholar
  366. 366.
    A. Carlini, A. Hosoya, T. Koike, Y. Okudaira, J. Phys. A 44, 145302 (2011) ADSMathSciNetCrossRefGoogle Scholar
  367. 367.
    M. Lapert, J. Salomon, D. Sugny, Phys. Rev. A 85, 033406 (2012) ADSCrossRefGoogle Scholar
  368. 368.
    A. Carlini, T. Koike, Phys. Rev. A 86, 054302 (2012) ADSCrossRefGoogle Scholar
  369. 369.
    M. Nimbalkar, R. Zeier, J.L. Neves, H. Elavarasi, S. B. Yuan, N. Khaneja, K. Dorai, S.J. Glaser, Phys. Rev. A 85, 012325 (2012) ADSCrossRefGoogle Scholar
  370. 370.
    A. Carlini, T. Koike, J. Phys. A 46, 045307 (2013) ADSMathSciNetCrossRefGoogle Scholar
  371. 371.
    B. Bonnard, O. Cots, N. Shcherbakova, Math. Control Relat. Fields 3, 287 (2013)MathSciNetMATHCrossRefGoogle Scholar
  372. 372.
    B. Bonnard, O. Cots, J.B. Pomet, N. Shcherbakova, ESAIM Control Optim. Calc. Var. 20, 864 (2014)MathSciNetMATHCrossRefGoogle Scholar
  373. 373.
    H. Yuan, D. Wei, Y. Zhang, S. Glaser, N. Khaneja, Phys. Rev. A 89, 042315 (2014) ADSCrossRefGoogle Scholar
  374. 374.
    L. Van Damme, R. Zeier, S.J. Glaser, D. Sugny, Phys. Rev. A 90, 013409 (2014) ADSCrossRefGoogle Scholar
  375. 375.
    S. Ehni, B. Luy, J. Magn. Reson. 247, 111 (2014) ADSCrossRefGoogle Scholar
  376. 376.
    M. Nimbalkar, B. Luy, T.E. Skinner, J.L. Neves, N.I. Gershenzon, K. Kobzar, W. Bermel, S.J. Glaser, J. Magn. Reson. 228, 16 (2013)ADSCrossRefGoogle Scholar
  377. 377.
    J.L. Neves, B. Heitmann, N. Khaneja, S.J. Glaser, J. Magn. Reson. 201, 7 (2009)ADSCrossRefGoogle Scholar
  378. 378.
    F. Schilling, N.I. Warner, T.E. Gershenzon, M. Sattler, S.J. Glaser, Angew. Chem. Int. Ed. 53, 4475 (2014) CrossRefGoogle Scholar
  379. 379.
    F. Schilling, S.J. Glaser, J. Magn. Reson. 223, 207 (2012) ADSCrossRefGoogle Scholar
  380. 380.
    G. Zhang, F. Schilling, S.J. Glaser, C. Hilty, Anal. Chem. 85, 2875 (2013) CrossRefGoogle Scholar
  381. 381.
    V.D.M. Koroleva, S. Mandal, Y.Q. Song, M.D. Hürlimann, J. Magn. Reson. 230, 64 (2013)ADSCrossRefGoogle Scholar
  382. 382.
    T.W. Borneman, M.D. Hürlimann, D.G. Cory, J. Magn. Reson. 207, 220 (2010) ADSCrossRefGoogle Scholar
  383. 383.
    S. Mandal, T.W. Borneman, V.D.M. Koroleva, M.D. Hürlimann, J. Magn. Reson. 247, 54 (2014)ADSCrossRefGoogle Scholar
  384. 384.
    M. Braun, S.J. Glaser, J. Magn. Reson 207, 114 (2010) ADSCrossRefGoogle Scholar
  385. 385.
    M. Braun, S.J. Glaser, New J. Phys. 16, 115002 (2014) ADSCrossRefGoogle Scholar
  386. 386.
    A. Enthart, J.C. Freudenberger, J. Furrer, H. Kessler, B. Luy, J. Magn. Reson. 192, 314 (2008) ADSCrossRefGoogle Scholar
  387. 387.
    P. Tzvetkova, S. Simova, B. Luy, J. Magn. Reson. 186, 193 (2007) ADSCrossRefGoogle Scholar
  388. 388.
    T. Reinsperger, B. Luy, J. Magn. Reson. 239, 110 (2014) ADSCrossRefGoogle Scholar
  389. 389.
