Frictionless atom cooling in harmonic traps: A time-optimal approach

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 82, Issue 6, 2010, Pages

  Stefanatos, Dionisis ^a   Ruths, Justin ^a   Li, Jr Shin ^a  

^a WASHINGTON UNIVERSITY IN ST LOUIS   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ATOM COOLING; BANG-BANG; COOLING TIME; HARMONIC TRAP; MINIMUM TIME; NUMERICAL OPTIMIZATIONS; PARABOLIC POTENTIAL; PSEUDO-SPECTRAL APPROXIMATION; TIME-OPTIMAL; TIME-OPTIMAL CONTROL PROBLEMS; TRANSIENT TIME; TRAP FREQUENCY;

NUMERICAL METHODS; OPTIMIZATION;

COOLING;

EID: 78650996089     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.82.063422     Document Type: Article

References (37)

1. A. E. Leanhardt, T. A. Pasquini, M. Saba, A. Schirotzek, Y. Shin, D. Kielpinski, D. E. Pritchard, and W. Ketterle, Science SCIEAS 0036-8075 10.1126/science.1088827 301, 1513 (2003).
2. S. Bize, J. Phys. B: At. Mol. Opt. Phys. JPAPEH 0953-4075 10.1088/0953-4075/38/9/002 38, S449 (2005).
3. D. Aharonov, W. van Dam, J. Kempe, Z. Landau, S. Lloyd, and O. Regev, SIAM J. Comput. SMJCAT 0097-5397 10.1137/S0097539705447323 37, 166 (2007).
4. P. Salamon, K. H. Hoffmann, Y. Rezek, and R. Kosloff, Phys. Chem. Chem. Phys. PPCPFQ 1463-9076 10.1039/b816102j 11, 1027 (2009).
5. X. Chen, A. Ruschhaupt, S. Schmidt, A. del Campo, D. Guéry-Odelin, and J. G. Muga, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.104. 063002 104, 063002 (2010).
6. H. R. Lewis and W. B. Riesenfeld, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1664991 10, 1458 (1969).
7. T.-J. Tarn, G. Huang, and J. W. Clark, Math. Model. MAMODZ 0270-0255 10.1016/0270-0255(80)90011-1 1, 109 (1980).
8. A. P. Peirce, M. A. Dahleh, and H. Rabitz, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.37.4950 37, 4950 (1988).
9. N. Khaneja, R. Brockett, and S. J. Glaser, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.63.032308 63, 032308 (2001).
10. D. D'Alessandro and M. Dahleh, IEEE Trans. Autom. Contr. IETAA9 0018-9286 10.1109/9.928587 46, 866 (2001).
11. S. Lloyd and L. Viola, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65. 010101 65, 010101 (R) (2001).
12. S. E. Sklarz and D. J. Tannor, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.66.053619 66, 053619 (2002).
13. U. Boscain, G. Charlot, J. P. Gauthier, S. Guerin, and H. R. Jauslin, J. Math. Phys. JMAPAQ 0022-2488 10.1063/1.1465516 43, 2107 (2002).
14. T. E. Skinner, T. Reiss, B. Luy, N. Khaneja, and S. J. Glaser, J. Magn. Reson. JMARF3 1090-7807 10.1016/S1090-7807(03)00153-8 163, 8 (2003).
15. D. Stefanatos, N. Khaneja, and S. J. Glaser, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.69.022319 69, 022319 (2004).
16. D. Stefanatos, S. J. Glaser, and N. Khaneja, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.72.062320 72, 062320 (2005).
17. J.-S. Li and N. Khaneja, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.030302 73, 030302 (R) (2006).
18. A. V. Gorshkov, T. Calarco, M. D. Lukin, and A. S. Sørensen, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.77.043806 77, 043806 (2008).
19. I. I. Maximov, Z. Toner, and N. C. Nielsen, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.2903458 128, 184505 (2008).
20. J.-S. Li, J. Ruths, and D. Stefanatos, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.3253796 131, 164110 (2009).
21. J.-S. Li, N. Khaneja, IEEE Trans. Autom. Control IETAA9 0018-9286 10.1109/TAC.2009.2012983 54, 528 (2009).
22. R. Wu, J. Dominy, T. S Ho, and H. Rabitz (2009), e-print arXiv: 0907.2354 [quant-ph].
23. M. Lapert, Y. Zhang, M. Braun, S. J. Glaser, and D. Sugny, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.104.083001 104, 083001 (2010).
24. T. Schulte-Herbrüggen, S. J. Glaser, G. Dirr, and U. Helmke, Rev. Math. Phys. RMPHEX 0129-055X 10.1142/S0129055X10004053 22, 597 (2010).
25. D. Stefanatos and J.-S. Li, Syst. Contr. Lett. 0167-6911 10.1016/j.sysconle.2010.07.004 59, 601 (2010).
26. L. S. Pontryagin, V. G. Boltyanskii, R. V. Gamkrelidze, and E. F. Mishchenko, The Mathematical Theory of Optimal Processes (Interscience Publishers, New York, 1962).
27. G. Elnagar, M. A. Kazemi, and M. Razzaghi, IEEE Trans. Autom. Contr. IETAA9 0018-9286 10.1109/9.467672 40, 1793 (1995).
28. I. Ross and F. Fahroo, in New Trends in Nonlinear Dynamics and Control, edited by, W. Kang, (Springer, Berlin, 2003), p. 327.
29. W. Kang, Q. Gong, and I. Ross, IEEE Trans. Autom. Contr. IETAA9 0018-9286 10.1109/TAC.2006.878570 51, 1115 (2006).
30. F. Fahroo and I. Ross, J. Guid. Control. Dyn. IETAA9 0731-5090 10.2514/2.4709 24, 270 (2001).
31. P. Williams, ANZIAM J. 47, C101 (2006).
32. C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. Zang, Spectral Methods (Springer, Berlin, 2006).
33. P. J. Davis, Interpolation and Approximation (Blaisdell, New York, 1963).
34. G. Szego, Orthogonal Polynomials (American Mathematical Society, New York, 1959).
35. B. Fornberg, A Practical Guide to Pseudospectral Methods (Cambridge University Press, New York, 1998).
36. J. Boyd, Chebyshev and Fourier Spectral Methods, 2nd ed. (Dover, New York, 2000).
37. D. Gottlieb, Y. Hussaini, and S. Orszag, in Spectral Methods for Partial Differential Equations, edited by, R. Voigt, (SIAM, Philadelphia, 1984), p. 1.