Abstract
One of the most fascinating frontiers of modern physics is the possibility to use laser light to manipulate the motion of atomic samples. In the last two decades, spectacular advances in laser cooling techniques have made the production of Bose-Einstein condensates of neutral atoms possible. These quantum objects, nowadays routinely produced in many laboratories all over the world, are invaluable tools for the study of fundamental problems of quantum mechanics on a macroscopic scale. The possibility to use far-detuned laser light to engineer specific kinds of potentials allows an unprecedented control of the forces exerted on a quantum system. In this review we present an introduction to the physics of Bose-Einstein condensates in optical potentials. The main body of the paper is focused on Bose-Einstein condensates in optical lattices, i.e. periodic potentials created with laser light standing waves. These systems have allowed the investigation of many fundamental problems of physics, throwing a bridge between the realm of atomic physics and the one of solid state physics. Furthermore, they represent promising resources for studies in the field of many-body quantum correlated systems, also in the perspective of applications in the field of quantum computation. Finally, we consider the possibility of producing disordered potentials with light, as realized in recent experiments aiming at the study of the emergence of disorder-induced localization effects.
Similar content being viewed by others
References
Inguscio M., Stringari S. and Wieman C. E.(Editors), Bose-Einstein condensation in atomic gases, Proceedings of the International School of Physics “Enrico Fermi”, Course CXL (IOS Press, Amsterdam) 1999.
Andrews M. R., Townsend C. G., Miesner H.-J., Durfee D. S., Kurn D. M. and Ketterle W., Science, 275 (1997) 637.
Einstein A., Sitzber. Kgl. Preuss. Akad. Wiss., (1924) 261; (1925) 3.
Bose S. N., Z. Phys., 26 (1924) 178.
Pitaevskii L. and Stringari S., Bose-Einstein Condensation (Oxford University Press) 2004.
Anderson M. H., Ensher J. R., Matthews M. R., Wieman C. E. and Cornell E. A., Science, 269 (1995) 198.
Davis K. B., Mewes M.-O., Andrews M. R., Van Druten N. J., Durfee D. S., Kurn D. M. and Ketterle W., Phys. Rev. Lett., 75 (1995) 3969.
Bradley C. C., Sackett C. A., Tollett J. J. and Hulet R. G., Phys. Rev. Lett., 75 (1995) 1687; 79 (1997) 1170.
Bradley C. C., Sackett C. A. and Hulet R. G., Phys. Rev. Lett., 78 (1997) 985.
Cornell E. A. and Wieman C. E., Rev. Mod. Phys., 74 (2002) 875.
Ketterle W., Rev. Mod. Phys., 74 (2002) 1131.
Fried D. G., Killian T. C., Willmann L., Landhuis D., Moss S. C., Kleppner D. and Greytak T. J., Phys. Rev. Lett., 81 (1998) 3811.
Cornish S. L., Claussen N. R., Roberts J. L., Cornell E. A. and Wieman C. E., Phys. Rev. Lett., 85 (2000) 001795.
Robert A., Sirjean O., Browaeys A., Poupard J., Nowak S., Boiron D., Westbrook C. I. and Aspect A., Science, 292 (2001) 5516.
Pereira Dos Santos F., Léonard J., Wang J., Barrelet C. J., Perales F., Rasel E., Unnikrishnan C. S., Leduc M. and Cohen-Tannoudji C., Phys. Rev. Lett., 86 (2001) 3459.
Modugno G., Ferrari G., Roati G., Brecha R. J., Simoni A. and Inguscio M., Science, 294 (2001) 1320.
Weber T., Herbig J., Mark M., Nägerl H.-C. and Grimm R., Science, 299 (2003) 232.
Takasu Y., Maki K., Komori K., Takano T., Honda K., Kumakura M., Yabuzaki T. and Takahashi Y., Phys. Rev. Lett., 91 (2003) 040404.
Griesmaier A., Werner J., Hensler S., Stuhler J. and Pfau T., Phys. Rev. Lett., 94 (2005) 160401.
Dalfovo F., Giorgini S., Pitaevskii L. and Stringari S., Rev. Mod. Phys., 71 (1999) 463.
Huang K., Statistical Mechanics (John Wiley & Sons) 1987.
Gross E. P., Nuovo Cimento, 20 (1961) 454.
Gross E. P., J. Math. Phys., 4 (1963) 195.
Pitaevskii L. P., Zh. Eksp. Teor. Fiz., 40 (1961) 646.
Rolston S. L. and Phillips W. D., Nature, 416 (2002) 219.