    D. Schulze-Suenninghausen, J. Becker, B. Luy, J. Am. Chem. Soc. 136, 1242 (2014) CrossRefGoogle Scholar
  390. 390.
    C. Kehlet, A.C. Sivertsen, M. Bjerring, T.O. Reiss, N. Khaneja, S.J. Glaser, N.C. Nielsen, J. Am. Chem. Soc. 126, 10202 (2004) CrossRefGoogle Scholar
  391. 391.
    T. Vosegaard, C. Kehlet, N. Khaneja, S.J. Glaser, N.C. Nielsen, J. Am. Chem. Soc. 127, 13768 (2005) CrossRefGoogle Scholar
  392. 392.
    Z. Tosner, S.J. Glaser, N. Khaneja, N.C. Nielsen, J. Chem. Phys. 125, 184502/1 (2006)ADSCrossRefGoogle Scholar
  393. 393.
    J.S. Lee, R.R. Regatte, A. Jerschow, J. Chem. Phys. 129, 224510 (2008) ADSCrossRefGoogle Scholar
  394. 394.
    A.W. MacGregor, L.A. O’Dell, R.W. Schurko, J. Magn. Reson. 208, 103 (2011) ADSCrossRefGoogle Scholar
  395. 395.
    T. Yi-Peng, N. Xin-Fang, L. Jun, C. Hong-Wei, Z. Xian-Yi, P. Xin-Hua, D. Jiang-Feng, Chin. Phys. Lett. 29, 127601 (2012) ADSCrossRefGoogle Scholar
  396. 396.
    N.M. Loening, B.J. van Rossum, H. Oschkinat, Magn. Reson. Chem. 50, 284 (2012)CrossRefGoogle Scholar
  397. 397.
    D. Xu, K.F. King, Y. Zhu, G.C. McKinnon, Z.P. Liang, Magn. Reson. Med. 59, 547 (2008)CrossRefGoogle Scholar
  398. 398.
    W.A. Grissom, D. Xu, A.B. Kerr, J.A. Fessler, IEEE Trans. Med. Imag. 28, 1548 (2009) CrossRefGoogle Scholar
  399. 399.
    A. Massire, M.A. Cloos, A. Vignaud, D. Le Bihan, A. Amadon, N. Boulant, J. Magn. Reson. 230, 76 (2013)ADSCrossRefGoogle Scholar
  400. 400.
    M.S. Vinding, I.I. Maximov, Z. Tošner, N.C. Nielsen, J. Chem. Phys. 137, 054203 (2012) ADSCrossRefGoogle Scholar
  401. 401.
    T.E. Skinner, N.I. Gershenzon, M. Nimbalkar, S.J. Glaser, J. Magn. Reson. 217, 53 (2012)ADSCrossRefGoogle Scholar
  402. 402.
    M. Janich, M. McLean, R. Noeske, S. Glaser, R.F. Schulte, J. Magn. Reson. 223, 129 (2012) ADSCrossRefGoogle Scholar
  403. 403.
    G. Rancan, T.T. Nguyen, S.J. Glaser, J. Magn. Reson. 252, 1 (2015)ADSCrossRefGoogle Scholar
  404. 404.
    I. Maximov, Z. Tosner, N.C. Nielsen, J. Chem. Phys. 128, 184505 (2008) ADSCrossRefGoogle Scholar
  405. 405.
    N. Pomplun, B. Heitmann, N. Khaneja, S.J. Glaser, Appl. Magn. Reson. 34, 331 (2008)CrossRefGoogle Scholar
  406. 406.
    N. Pomplun, S.J. Glaser, Phys. Chem. Chem. Phys. 12, 5791 (2010) CrossRefGoogle Scholar
  407. 407.
    Y. Hovav, A. Feintuch, S. Vega, D. Goldfarb, J. Magn. Reson. 238, 94 (2014)ADSCrossRefGoogle Scholar
  408. 408.
    C. Bretschneider, A. Karabanov, N. Nielsen, W. Köckenberger, J. Chem. Phys. 136, 094201 (2012) ADSCrossRefGoogle Scholar
  409. 409.
    S.S. Köcher, T. Heydenreich, S.J. Glaser, J. Magn. Reson. 249, 63 (2014)ADSCrossRefGoogle Scholar
  410. 410.
    I. Kuprov, J. Magn. Reson. 233, 107 (2013) ADSCrossRefGoogle Scholar
  411. 411.
