Abstract
We calculate the critical temperature of the Bose-Einstein condensation of an ideal Bosegas in the presence of an external periodic potential in one, two, or three directions. A number of assumed approximations enables us to show that the only parameter determining the critical temperature of condensation is the width of the lower energy band with the direct proportionality to the one-third power of this width for each direction of periodicity of the external potential. This also proves the result, obtained earlier by means of numerical calculation, that deepening of the periodic potential (which is known to lead to narrowing of energy bands) leads to lowering of the critical temperature. The fundamental role of quantum tunneling in establishing this regularity is emphasized.
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References
Bose-Einstein Condensation in Atomic Gases, Inguscio, M., Stringari, S., and Wieman, C., Eds., Amsterdam: IOS Press, 1999, Anglin, J.R. and Ketterle, W., Nature, 2002, vol. 416, p. 211; Castin, Y., arXive:condmat/0105058; Leggett, A.J., Rev. Mod. Phys., 2001, vol. 73, p. 307; Pethick, C.J. and Smith, H., Bose-Einstein Condensation in Dilute Gases, Cambridge, 2004.
Muradyan, A.Zh. and Arutyunyan, G.L., J. Contemp. Phys. (Armenian Ac. Sci.), 2000, vol. 35, no. 1, p. 1.
Burger, S., Cataliotti, F.S., Fort, C., Maddaloni, P., Minardi, F., and Inguscio, M., Europhys. Lett., 2002, vol. 57, p. 1.
Muradyan, A.Zh. and Muradyan, G.A., arXive:cond-mat/0302108.
Bloch, I., J. Phys. B: At. Mol. Opt. Phys., 2005, vol. 38, p. s629; Oberthaler, M.K., Abfalterer, R., Bernet, S., Schmiedmayer, J., and Zeilinger, A., Phys. Rev. Lett., 1996, vol. 77, p. 4980; Cohen, J.L., Dubetsky, B., and Berman, P.R., Phys. Rev. A, 1999, vol. 60, p. 4886; Berg-Sorensen, K. and Molmer, K., Phys. Rev. A, 1998, vol. 58, p. 1480; Jaksch, D., Bruder, C., Cirac, J.I., Gardiner, C.W., and Zoller, P., Phys. Rev. Lett., 1998, vol. 81, p. 3108; Burger, S., Cataliotti, F., Fort, C., Minardi, F., Inguscio, M., Chiofalo, M.L., and Tosi, M.P., Phys. Rev. Lett., 2001, vol. 86, p. 4447; Cataliotti, F.S., Burger, S., Fort, C., Maddaloni, P., Minardi, F., Trombettoni, A., Smerzi, A., and Inguscio, M., Science, 2001, vol. 293, p. 843; Greiner, M., Mandel, O., Esslinger, T., Hansch, T.W., and Bloch, I., Nature, 2002, vol. 415, p. 6867; Giampaolo, S.M., Illuminati, F., Mazzarella, G., and De Siena, S., Phys. Rev. A, 2004, vol. 70, p. 061601(R); Messignan, P. and Castin, Y., arXive:cond-mat/0604232, Blakie, P.B., Rey, A.-M., and Bezett, A., arXive:cond-mat/0608522.
Huang, K., Statistical Mechanics, New York: Wiley, 1963; Balescu, R., Equilibrium and Nonequilibrium Statistical Mechanics, New York: Wiley, 1975.
Vogels, J.M., Xu, K., Raman, C., Abo-Shaeer, J.R., and Ketterle, W., Phys. Rev. Lett., 2002, vol. 88, p. 060402; Stöferle, T., Moritz, H., Schori, C., Köhl, M., and Esslinger, T., Phys. Rev. Lett., 2004, vol. 92, p. 130403; Fallani, L., De Sarlo, L., Lye, J.E., Modugno, M., Saers, R., Fort, C., and Inguscio, M., Phys. Rev. Lett., 2004, vol. 93, p. 140406; Gerbier, F., Widera, A., Fölling, S., Mandel, O., Gericke, T., and Bloch, I., Phys. Rev. Lett., 2005, vol. 95, p. 050404.
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Original Russian Text © G.A. Muradyan, A.Zh. Muradyan, 2007, published in Izvestiya NAN Armenii, Fizika, 2007, Vol. 42, No. 3, pp. 138–140.
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Muradyan, G.A., Muradyan, A.Z. Theory of adiabatic variation of critical temperature of the Bose-Einstein condensation of an ideal gas in optical lattice. J. Contemp. Phys. 42, 94–100 (2007). https://doi.org/10.3103/S1068337207030034
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DOI: https://doi.org/10.3103/S1068337207030034