Gerton J. M., Strekalov D., Prodan I. and Hulet R. G., Nature, 408 (2000) 692.
Roberts J. L., Claussen N. R., Cornish S. L., Donley E. A., Cornell E. A. and Wieman C. E., Phys. Rev. Lett., 86 (2001) 4211.
Donley E. A., Claussen N. R., Cornish S. L., Roberts J. L., Cornell E. A. and Wieman C. E., Nature, 412 (2001) 295.
Tino G. M. and Inguscio M., Rivista del Nuovo Cimento, 22 (1999) 4.
Chu S., Rev. Mod. Phys., 70 (1998) 685.
Cohen-Tannoudji C., Rev. Mod. Phys., 70 (1998) 707.
Phillips W. D., Rev. Mod. Phys., 70 (1998) 721.
Hänsch T. W. and Schawlow A. L., Opt. Commun., 13 (1975) 68.
Masuhara N., Doyle J. M., Sandberg J. C., Kleppner D., Greytak T. J., Hess H. F. and Kochanski G. P., Phys. Rev. Lett., 61 (1988) 000935.
Raab E. L., Prentiss M., Cable A., Chu S. and Pritchard D. E., Phys. Rev. Lett., 59 (1987) 2631.
Monroe C., Swann W., Robinson H. and Wieman C., Phys. Rev. Lett., 65 (1990) 1571.
Migdall A. L., Prodan J. V., Phillips W. D., Bergeman T. H. and Metcalf H. J., Phys. Rev. Lett., 54 (1985) 2596.
Wing W. H., Progr. Quantum Electron., 8 (1994) 181.
Söding J., Guéry-Odelin D., Desbiolles P., Ferrari G. and Dalibard J., Phys. Rev. Lett., 80 (1998) 1869.
Esslinger T., Bloch I. and Hänsch T. W., Phys. Rev. A, 58 (1998) R2664.
Pritchard D. E., Phys. Rev. Lett., 51 (1983) 1336.
Majorana E., Nuovo Cimento, 9 (1932) 43.
Ketterle W. and Van Duten N. J., Evaporative cooling of trapped atoms, in Advances in Atomic, Molecular and Ocptical Physics, edited by Bederson B. and Walther H., vol. 37 (Academic Press, San Diego) 1996, pp. 181–236.
Roati G., Riboli F., Modugno G. and Inguscio M., Phys. Rev. Lett., 89 (2002) 150403.
Ketterle W., Durfee D. S. and Stamper-Kurn D. M., Making, probing and understanding Bose-Einstein condensates, in Bose-Einstein condensation in atomic gases, in Proceedings of the International School of Physics “Enrico Fermi”, edited by Inguscio M., Stringari S. and Wieman C. E., Course CXI (IOS Press, Amsterdam) 1999.
Cohen-Tannoudji C., Atomic motion in laser light, in Fundamental systems in Quantum optics, Les Houches, Session LIII (July 1990), edited by Dalibard J., Raimond J. M. and Zinn-Justin J. (Elsevier) 1992.
Grimm R., Weidemu¨ller M. and Ovchinnikov Y. B., Adv. At. Mol. Opt. Phys., 42 (2000) 95.
Allen L., Eberly J. H., Optical Resonance and Two Level Atoms (Dover Publications) 1987.
Metcalf H. J. and Van der Straten P., Laser Cooling and Trapping (Springer Verlag) 1999.
Siegman A. E., Lasers (University Science Books) 1986.
Stamper-Kurn D. M., Andrews M. R., Chikkatur A. P., Inouye S., Miesner H.-J., Stenger J. and Ketterle W., Phys. Rev. Lett., 80 (1998) 2027.
Barrett M. D., Sauer J. A. and Chapman M. S., Phys. Rev. Lett., 87 (2001) 010404.
Granade S. R., Gehm M. E., O’Hara K. M. and Thomas J. E., Phys. Rev. Lett., 88 (2002) 120405.
Fano U., Phys. Rev., 124 (1961) 1866.
Feshbach H., Ann. Phys. (N. Y.), 5 (1958) 357; 19 (1962) 287.
Tiesinga E., Verhaar B. J. and Stoof H. T. C., Phys. Rev. A, 47 (1993) 4114.
Donley E. A., Claussen N. R., Thompson S. T. and Wieman C. E., Nature, 417 (2002) 529.
O’Hara K. M., Hemmer S. L., Gehm M. E., Granade S. R., Thomas J. E., Science, 298 (2002) 2179.
Cubizolles J., Bourdel T., Kokkelmans S. J. J. M. F., Shlyapnikov G. V. and Salomon C., Phys. Rev. Lett., 91 (2003) 240401.