    A. Garon, R. Zeier, S. Glaser, Phys. Rev. A 91, 042122 (2015) ADSCrossRefGoogle Scholar
  412. 412.
    N. Khaneja, Phys. Rev. A 76, 032326 (2007) ADSCrossRefGoogle Scholar
  413. 413.
    J.S. Hodges, J.C. Yang, C. Ramanathan, D.G. Cory, Phys. Rev. A 78, 010303 (2008) ADSCrossRefGoogle Scholar
  414. 414.
    A. Dementyev, D.G. Cory, C. Ramanathan, Phys. Rev. B 77, 024413 (2008) ADSCrossRefGoogle Scholar
  415. 415.
    S. van Frank, A. Negretti, T. Berrada, R. Bücker, S. Montangero, J.F. Schaff, T. Schumm, T. Calarco, J. Schmiedmayer, Nat. Commun. 5, 4009 (2014)Google Scholar
  416. 416.
    S. Rosi, A. Bernard, N. Fabbri, L. Fallani, C. Fort, M. Inguscio, T. Calarco, S. Montangero, Phys. Rev. A 88, 021601 (2013) ADSCrossRefGoogle Scholar
  417. 417.
    N. Timoney, V. Elman, S. Glaser, C. Weiss, M. Johanning, W. Neuhauser, C. Wunderlich, Phys. Rev. A 77, 052334 (2008) ADSCrossRefGoogle Scholar
  418. 418.
    J. Scheuer et al., New J. Phys. 16, 093022 (2014) ADSCrossRefGoogle Scholar
  419. 419.
    F. Motzoi, J.M. Gambetta, P. Rebentrost, F.K. Wilhelm, Phys. Rev. Lett. 103, 110509 (2009) CrossRefGoogle Scholar
  420. 420.
    J.M. Chow, L. DiCarlo, J.M. Gambetta, F. Motzoi, L. Frunzio, S.M. Girvin, R.J. Schoelkopf, Phys. Rev. A 82, 040305 (2010) ADSCrossRefGoogle Scholar
  421. 421.
    E. Lucero et al., Phys. Rev. A 82, 042339 (2010) ADSCrossRefGoogle Scholar
  422. 422.
    R. Schutjens, F.A. Dagga, D.J. Egger, F.K. Wilhelm, Phys. Rev. A 88, 052330 (2013) ADSCrossRefGoogle Scholar
  423. 423.
    V. Vesterinen, O.P. Saira, A. Bruno, L. DiCarlo (2014), e-prints arXiv:1405.0450
  424. 424.
    J. Kelly et al., Phys. Rev. Lett. 112, 240504 (2014) ADSCrossRefGoogle Scholar
  425. 425.
    J.T. Muhonen et al., J. Phys: Condens. Matter 27, 154205 (2015) ADSGoogle Scholar
  426. 426.
    J.J. Pla, K.Y. Tan, J.P. Dehollain, W.H. Lim, J.J. Morton, D.N. Jamieson, A. Morello, Nature 489, 541 (2012) ADSCrossRefGoogle Scholar
  427. 427.
    E. Kawakami, P. Scarlino, D.R. Ward, F.R. Braakman, D.E. Savage, M.G. Lagally, L.M.K. Vandersypen, Nat. Nanotechnol. 9, 666 (2014)ADSCrossRefGoogle Scholar
  428. 428.
    J.R. Petta, A.C. Johnson, J.M. Taylor, E.A. Laird, A. Yacoby, M.D. Lukin, C.M. Marcus, A.C. Gossard, Science 309, 2180 (2005) ADSCrossRefGoogle Scholar
  429. 429.
    B.M. Maune, M.G. Borselli, B. Huang, T.D. Ladd, P.W. Deelman, K.S. Holabird, A.T. Hunter, Nature 481, 344 (2012) ADSCrossRefGoogle Scholar
  430. 430.
    D. Kim, Z. Shi, C.B. Simmonds, D.R. Ward, J.R. Prance, T.S. Koh, M.A. Eriksson, Nature 511, 70 (2014)ADSCrossRefGoogle Scholar
  431. 431.
    A.D. Greentree, J.H. Cole, A.R. Hamilton, L.C.L. Hollenberg, Phys. Rev. B 70, 235317 (2004) ADSCrossRefGoogle Scholar
  432. 432.
    E. Ferraro, M. De Michielis, M. Fanciulli, E. Prati, Phys. Rev. B 91, 075435 (2015) ADSCrossRefGoogle Scholar
  433. 433.
