Multilayer “dielectric” mirror for atoms

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 58, Issue 3, 1998, Pages 2407-2412

  Santos, Luis ^a   Roso, Luis ^a  

^a UNIVERSITY OF SALAMANCA   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001540717     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.58.2407     Document Type: Article

References (28)

1. D. W. Keith, M. L. Schattenburg, H. I. Smith, and D. E. Pritchard, Phys. Rev. Lett. 61, 1580 (1988).PRLTAO
2. O. Carnal and J. Mlynek, Phys. Rev. Lett. 66, 2689 (1991).PRLTAO
3. O. Carnal, M. Sigel, T. Sleator, H. Takuma, and J. Mlynek, Phys. Rev. Lett. 67, 3231 (1991).PRLTAO
4. M. O. Mewes, M. R. Andrews, D. M. Kurn, D. S. Durfee, C. G. Townsend, and W. Ketterle, Phys. Rev. Lett. 78, 582 (1997).PRLTAO
5. V. I. Balykin, V. S. Letokhov, Yu. B. Ovchinnikov, and A. I. Sidorov, Phys. Rev. Lett. 60, 2137 (1988).PRLTAO
6. T. Roach, H. Abele, M. G. Boshier, H. L. Grossman, K. P. Zetie, and E. A. Hinds, Phys. Rev. Lett. 75, 629 (1995).PRLTAO
7. See, for example, M. Wilkens, E. Schumacher, and P. Meystre, Phys. Rev. A 44, 3130 (1991).PLRAAN
8. P. J. Martin, B. G. Oldaker, A. H. Miklich, and D. E. Pritchard, Phys. Rev. Lett. 60, 515 (1988); PRLTAO
9. L. Santos and L. Roso, J. Phys. B 30, 5169 (1997).JPAPEH
10. E. M. Rasel, M. K. Oberthaler, H. Batelaan, J. Schmiedmayer, and A. Zeilinger, Phys. Rev. Lett. 75, 2633 (1995); PRLTAO
11. Phys. Rev. Lett.D. M. Giltner, R. W. McGowan, and S. A. Lee, 75, 2638 (1995).
12. E. Yablonovitch, Phys. Rev. Lett. 58, 2059 (1987). PRLTAOBragg scattering is a special case of PBGS for a tiny refractive index;
13. see the discussion in E. Yablonovitch, J. Opt. Soc. Am. B 10, 283 (1993).JOBPDE
14. A. Messiah, Quantum Mechanics (North-Holland, Amsterdam, 1961), Vol. I.
15. C. Henkel, C. Y. Westbrook, and A. Aspect, J. Opt. Soc. Am. B 13, 233 (1996).JOBPDE
16. The adiabatic approximation is valid if the precession frequency of the two-level system, given by the generalized Rabi frequency, is very large compared to the reciprocal rise time of the electric-field amplitude. For very large detuning, this condition is satisfied and we can use the so-called adiabatic approximation, in which the spatial derivatives of the eigenvectors of the Hamiltonian can be neglected. This approximation allows splitting of the Schrödinger equation, which initially has a spinorial form, into two scalar Schrödinger equations, each one describing the evolution of one dressed state. For a more detailed analysis of the adiabatic approximation, see, for example, R. Deutschmann, W. Ertmer, and H. Wallis, Phys. Rev. A 47, 2169 (1993). In contrast to this reference, in the present paper we approximate (Formula presented) because Δ is very large.PLRAAN
17. W. Zhang and B. C. Sanders, J. Phys. B 27, 795 (1994).JPAPEH
18. See, for example, N. W. Ashcroft and N. D. Mermin, Solid State Physics (Saunders, Philadelphia, 1976).
19. G. J. Liston, S. M. Tan, and D. F. Walls, Appl. Phys. B: Lasers Opt. 60, 211 (1995).APBOEM
20. S. M. Tan and D. F. Walls, Phys. Rev. A 50, 1561 (1994).PLRAAN
21. This approximation leads to a good explanation of the details of the exact numerical results. Its validity is based on the following considerations. In the cases analyzed in the present paper the width of the Gaussian envelope of the potential at (Formula presented) is 245 cosine-squared periods. Since the width of the Gaussian is much larger than the periodicity of the cosine squared, we can consider that within small intervals of the envelope we have a large number of cosine-squared oscillations of approximately constant amplitude, for which we can define a band structure. We can extend this reasoning and define a band structure for each value of the envelope function (Formula presented) This is the band structure calculated for a cosine-squared potential of infinite periods of constant amplitude (Formula presented)
22. M. Kasevich and S. Chu, Phys. Rev. Lett. 69, 1741 (1992). PRLTAO
23. In this reference, a large detuning from the optical resonance is assumed. If this detuning is very large, the two ground states form a two-level system with an effective Rabi frequency [K. Moler, D. S. Weiss, M. Kasevich, and S. Chu, Phys. Rev. A 45, 342 (1992)]. We can use our theory with this two-level atom, where the detuning that we use is the detuning from the Raman transition. Spontaneous emission is then suppressed, even though this last detuning is small.PLRAAN
24. Recently some studies on the effects of the acceleration of an atom inside a periodic potential have been reported. See, for example, Q. Niu, X. G. Zhao, G. A. Georgiakis, and M. G. Raizen, Phys. Rev. Lett. 76, 4504 (1996); PRLTAO
25. Phys. Rev. Lett.M. B. Dahan, E. Peik, J. Reichel, Y. Castin, and C. Salomon, 76, 4508 (1996);
26. Phys. Rev. Lett.S. R. Wilkinson, C. F. Bharucha, K. W. Madison, Q. Niu, and M. G. Raizen, 76, 4512 (1996).
27. In these references, experimental observations of the well-known Bloch oscillations (BOs) and their stationary counterpart, i.e., the Wannier-Stark (WS) ladders, are reported. BOs can be easily understood for weak potentials [E. Peik, M. B. Dahan, Y. Bouchoule, Yvan Castin, and C. Salomon, Phys. Rev. A 55, 2989 (1997)]. PLRAAN
28. Due to acceleration, q increases linearly according to Newton’s law until it reaches a critical value satisfying the Bragg condition. The atomic wave is then reflected and its momentum is reversed. The atom travels again under Newton’s law until it reaches another Bragg condition and is then reflected again. BOs can therefore be understood as oscillations between two Bragg reflections. In our problem, BOs would be produced if the atoms were spatially confined between two gravitationally tilted forbidden regions. Multiple reflections would then occur at the edges of the forbidden regions, leading to an oscillatory motion. However, in our case, the atoms come from outside the laser. If the atoms reach a forbidden region, they cannot be transmitted and are reflected back to free space. The atoms are therefore not between two gaps and hence cannot develop such multiple oscillations. Accordingly, the gravitational field does not lead to Bloch oscillations and so no effect of the WS ladders is observed in the reflection spectrum. Only if the first forbidden region were very narrow could the atom tunnel through the forbidden region (in a similar way to Landau-Zener tunneling) and enter an allowed region, finally reaching another forbidden region and producing multiple reflections. [For a review of the BOs, and WS ladders in the context of solid-state physics see E. E. Mendez and G. Bastard, Phys. Today 46 (6), 34 (1993)].PHTOAD