Jochim S., Bartenstein M., Altmeyer A., Hendl G., Chin C., Hecker Denschlag J. and Grimm R., Phys. Rev. Lett., 91 (2003) 240402.
Greiner M., Regal C. A. and Jin D. S., Nature, 426 (2003) 537.
Gustavson T. L., Chikkatur A. P., Leanhardt A. E., Görlitz A., Gupta S., Pritchard D. E. and Ketterle W., Phys. Rev. Lett., 88 (2002) 020401.
Chikkatur A. P., Shin Y., Leanhardt A. E., Kielpinski D., Tsikata E., Gustavson T. L., Pritchard D. E. and Ketterle W., Science, 296 (2002) 2193.
Shin Y., Saba S., Pasquini T., Ketterle W., Pritchard D. E. and Leanhardt A. E., Phys. Rev. Lett., 92 (2004) 050405.
Kozuma M., Deng L., Hagley E. W., Wen J., Lutwak R., Helmerson K., Rolston S. L. and Phillips W. D., Phys. Rev. Lett., 82 (1999) 871.
Ovchinnikov Yu. B., Mu¨ller J. H., Doery M. R., Vredenbregt E. J. D., Helmerson K., Rolston S. L. and Phillips W. D., Phys. Rev. Lett., 83 (1999) 284.
Raizen M., Salomon C. and Niu Q., Phys. Today, 50 (1997) 30.
Burger S., Bongs K., Dettmer S., Ertmer W., Sengstock K., Sanpera A., Shlyapnikov G. V. and Lewenstein M., Phys. Rev. Lett., 83 (1999) 5198.
Deng L., Hagley E. W., Wen J., Trippenbach M., Band Y. B., Julienne P. S., Simsarian J. E., Helmerson K., Rolston S. L. and Phillips W. D., Nature, 398 (1999) 218.
Wu B. and Niu Q., Phys. Rev. A, 64 (2001) 061603R.
Roati G., De Mirandes E., Ferlaino F., Ott H., Modugno G. and Inguscio M., Phys. Rev. Lett., 92 (2004) 230402.
London F., Phys. Rev., 54 (1938) 947.
Matthews M. R., Anderson B. P., Haljan P. C., Hall D. S., Wieman C. E. and Cornell E. A., Phys. Rev. Lett., 83 (1999) 2498.
Chevy F., Madison K. W. and Dalibard J., Phys. Rev. Lett., 85 (2000) 2223.
Maragò O. M., Hopkins S. A., Arlt J., Hodby E., Hechenblaikner G. and Foot C. J., Phys. Rev. Lett., 84 (2000) 2056.
Guéry-Odelin D. and Stringari S., Phys. Rev. Lett., 83 (2003) 4452.
Jin D. S., Ensher J. R., Matthews M. R., Wieman C. E. and Cornell E. A., Phys. Rev. Lett., 77 (1996) 420.
Mewes M.-O., Andrews M. R., Van Druten N. J., Kurn D. M., Durfee D. S., Townsend C. G. and Ketterle W., Phys. Rev. Lett., 77 (1996) 988.
Anderson B. P. and Kasevich M. A., Science, 282 (1998) 1686.
Greiner M., Bloch I., Mandel O., Hänsch T. W. and Esslinger T., Phys. Rev. Lett., 87 (2001) 160405.
Pedri P., Pitaevskii L., Stringari S., Fort C., Burger S., Cataliotti F. S., Maddaloni P., Minardi F. and Inguscio M., Phys. Rev. Lett., 87 (2001) 220401.
Cataliotti F. S., Burger S., Fort C., Maddaloni P., Minardi F., Trombettoni A., Smerzi A. and Inguscio M., Science, 293 (2001) 843.
Greiner M., Mandel O., Esslinger T., Hänsch T. W. and Bloch I., Nature, 415 (2002) 39.
Brennen G. K., Caves C. M., Jessen P. S. and Deutsch I. H., Phys. Rev. Lett., 82 (1999) 1060.
Jaksch D., Briegel H.-J., Cirac J. I., Gardiner C. W. and Zoller P., Phys. Rev. Lett., 82 (1999) 1975.
Schmidt-Kaler F., Häffner H., Riebe M., Gulde S., Lancaster G. P. T., Deuschle T., Becher C., Roos C. F., Eschner J. and Blatt R., Nature, 422 (2003) 408.
Leibfried D., DeMarco B., Meyer V., Lucas D., Barrett M., Britton J., Itano W. M., Jelenković B., Langer C., Rosenband T. and Wineland D. J., Nature, 422 (2003) 412.
