Photon storage in -type optically dense atomic media. IV. Optimal control using gradient ascent

Physical Review A - Atomic, Molecular, and Optical Physics

Volumn 77, Issue 4, 2008, Pages

  Gorshkov, Alexey V ^a   Calarco, Tommaso ^b   Lukin, Mikhail D ^a   Sørensen, Anders S ^c  

^a HARVARD UNIVERSITY   (United States)

^b UNIVERSITY OF ULM   (Germany)

^c UNIVERSITY OF COPENHAGEN   (Denmark)

Author keywords

[No Author keywords available]

Indexed keywords

ATOMIC PHYSICS; BANDWIDTH; EQUATIONS OF MOTION; LASER PULSES; OPTIMAL CONTROL SYSTEMS; OPTIMIZATION;

NONADIABATIC LIMIT; OPTIMIZATION TECHNIQUES; ORDER OF MAGNITUDE; PHOTON STORAGE;

PHOTONS;

EID: 41849120785     PISSN: 10502947     EISSN: 10941622     Source Type: Journal    
DOI: 10.1103/PhysRevA.77.043806     Document Type: Article

References (52)

1. A. V. Gorshkov, A. André, M. Fleischhauer, A. S. Sørensen, and M. D. Lukin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.123601 98, 123601 (2007).
2. I. Novikova, A. V. Gorshkov, D. F. Phillips, A. S. Sørensen, M. D. Lukin, and R. L. Walsworth, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.243602 98, 243602 (2007).
3. A. V. Gorshkov, A. André, M. D. Lukin, and A. S. Sørensen, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.76.033804 76, 033804 (2007).
4. A. V. Gorshkov, A. André, M. D. Lukin, and A. S. Sørensen, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.76.033805 76, 033805 (2007).
5. A. V. Gorshkov, A. André, M. D. Lukin, and A. S. Sørensen, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.76.033806 76, 033806 (2007).
6. V. F. Krotov, Global Methods in Optimal Control Theory (Marcel Decker, New York, 1996).
7. A. E. Bryson, Jr. and Y.-C. Ho, Applied Optimal Control (Hemisphere, Washington, DC, 1975).
8. M. U. Staudt, S. R. Hastings-Simon, M. Afzelius, D. Jaccard, W. Tittel, and N. Gisin, Opt. Commun. OPCOB8 0030-4018 10.1016/j.optcom.2006.05.007 266, 720 (2006).
9. J. Simon, H. Tanji, J. K. Thompson, and V. VuletiÄ, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.183601 98, 183601 (2007).
10. M. D. Eisaman, A. André, F. Massou, M. Fleischhauer, A. S. Zibrov, and M. D. Lukin, Nature (London) NATUAS 0028-0836 10.1038/nature04327 438, 837 (2005).
11. T. Chaneliére, D. Matsukevich, S. D. Jenkins, S.-Y. Lan, T. A. B. Kennedy, and A. Kuzmich, Nature (London) NATUAS 0028-0836 10.1038/nature04315 438, 833 (2005).
12. C. W. Chou, H. de Riedmatten, D. Felinto, S. V. Polyakov, S. J. van Enk, and H. J. Kimble, Nature (London) NATUAS 0028-0836 10.1038/nature04353 438, 828 (2005).
13. J. J. Longdell, E. Fraval, M. J. Sellars, and N. B. Manson, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.95.063601 95, 063601 (2005).
14. M. U. Staudt, S. R. Hastings-Simon, M. Nilsson, M. Afzelius, V. Scarani, R. Ricken, H. Suche, W. Sohler, W. Tittel, and N. Gisin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.113601 98, 113601 (2007).
15. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.74.145 74, 145 (2002).
16. C. Simon, H. de Riedmatten, M. Afzelius, N. Sangouard, H. Zbinden, and N. Gisin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.98.190503 98, 190503 (2007).
17. R. Kosloff, S. A. Rice, P. Gaspard, S. Tersigni, and D. J. Tannor, J. Chem. Phys. JCPSA6 0021-9606 10.1016/0301-0104(89)90012-8 139, 201 (1989).
18. M. Shapiro and P. Blumer, Principles of the Quantum Control of Molecular Processes (John Wiley & Sons, Hoboken, NJ, 2003).
19. Y. Ohtsuki, G. Turinici, and H. Rabitz, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.1650297 120, 5509 (2004).
20. N. Khaneja, T. Reiss, C. Kehlet, T. Schulte-Herbrüggen, and S. J. Glaser, J. Magn. Reson. JMARF3 1090-7807 10.1016/j.jmr.2004.11.004 172, 296 (2005).
21. S. E. Sklarz and D. J. Tannor, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.66.053619 66, 053619 (2002).
22. T. Calarco, U. Dorner, P. S. Julienne, C. J. Williams, and P. Zoller, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.70.012306 70, 012306 (2004).
