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@ARTICLE{Slim:1019009,
      author       = {Slim, J. and Nikolaev, N. N. and Rathmann, F. and Wirzba,
                      A.},
      title        = {{Q}uantum mechanical derivation of radio-frequency-driven
                      coherent beam oscillations in storage rings},
      journal      = {Physical review accelerators and beams},
      volume       = {26},
      number       = {1},
      issn         = {2469-9888},
      address      = {College Park, MD},
      publisher    = {American Physical Society},
      reportid     = {FZJ-2023-05078},
      pages        = {014201},
      year         = {2023},
      abstract     = {The study of the approach to the quantum ground state and
                      the possibility to detect displacements of macroscopic
                      bodies close to the quantum limit represent pressing
                      challenges in modern physics. In the recent experiment of
                      the JEDI Collaboration at the COSY storage ring, the
                      coherent oscillations of a deuteron beam were detected with
                      an amplitude of only one order of magnitude above the limit
                      of the Heisenberg uncertainty principle of about 40 nm for
                      the one-particle betatron motion. On the other hand, the
                      much discussed search for the permanent electric dipole
                      moment of the proton with an ultimate sensitivity of
                      10−29  e cm requires control of the position of the
                      beam center of gravity with an accuracy of ≈5  pm. In
                      this paper, we develop the full quantum mechanical treatment
                      of the coherent beam oscillations with ultrasmall
                      amplitudes. In agreement with the Ehrenfest theorem, we find
                      a continuity of the description of the coherent betatron
                      motion from the large classical amplitudes down to the deep
                      quantum region below the one-particle Heisenberg limit. We
                      argue that quantum mechanics does not preclude control of
                      the beam center with subpicometer accuracy.},
      cin          = {IKP-2 / IAS-4 / IKP-3},
      ddc          = {530},
      cid          = {I:(DE-Juel1)IKP-2-20111104 / I:(DE-Juel1)IAS-4-20090406 /
                      I:(DE-Juel1)IKP-3-20111104},
      pnm          = {612 - Cosmic Matter in the Laboratory (POF4-612) / 5111 -
                      Domain-Specific Simulation $\&$ Data Life Cycle Labs (SDLs)
                      and Research Groups (POF4-511) / srEDM - Search for electric
                      dipole moments using storage rings (694340)},
      pid          = {G:(DE-HGF)POF4-612 / G:(DE-HGF)POF4-5111 /
                      G:(EU-Grant)694340},
      experiment   = {EXP:(DE-Juel1)JEDI-20170712},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000912897300001},
      doi          = {10.1103/PhysRevAccelBeams.26.014201},
      url          = {https://juser.fz-juelich.de/record/1019009},
}