Mandel O., Greiner M., Widera A., Rom T., Hänsch T. W. and Bloch I., Nature, 425 (2003) 937.
Ashcroft N. W. and Mermin N. D., Solid State Physics (Saunders College Publishing) 1976.
Bassani F. and Grassano U. M., Fisica dello stato solido (Bollati Boringhieri) 2000.
Slater J. C., Phys. Rev., 87 (1976) 807.
Zener C., Proc. R. Soc. London A, 145 (1934) 523.
Wu B. and Niu Q., New Journ. Phys., 5 (2003) 104.
Machholm M., Pethick C. J. and Smith H., Phys. Rev. A, 67 (2003) 053613.
Seaman B. T., Carr L. D. and Holland M. J., Phys. Rev. A, 71 (2005) 033622.
Machholm M., Nicolin A., Pethick C. J. and Smith H., Phys. Rev. A, 69 (2004) 043604.
Louis P. J. Y., Ostrovskaya E. A., Savage C. M. and Kivshar Y. S., Phys. Rev. A, 67 (2003) 013602.
Trombettoni A. and Smerzi A., Phys. Rev. Lett., 86 (2001) 2353.
Fisher M. P. A., Weichman P. B., Grinstein G. and Fisher D. S., Phys. Rev. B, 40 (1989) 546.
Jaksch D., Bruder C., Cirac J. I., Gardiner C. W. and Zoller P., Phys. Rev. Lett., 81 (1998) 3108.
Fallani L., Fort C., Lye J. E. and Inguscio M., Opt. Express, 13 (2005) 4303.
Hadzibabic Z., Stock S., Battelier B., Bretin V. and Dalibard J., Phys. Rev. Lett., 93 (2004) 180403.
Cennini G., Geckeler C., Ritt G. and Weitz M., Phys. Rev. A, 72 (2005) 051601(R).
Modugno G., De Mirandes E., Ferlaino F., Ott H., Roati G. and Inguscio M., Fortschr. Phys., 52 (2004) 1173.
Carusotto I., Pitaevskii L., Stringari S., Modugno G. and Inguscio M., Phys. Rev. Lett., 95 (2005) 093202.
Ferlaino F., Maddaloni P., Burger S., Cataliotti F. S., Fort C., Modugno M. and Inguscio M., Phys. Rev. A, 66 (2002) 011604R.
Denschlag J. H., Simsarian J. E., Häffner H., McKenzie C., Browaeys A., Cho D., Helmerson K., Rolston S. L. and Phillips W. D., J. Phys. B, 35 (2002) 3095.
Morsch O., Mu¨ller J. H., Cristiani M., Ciampini D. and Arimondo E., Phys. Rev. Lett., 87 (2001) 140402.
Fallani L., Cataliotti F. S., Catani J., Fort C., Modugno M., Zawada M. and Inguscio M., Phys. Rev. Lett., 91 (2003) 240405.
Eiermann B., Treutlein P., Anker Th., Albiez M., Taglieber M., Marzlin K. P. and Oberthaler M. K., Phys. Rev. Lett., 91 (2003) 060402.
Cataliotti F. S., Fallani L., Ferlaino F., Fort C., Maddaloni P. and Inguscio M., New J. Phys., 5 (2003) 71.
Nesi F. and Modugno M., J. Phys. B, 37 (2004) S101.
Smerzi A., Trombettoni A., Kevrekidis P. G. and Bishop A. R., Phys. Rev. Lett., 89 (2002) 170402.
Fallani L., De Sarlo L., Lye J. E., Modugno M., Saers R., Fort C. and Inguscio M., Phys. Rev. Lett., 93 (2004) 140406.
Modugno M., Tozzo C. and Dalfovo F., Phys. Rev. A, 70 (2004) 043625.
De Sarlo L., Fallani L., Lye J. E., Modugno M., Saers R., Fort C. and Inguscio M., Phys. Rev. A, 72 (2005) 013603.
Khaykovich L., Schreck F., Ferrari G., Bourdel T., Cubizolles J., Carr L. D., Castin Y. and Salomon C., Science, 296 (2002) 1290.
Strecker K. E., Partridge G. B., Truscott A. G. and Hulet R. G., Nature, 417 (2002) 150.
Eiermann B., Anker Th., Albiez M., Taglieber M., Treutlein P., Marzlin K. P. and Oberthaler M. K., Phys. Rev. Lett., 92 (2004) 230401.
Fertig C. D., O’Hara K. M., Huckans J. H., Rolston S. L., Phillips W. D. and Porto J. V., Phys. Rev. Lett., 94 (2005) 120403.
