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2
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84927321540
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The device is mentioned earlier by D. Bohm, Quantum Theory (Prentice-Hall, Englewood Cliffs, NJ, 1951).
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6
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84927321539
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The original Humpty-Dumpty problem:
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9
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84927321538
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and earlier work cited therein.
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12
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84927321537
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Realistic experiments will have to use electric dipole interactions instead. Nevertheless, we present a detailed treatment of a magnetic coupling, because it avoids the introduction of additional internal atomic degrees of freedom.
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13
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84927321536
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B.-G. Englert, J. Schwinger, and M. O. Scully (unpublished).
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16
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84927321535
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We have, only for the sake of simplicity, assumed that the coupling of the atoms to the cavity photons is via the magnetic moment. It is, however, much more practical to have electric dipole coupling to a transition between two highly excited states (so-called Rydberg states). In the first cavity, for example, the transition from the higher to the lower one of these states would occur, to be reversed in the second one, so that the atom emerges in the same Rydberg state in which it was prepared and with the same orientation of the magnetic moment to ensure the focusing by the final section of the SGI. By using such Rydberg transitions, the coupling strength is increased by, roughly, a factor of 105, whereby the required number of photons is reduced to app 1010/(105)2=1. The preparation of a number state with a few photons is feasible; see Sec. IIIB. .ti 1P This also lends justification to the way in which we arrived at the resonant Hamiltonian (33). The additional homogeneous magnetic field was there taken to be the same inside the cavities and outside. For the high-quality cavities that are actually needed, with superconducting walls, this is—to say the least— far fetched. (Incidentally, for the typical numbers used above, resonance requires a field strength app 1 kG inside the cavities.) However, keeping in mind that a realistic experiment would use a Rydberg transition, the Hamiltonian (33) is fine if one understands that the sigma operators therein do not refer to the spin degree of freedom but to the two-level system consisting of the two Rydberg states.
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