    F.R. Braakman, P. Barthelmy, C. Reichl, W. Wegscheider, L.M.K. Vandersypen, Nat. Nanotechnol. 8, 432 (2013)ADSCrossRefGoogle Scholar
  434. 434.
    B.E. Anderson, H. Sosa-Martinez, C.A. Riofrío, I.H. Deutsch, P.S. Jessen, Phys. Rev. Lett. 114, 240401 (2015) ADSCrossRefGoogle Scholar
  435. 435.
    J.M. Cai, B. Naydenov, R. Pfeiffer, L.P. McGuinness, K.D. Jahnke, F. Jelezko, M.B. Plenio, A. Retzker, New J. Phys. 14, 113023 (2012) ADSMathSciNetCrossRefGoogle Scholar
  436. 436.
    G. De Chiara, T. Calarco, M. Anderlini, S. Montangero, P.J. Lee, B.L. Brown, W.D. Phillips, J.V. Porto, Phys. Rev. A 77, 052333 (2008) ADSCrossRefGoogle Scholar
  437. 437.
    K. Singer, U. Poschinger, M. Murphy, P. Ivanov, F. Ziesel, T. Calarco, F. Schmidt-Kaler, Rev. Mod. Phys. 82, 2609 (2010) ADSCrossRefGoogle Scholar
  438. 438.
    H.A. Fürst, M.H. Goerz, U.G. Poschinger, M. Murphy, S. Montangero, T. Calarco, F. Schmidt-Kaler, K. Singer, C.P. Koch, New J. Phys. 16, 075007 (2014) CrossRefGoogle Scholar
  439. 439.
    T. Caneva, M. Murphy, T. Calarco, R. Fazio, S. Montangero, V. Giovannetti, G.E. Santoro, Phys. Rev. Lett. 103, 240501 (2009) ADSCrossRefGoogle Scholar
  440. 440.
    M. Murphy, S. Montangero, V. Giovannetti, T. Calarco, Phys. Rev. A 82, 022318 (2010) ADSCrossRefGoogle Scholar
  441. 441.
    A. Gorshkov, T. Calarco, M. Lukin, A. Sørensen, Phys. Rev. A 77, 043806 (2008) ADSCrossRefGoogle Scholar
  442. 442.
    J. Grond, J. Schmiedmayer, U. Hohenester, Phys. Rev. A 79, 021603 (2009) ADSCrossRefGoogle Scholar
  443. 443.
    R. Fisher, H. Yuan, A. Spörl, S.J. Glaser, Phys. Rev. A 79, 042304 (2009) ADSCrossRefGoogle Scholar
  444. 444.
    K. Rojan, D. Reich, I. Dotsenko, J. Raimond, C. Koch, G. Morigi, Phys. Rev. A 90, 023824 (2014) ADSCrossRefGoogle Scholar
  445. 445.
    T. Caneva, T. Calarco, R. Fazio, G. Santoro, S. Montangero, Phys. Rev. A 84, 012312 (2011) ADSCrossRefGoogle Scholar
  446. 446.
    T. Caneva, T. Calarco, S. Montangero, New J. Phys. 14, 093041 (2012) ADSCrossRefGoogle Scholar
  447. 447.
    T. Calarco, U. Dorner, P.S. Julienne, C.J. Williams, P. Zoller, Phys. Rev. A 70, 012306 (2004) ADSCrossRefGoogle Scholar
  448. 448.
    U. Dorner, T. Calarco, P. Zoller, P. Grangier, J. Opt. B 7, S341 (2005)ADSCrossRefGoogle Scholar
  449. 449.
    P. Treutlein, T.W. Hänsch, J. Reichel, A. Negretti, M.A. Cirone, T. Calarco, Phys. Rev. A 74, 022312 (2006) ADSCrossRefGoogle Scholar
  450. 450.
    M. Cozzini, T. Calarco, A. Recati, P. Zoller, Opt. Commun. 264, 375 (2006) ADSCrossRefGoogle Scholar
  451. 451.
    M. Goerz, T. Calarco, C. Koch, J. Phys. B 44, 154011 (2011) ADSCrossRefGoogle Scholar
  452. 452.
    U. Poulsen, S. Sklarz, D. Tannor, T. Calarco, Phys. Rev. A 82, 012339 (2010) ADSCrossRefGoogle Scholar
  453. 453.