Polkovnikov A., Altman E., Demler E., Halperin B. and Lukin M. D., Phys. Rev. A, 71 (2005) 063613.
Gea-Banacloche J., Rey A. M., Pupillo G., Williams C. J. and Clark C. W., Phys. Rev. A, 73 (2006) 013605.
Paredes B., Widera A., Murg V., Mandel O., Fölling S., Cirac I., Shlyapnikov G. V., Hänsch T. W. and Bloch I., Nature, 429 (2004) 277.
Kinoshita T., Wenger T. and Weiss D. S., Science, 305 (2004) 1125.
Boiron D., Mennerat-Robilliard C., Fournier J.-M., Guidoni L., Salomon C. and Grynberg G., Eur. Phys. J. D, 7 (1999) 373.
Reppy J. D., J. Low Temp. Phys., 87 (1992) 205.
Astrakharchik G. E., Boronat J., Casulleras J. and Giorgini S., Phys. Rev. A, 66 (2002) 023603.
Giorgini S., Pitaevskii L. and Stringari S., Phys. Rev. B, 49 (1994) 12938.
Huang K. and Meng H. F., Phys. Rev. Lett., 69 (1992) 644
Fisher M. P. A., Weichman P. B., Grinstein G. and Fisher D. S., Phys. Rev. B, 40 (1989) 546.
Scalettar R. T., Batrouni G. G. and Zimanyi G. T., Phys. Rev. Lett., 66 (1991) 3144.
Krauth W., Trivedi N. and Ceperley D., Phys. Rev. Lett., 67 (1991) 2307.
Anderson P. W., Phys. Rev., 109 (1958) 1492.
Lee P. A. and Ramakrishnan T. V., Rev. Mod. Phys, 57 (1985) 287.
Wiersma D. S., Bartolini P., Lagendijk A. and Righini R., Nature, 390 (1997) 671.
Roth R. and Burnett K., Phys. Rev. A, 68 (2003) 023604.
Damski B., Zakrzewski J., Santos L., Zoller P. and Lewenstein M., Phys. Rev. Lett., 91 (2003) 080403.
Fortágh J., Ott H., Kraft S., Günther A. and Zimmermann C., Phys. Rev. A, 66 (2002) 041604(R).
Leanhardt A. E., Chikkatur A. P., Kielpinski D., Shin Y., Gustavson T. L., Ketterle W. and Pritchard D. E., Phys. Rev. Lett., 89 (2002) 040401.
Estève J., Aussibal C., Figl C., Mailly D., Bouchoule I., Westbrook C. I. and Aspect A., Phys. Rev. A, 70 (2004) 043629.
Jones M. P. A., Vale C. J., Sahagun D., Hall B. V. and Hinds E. A., Phys. Rev. Lett., 91 (2003) 080401.
Wang D. W., Lukin M. D. and Demler E., Phys. Rev. Lett., 92 (2004) 076802.
Lye J. E., Fallani L., Modugno M., Wiersma D., Fort C. and Inguscio M., Phys. Rev. Lett., 95 (2005) 070401.
Dettmer S., Hellweg D., Ryytty P., Arlt J. J., Ertmer W., Sengstock K., Petrov D. S., Shlyapnikov G. V., Kreutzmann H., Santos L. and Lewenstein M., Phys. Rev. Lett., 87 (2001) 160406.
Richard S., Gerbier F., Thywissen J. H., Hugbart M., Bouyer P. and Aspect A., Phys. Rev. Lett., 91 (2003) 010405.
Fort C., Fallani L., Guarrera V., Lye J. E., Modugno M., Wiersma D. S. and Inguscio M., Phys. Rev. Lett., 95 (2005) 170410.
Clément D., Varo´n A. F., Hugbart M., Retter J. A., Bouyer P., Sanchez-Palencia L., Gangardt D. M., Shlyapnikov G. V. and Aspect A., Phys. Rev. Lett., 95 (2005) 170409.
Modugno M., Phys. Rev. A, 73 (2006) 013606.
Gavish U. and Castin Y., Phys. Rev. Lett., 95 (2005) 020401.
Gimperlein H., Wessel S., Schmiedmayer J. and Santos L., Phys. Rev. Lett., 95 (2005) 170401.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Fallani, L., Fort, C. & Inguscio, M. Bose-Einstein condensates in optical potentials. Riv. Nuovo Cim. 28, 1–57 (2005). https://doi.org/10.1393/ncr/i2005-10009-7
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1393/ncr/i2005-10009-7