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Communication Dans Un Congrès Année : 2017

Casimir-Polder shifts on quantum levitation states

Résumé

Ultracold atoms can be held in quantum levitation states by the joint effect of gravity and quantum reflection from the attractive Casimir-Polder interaction above a horizontal mirror. We calculate the Casimir-Polder shifts of the energies of these states with a precision sufficient to discuss spectroscopy experiments aiming at tests of the weak equivalence principle on antihydrogen. Gravitationally bound quantum states have been observed with ultracold neutrons 1,2 , but not with neutral atoms. At the low energies corresponding to such bound states, an efficient quantum reflection is produced by the Casimir-Polder (CP) tail above a surface 3,4,5,6 , so that quantum levitation states of atoms can be created, where quantum reflection above a horizontal mirror balances gravity 7. It has recently be proposed to test the weak equivalence principle with antihydrogen by timing its free fall from a trapping device 8. The precision of this test, of the order of 1%, could be improved by spectroscopic measurements of quantum levitation states of antihydrogen above a material surface, since the properties of these states are essentially determined by gravity 9,10. However an accurate determination of the acceleration requires a precise evaluation of Casimir-Polder shifts on quantum levitation states 11. We consider an atom of mass m and energy E bouncing in the gravity potential mgz and reflected on a plane horizontal mirror due to quantum reflection on the CP potential V CP (z). The wavefunction ψ(z) obeys the one-dimensional Schrödinger equation − 2 2m d 2 ψ dz 2 (z) + V (z)ψ(z) = Eψ(z) , V (z) = mgz + V CP (z) , (1) with the potential V depending only on the altitude z of the particle above the mirror sitting at z = 0. We also suppose that atoms are absorbed when touching the surface, which corresponds to the physical boundary condition for antihydrogen annihilated at contact with matter. Length and energy scales associated with the Casimir-Polder potential are respectively much smaller and much larger than those associated with the gravitational potential g = 2 2m 2 g 1/3 ≈ 5.87 µm , g = mg g ≈ 0.602 peV , (for g ≈ 9.81 m.s −2). (2) An approximate solution of the problem is thus found by decoupling the effects of gravity and CP interactions. For quantum levitation states with low values of the quantum number n, the scattering amplitudes are mainly given by the scattering length a. It follows that the energies E 0 n
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Dates et versions

hal-01802015 , version 1 (28-05-2018)

Identifiants

  • HAL Id : hal-01802015 , version 1
  • INSPIRE : 1671220

Citer

P-P Crépin, G. Dufour, R. Guérout, A. Lambrecht, S. Reynaud. Casimir-Polder shifts on quantum levitation states. 52nd Rencontres de Moriond on Gravitation, Mar 2017, La Thuile, Italy. pp.179-184. ⟨hal-01802015⟩
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