## IV. CONCLUSIONS 

In conclusions, we show how the atomic coherence in an optical double-well lattice can be preserved by a suitable control technique. We choose an extended lattice in one dimen- sion and model the decoherence as a sequence of random phase kicks during spontaneous emission. We show that upon suitable choice of particular initial superposition of the lattice eigenfunctions, one can preserve the coherence in atomic external state even in the pres- ence of decoherence in its internal states. This control relies upon the quantum interference between the several pathways that are led due to initial choice of the superposition states. 

## V. ACKNOWLEDGEMENTS 

I gratefully thank Prof. Paul Brumer for his useful advice and suggestions during this work. I also thank Prof. Aephraim Steinberg, Dr. Michael Spanner, and Dr. Carlos Arango for their useful comments on this work. 

[1] F. Grossman et al. , J. Stat. Phys. 70 , 229 (1993). 

[2] L. G. C. Rego, J. Mod. Opt. 54 , 2617 (2007). 

[3] A. O. Caldeira and A. J. Leggett, Phys. Rev. Lett. 46 , 211 (1981). 

[4] R. Graham and S. Miyazaki, Phys. Rev. A 53 , 2683 (1996). 

[5] M. Shapiro and P. Brumer, Principles of the Quantum Control of Molecular Processes , (Wiley, New Jersey, 2003). 

[6] J. Sebby-Strabley et al. , Phys. Rev. A 73 , 33605 (2006); M. Anderlini et al. , J. Phys. B 39 , S199 (2006). 

[7] F. W. Strauch et al. , Phys. Rev. A 77 , 050304 (2008). 

[8] M. Anderlini et al. , Nature 448 , 452 (2007). 

[9] D. Braun and J. Martin, Phys. Rev. A 77 , 032102 (2008). 

[10] G. Ball, K. Vant, and N. Christensen, Phys. Rev. E 61 , 1299 (2000). 

