Atomic beam splitters with achromatic transverse-momentum transfer

Journal of the Optical Society of America B: Optical Physics

Volumn 13, Issue 7, 1996, Pages 1352-1361

  Chu, A P ^a   Johnson, K S ^a   Prentiss, M G ^a  

^a HARVARD UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030505488     PISSN: 07403224     EISSN: None     Source Type: Journal    
DOI: 10.1364/JOSAB.13.001352     Document Type: Article

References (19)

1. See, for example, the feature on optics and interferometry with atoms, Appl. Phys. B 54, 319 (1992).
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5. U. Janicke and M. Wilkens, Phys. Rev. A 50, 3265 (1994).
6. K. S. Johnson, A. Chu, T. W. Lynn, K. K. Berggren, M. S. Shahriar, and M. Prentiss, Opt. Lett. 20, 1310 (1995).
7. R. Grimm, J. Soding, and Yu. B. Ovchinnikov, Opt. Lett. 19, 658 (1994).
8. J. Lawall and M. G. Prentiss, Phys. Rev. Lett. 72, 993 (1994).
9. L. S. Goldner, C. Gerz, R. J. C. Spreew, S. L. Rolston, C. I. Westbrook, W. D. Phillips, P. Marte, and P. Zoller, Phys. Rev. Lett. 72, 997 (1994).
10. M. Weitz, B. C. Young, and S. Chu, Phys. Rev. Lett. 72, 2563 (1994).
11. P. J. Martin, B. G. Oldaker, A. H. Miklich, and D. E. Pritchard, Phys. Rev. Lett. 60, 515 (1988).
12. For higher-order Bragg scattering there can be multiple velocity classes satisfying the Bragg condition. Therefore it is difficult to achieve efficient momentum splittings of greater than approximately ±6ℏk for a thermal or a supersonic atomic beam.
13. For example, ±3ℏk was the maximum splitting achieved in a recent interferometer based on Bragg scattering [D. M. Giltner, R. W. McGowan, and S. A. Lee, Phys. Rev. Lett. 75, 2638 (1995)].
14. -7.
15. R. Kosloff, J. Phys. Chem. 92, 2087 (1988).
16. The fluctuation F(Δ) for the approximate blazed-grating case is not a monotonic function of Δ; the oscillations in the fluctuation appear because each transition is driven by two fields of different frequencies. For example, we found such oscillatory behavior in δ p, the mean momentum transfer, as a function of detuning and Rabi frequency, when a two-level system is driven by bichromatic standing waves [K. S. Johnson, A. P. Chu, K. K. Berggren, and M. G. Prentiss, Opt. Commun. (to be published)].
17. There are atomic-interferometry experiments in which the spatial profile of the wave packet is the relevant quantity. For example, in the case of rotations the phase shift that is due to rotation is proportional to the enclosed area in the interferometer. In this case, if one wanted to see the same rotation-induced phase shift for all velocity classes, it would be necessary to bend different velocity classes through the same angle in position space.
18. The distribution Π(p, v) is nonzero for odd momentum orders because the state |D〉 contains momentum components at ±ℏk; thus the initial state is a two-peaked momentum distribution at ±ℏk. The diffraction transfers momenta in units of 2ℏk, leading to the population of odd momentum orders.
19. The following is a possible way to load atoms into |D〉 by adiabatic passage; all of the fields described here are spatially separated from the achromatic beam-splitter region. As discussed previously, the laser configuration with two circularly polarized standing waves with a spatial phase shift of π/2 is equivalent to the configuration with two counter-propagating traveling waves with orthogonal linear polarization. We take counterpropagating, partially overlapping traveling waves polarized along x̂ and ŷ and prepare the atom in the ŷ-polarized state. The traveling waves propagate orthogonal to the atomic beam and overlap such that an atom first encounters only x̂-polarized light and then encounters both x̂ and ŷ light. Since the first traveling wave is x̂ polarized, the atom is decoupled from the driving fields and is in a dark state. As the atom passes through the excitation fields and the intensity of the x̂-polarized light increases, the atom adiabatically follows the dark state corresponding to the particular ratio of the x̂- and the ŷ light intensities. By clipping the laser beams at a point at which the intensities of the x̂ and the ŷ beams are equal, the atom exits the preparation region in an equal superposition of x̂ and ŷ-polarized atomic states. Because the laser configuration with two circularly polarized standing waves with a spatial phase shift of π/2 is equivalent to the configuration with two counterpropagating, orthogonally linearly polarized traveling waves, the dark state exiting the preparation is exactly the state |D〉 required for scattering from the achromatic potential.