    H. Doerk, Z. Idziaszek, T. Calarco, Phys. Rev. A 81, 012708 (2010) ADSCrossRefGoogle Scholar
  454. 454.
    G. Waldherr et al., Nature 506, 204 (2014) ADSCrossRefGoogle Scholar
  455. 455.
    J. Clarke, F.K. Wilhelm, Nature 453, 1031 (2008) ADSCrossRefGoogle Scholar
  456. 456.
    S. Montangero, T. Calarco, R. Fazio, Phys. Rev. Lett. 99, 170501 (2007) ADSCrossRefGoogle Scholar
  457. 457.
    A. Spörl, T. Schulte-Herbrüggen, S.J. Glaser, V. Bergholm, M.J. Storcz, J. Ferber, F.K. Wilhelm, Phys. Rev. A 75, 012302 (2007) ADSCrossRefGoogle Scholar
  458. 458.
    H. Jirari, F.W.J. Hekking, O. Buisson, Europhys. Lett. 87, 28004 (2009) ADSCrossRefGoogle Scholar
  459. 459.
    A. Cross, J. Gambetta, Phys. Rev. A 91, 032325 (2015) ADSCrossRefGoogle Scholar
  460. 460.
    D.J. Egger, F.K. Wilhelm, Supercond. Sci. Technol. 27, 014001 (2014) ADSCrossRefGoogle Scholar
  461. 461.
    P. Rebentrost, I. Serban, T. Schulte-Herbrüggen, F.K. Wilhelm, Phys. Rev. Lett. 102, 090401 (2009) ADSCrossRefGoogle Scholar
  462. 462.
    D.J. Egger, F.K. Wilhelm, Phys. Rev. A 90, 052331 (2014) ADSCrossRefGoogle Scholar
  463. 463.
    M.M. Müller, U. Poschinger, T. Calarco, F. Montangnero, S. Schmidt-Kaler, Phys. Rev. A 92, 053423 (2015) ADSCrossRefGoogle Scholar
  464. 464.
    G. Jäger, U. Hohenester, Phys. Rev. A 88, 035601 (2013) ADSCrossRefGoogle Scholar
  465. 465.
    M. Möttönen, R. de Sousa, J. Zhang, K.B. Whaley, Phys. Rev. A 73, 022332 (2006) ADSCrossRefGoogle Scholar
  466. 466.
    T. Rybár, S.N. Filippov, M. Ziman, V. Buzek, J. Phys. B 45, 154006 (2012) ADSCrossRefGoogle Scholar
  467. 467.
    G. Passante, O. Moussa, C. Ryan, R. Laflamme, Phys. Rev. Lett. 103, 250501 (2009) ADSCrossRefGoogle Scholar
  468. 468.
    R. Marx, A.F. Fahmy, L. Kauffman, S. Lomonaco, A. Spörl, N. Pomplun, T. Schulte-Herbrüggen, J. Myers, S. Glaser, Phys. Rev. A 81, 032319 (2010) ADSCrossRefGoogle Scholar
  469. 469.
    T. Schulte-Herbrüggen, R. Marx, A. Fahmy, L. Kauffman, S. Lomonaco, N. Khaneja, S.J. Glaser, Phil. Trans. R. Soc. A 370, 4651 (2012) ADSCrossRefGoogle Scholar
  470. 470.
    J.P. Palao, R. Kosloff, Phys. Rev. Lett. 89, 188301 (2002) ADSCrossRefGoogle Scholar
  471. 471.
    J.P. Palao, R. Kosloff, Phys. Rev. A 68, 062308 (2003) ADSCrossRefGoogle Scholar
  472. 472.
    C.M. Tesch, R. de Vivie-Riedle, Phys. Rev. Lett. 89, 157901 (2002) ADSCrossRefGoogle Scholar
  473. 473.
    V. Mukherjee, V. Giovannetti, R. Fazio, S. Huelga, T. Carlarco, M. S., New J. Phys. 17, 063031 (2015)ADSCrossRefGoogle Scholar
  474. 474.
    M.D. Grace, J. Dominy, R. Kosut, C. Brif, H. Rabitz, New J. Phys. 12, 015001 (2010) ADSMathSciNetCrossRefGoogle Scholar
  475. 475.
    M.M. Müller, D.M. Reich, M. Murphy, H. Yuan, J. Vala, K.B. Whaley, T. Calarco, C.P. Koch, Phys. Rev. A 84, 042315 (2011) ADSCrossRefGoogle Scholar
  476. 476.