23. S. Chaudhury, S. Merkel, T. Herr, A. Silberfarb, I. H. Deutsch, and P. S. Jessen, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.163002 99, 163002 (2007).
24. S. Montangero, T. Calarco, and R. Fazio, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.99.170501 99, 170501 (2007).
25. P. Rebentrost, I. Serban, T. Schulte-Herbrüggen, and F. K. Wilhelm, e-print arXiv:quant-ph/0612165v2.
26. V. F. Krotov, Autom. Remote Control (Engl. Transl.) AURCAT 0005-1179 34, 1863 (1973)
27. V. F. Krotov, Autom. Remote Control (Engl. Transl.) AURCAT 0005-1179 35, 1 (1974)
28. V. F. Krotov, Autom. Remote Control (Engl. Transl.) AURCAT 0005-1179 35, 345 (1974).
29. V. F. Krotov and I. N. Feldman, Eng. Cybern. ENCYAF 0013-788X 21, 123 (1983).
30. A. I. Konnov and V. F. Krotov, Autom. Remote Control (Engl. Transl.) AURCAT 0005-1179 60, 1427 (1999).
31. S. A. Moiseev and S. KrÃll, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.87.173601 87, 173601 (2001).
32. B. Kraus, W. Tittel, N. Gisin, M. Nilsson, S. KrÃll, and J. I. Cirac, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.73.020302 73, 020302 (R) (2006).
33. J. S. Neergaard-Nielsen, B. M. Nielsen, H. Takahashi, A. I. Vistnes, and E. S. Polzik, Opt. Express OPEXFF 1094-4087 10.1364/OE.15.007940 15, 7940 (2007).
34. J. Wrachtrup and F. Jelezko, J. Phys.: Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/18/21/S08 18, S807 (2006).
35. A. Kalachev, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.76.043812 76, 043812 (2007).
36. In order to understand why complex conjugates have to be added in Eq. 3 and how to take variations with respect to complex variables, one could rewrite the equations in terms of real variables, that is, the real and imaginary parts of P and S. The variations with respect to the real and imaginary parts can now be seen to be equivalent to treating the variables and their complex conjugates as independent variables. Note, however, that this convention means that the gradient ascent update for any complex variable Q is Q Q+ (1/λ) Î J/Î Qâ [we will use this for the optimization with respect to complex Ein (t) and complex Ω (t)].
37. S. A. Moiseev and B. S. Ham, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.70.063809 70, 063809 (2004);
38. S. A. Moiseev and M. I. Noskov, Laser Phys. Lett. LPLABC 1612-2011 10.1002/lapl.200310071 1, 303 (2004)
39. S. A. Moiseev, Izv. Ross. Akad. Nauk, Ser. Fiz. IANFAY 0367-6765 68, 1260 (2004)
40. S. A. Moiseev, [Bull. Russ. Acad. Sci. Phys. BUPSAA 0001-432X 68, 1408 (2004)]
41. S. A. Moiseev, C. Simon, and N. Gisin, e-print arXiv:quant-ph/0609173.
42. M. Nilsson and S. KrÃll, Opt. Commun. OPCOB8 0030-4018 10.1016/j.optcom.2004.11.077 247, 393 (2005).
43. N. Sangouard, C. Simon, M. Afzelius, and N. Gisin, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.75.032327 75, 032327 (2007).
44. A. E. Kozhekin, K. Mølmer, and E. Polzik, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.62.033809 62, 033809 (2000).
45. M. Fleischhauer, S. F. Yelin, and M. D. Lukin, Opt. Commun. OPCOB8 0030-4018 10.1016/S0030-4018(99)00679-3 179, 395 (2000)
46. M. Fleischhauer and M. D. Lukin, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.84.5094 84, 5094 (2000)
47. M. Fleischhauer and M. D. Lukin, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.65.022314 65, 022314 (2002).
48. M. F. Yanik, W. Suh, Z. Wang, and S. Fan, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.93.233903 93, 233903 (2004).
49. M. Erhard and H. Helm, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.63. 043813 63, 043813 (2001).
50. M. Graf, E. Arimondo, E. S. Fry, D. E. Nikonov, G. G. Padmabandu, M. O. Scully, and S.-Y. Zhu, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.51.4030 51, 4030 (1995).
51. M. O. Scully and M. S. Zubairy, Quantum Optics (Cambridge University Press, Cambridge, England, 1997).
52. J. Nunn, I. A. Walmsley, M. G. Raymer, K. Surmacz, F. C. Waldermann, Z. Wang, and D. Jaksch, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.75.011401 75, 011401 (R) (2007).