    P. Watts, J. Vala, M.M. Müller, T. Calarco, K.B. Whaley, D.M. Reich, M.H. Goerz, C.P. Koch, Phys. Rev. A 91, 062306 (2015) ADSCrossRefGoogle Scholar
  477. 477.
    M.H. Goerz, G. Gualdi, D.M. Reich, C.P. Koch, F. Motzoi, K.B. Whaley, J. Vala, M.M. Müller, S. Montangero, T. Calarco, Phys. Rev. A 91, 062307 (2015) ADSCrossRefGoogle Scholar
  478. 478.
    F. Platzer, F. Mintert, A. Buchleitner, Phys. Rev. Lett. 105, 020501 (2010) ADSCrossRefGoogle Scholar
  479. 479.
    S. Sklarz, D. Tannor, Phys. Rev. A 66, 053619 (2002) ADSCrossRefGoogle Scholar
  480. 480.
    U. Hohenester, P.K. Rekdal, A. Borzì, J. Schmiedmayer, Phys. Rev. A 75, 023602 (2007) ADSCrossRefGoogle Scholar
  481. 481.
    G. Jäger, D. Reich, M.H. Goerz, C.P. Koch, U. Hohenester, Phys. Rev. A 90, 033628 (2014) ADSCrossRefGoogle Scholar
  482. 482.
    T. Schulte-Herbrüggen, A.K. Spörl, K. Waldherr, T. Gradl, S.J. Glaser, T. Huckle, in High-Performance Computing in Science and Engineering, Garching 2007 (Springer, Berlin, 2008), pp. 517–533, (an extended version: http://arXiv.org/pdf/0712.3227)
  483. 483.
    A.G. Fowler, J.M. Martinis, Phys. Rev. A 89, 032316 (2014) ADSCrossRefGoogle Scholar
  484. 484.
    R. Barends et al., Nature 508, 500 (2014) ADSCrossRefGoogle Scholar
  485. 485.
    J. Preskill, e-prints arXiv:1203.5813, 25th Solvay Conference on Physics, 19-22 October 2011. (2012)
  486. 486.
    G. Kurizki, P. Bertet, Y. Kubo, K. Mølmer, D. Petrosyan, P. Rabl, J. Schmiedmayer, Proc. Natl. Acad. Sci. USA 112, 3866 (2015) ADSCrossRefGoogle Scholar

Copyright information

© The Author(s) 2015

Authors and Affiliations

  • Steffen J. Glaser
    • 1
  • Ugo Boscain
    • 2
  • Tommaso Calarco
    • 3
  • Christiane P. Koch
    • 4
  • Walter Köckenberger
    • 5
  • Ronnie Kosloff
    • 6
  • Ilya Kuprov
    • 7
  • Burkhard Luy
    • 8
  • Sophie Schirmer
    • 9
  • Thomas Schulte-Herbrüggen
    • 1
  • Dominique Sugny
    • 10
    • 11
  • Frank K. Wilhelm
    • 12
  1. 1.Department Chemie, TU-München (TUM)GarchingGermany
  2. 2.CNRS, CMAP École PolytechniqueINRIA SaclayIle-de-France
  3. 3.Institute for Complex Quantum Systems and Center for Integrated Quantum Science and Technology, University of UlmUlmGermany
  4. 4.Theoretische Physik, Universität KasselKasselGermany
  5. 5.Sir Peter Mansfield Magnetic Resonance Centre, University of NottinghamUniversity ParkUK
  6. 6.Institute of Chemistry, the Fritz Haber Research Center for Molecular Dynamics, The Hebrew UniversityJerusalemIsrael
  7. 7.School of Chemistry, University of Southampton, University RoadSouthamptonUK
  8. 8.Institut für Organische Chemie and Institut für Biologische Grenzflächen, Karlsruher Institut für Technologie (KIT)KarlsruheGermany
  9. 9.College of Science, Swansea UniversityWalesUK
  10. 10.Laboratoire Interdisciplinaire Carnot de Bourgogne (ICB), UMR 6303 CNRS-Université de Bourgogne-Franche ComtéDijon CedexFrance
  11. 11.Institute for Advanced Study, Technische Universität MünchenGarchingGermany
  12. 12.Theoretische Physik, Saarland UniversitySaarbrückenGermany

Personalised recommendations