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Effects of Interactions and Temperature in Disordered Ultra-Cold Bose Gases

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DOI: 10.4236/jmp.2014.58077    2,510 Downloads   3,190 Views   Citations

ABSTRACT

We simulate ultra-cold interacting bosons in quasi-one-dimensional, incommensurate optical lattices. In the tight-binding limit, these lattices have pseudo-random on-site energies and thus can potentially lead to Anderson localization. We use the Hartree-Fock-Bogoliubov formalism in the Bose-Hubbard model to explore the parameter regimes that lead to exponential localization of the ground state in a 3-colour optical lattice and investigate the role of repulsive interactions, harmonic confinement and finite temperature.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Adolphs, C. , Towers, J. , Piraud, M. , Krutitsky, K. and Hutchinson, D. (2014) Effects of Interactions and Temperature in Disordered Ultra-Cold Bose Gases. Journal of Modern Physics, 5, 661-672. doi: 10.4236/jmp.2014.58077.

References

[1] Morsch, O. and Oberthaler, M. (2006) Reviews of Modern Physics, 78, 179-215.
http://dx.doi.org/10.1103/RevModPhys.78.179
[2] Lewenstein, M., Sanpera, A., Ahufinger, V., Damski, B., Sen(De), A. and Sen, U. (2007) Advances in Physics, 56, 243-379.
http://dx.doi.org/10.1080/00018730701223200
[3] Fallani, L., Fort, C. and Inguscio, M. (2008) Advances in Atomic, Molecular, and Optical Physics, 56, 119-160.
http://dx.doi.org/10.1016/S1049-250X(08)00012-8
[4] Bloch, I., Dalibard, J. and Zwerger, W. (2008) Reviews of Modern Physics, 80, 885-964.
http://dx.doi.org/10.1103/RevModPhys.80.885
[5] Sanchez-Palencia, L. and Lewenstein, M. (2010) Nature Physics, 6, 87-95.
http://dx.doi.org/10.1038/nphys1507
[6] Modugno, G. (2010) Reports on Progress in Physics 73, Article ID: 102401.
http://dx.doi.org/10.1088/0034-4885/73/10/102401
[7] Inouye, S., Andrews, M.R., Stenger, J., Miesner, H.-J., Stamper-Kurn, D.M. and Ketterle, W. (1998) Nature (London), 392, 151-154.
http://dx.doi.org/10.1038/32354
[8] Olshanii, M. (1998) Physical Review Letters, 81, 938-941.
http://dx.doi.org/10.1103/PhysRevLett.81.938
[9] Dunjko, V., Lorent, V. and Olshanii, M. (2001) Physical Review Letters, 86, 5413-5416.
http://dx.doi.org/10.1103/PhysRevLett.86.5413
[10] Haller, E., Gustavsson, M., Mark, M.J., Danzl, J.G., Hart, R., Pupillo, G. and Nager, H.-C. (2009) Science, 325, 1224-1227.
http://dx.doi.org/10.1126/science.1175850
[11] Schulte, T., Drenkelforth, S., Kruse, J., Ertmer, W., Arlt, J., Sacha, K., Zakrzewski, J. and Lewenstein, M. (2005) Physical Review Letters, 95, Article ID: 170411.
http://dx.doi.org/10.1103/PhysRevLett.95.170411
[12] White, M., Pasienski, M., McKay, D., Zhou, S.Q., Ceperley, D. and DeMarco, B. (2009) Physical Review Letters, 102, Article ID: 055301.
http://dx.doi.org/10.1103/PhysRevLett.102.055301
[13] Pasienski, M., McKay, D., White, M. and DeMarco, B. (2010) Nature Physics, 6, 677-680.
http://dx.doi.org/10.1038/nphys1726
[14] Fallani, L., Lye, J.E., Guarrera, V., Fort, C. and Inguscio, M. (2007) Physical Review Letters, 98, Article ID: 130404.
http://dx.doi.org/10.1103/PhysRevLett.98.130404
[15] Roati, G., D’Errico, C., Fallani, L., Fattori, M., Fort, C., Zaccanti, M., Modugno, G., Modugno, M. and Inguscio, M. (2008) Nature (London), 453, 895-898.
http://dx.doi.org/10.1038/nature07071
[16] Schulte, T., Drenkelforth, S., Kruse, J., Tiemeyer, R., Sacha, K., Zakrzewski, J., Lewenstein, M., Ertmer, W. and Arlt, J.J. (2006) New Journal of Physics, 8, 230.
http://dx.doi.org/10.1088/1367-2630/8/10/230
[17] Guarrera, V., Fallani, L., Lye, J.E., Fort, C. and Inguscio, M. (2007) New Journal of Physics, 9, 107.
http://dx.doi.org/10.1088/1367-2630/9/4/107
[18] Guidoni, L., Triché, C., Verkerk, P. and Grynberg, G. (1997) Physical Review Letters, 79, 3363-3366.
http://dx.doi.org/10.1103/PhysRevLett.79.3363
[19] Lye, J.E., Fallani, L., Fort, C., Guarrera, V., Modugno, M., Wiersma, D.S. and Inguscio, M. (2007) Physical Review A, 75, Article ID: 061603(R).
http://dx.doi.org/10.1103/PhysRevA.75.061603
[20] Deissler, B., Zaccanti, M., Roati, G., D’Errico, C., Fattori, M., Modugno, M., Modugno, G. and Inguscio, M. (2010) Nature Physics, 6, 354-358.
http://dx.doi.org/10.1038/nphys1635
[21] Deissler, B., Lucioni, E., Modugno, M., Roati, G., Tanzi, L., Zaccanti, M., Inguscio, M. and Modugno, G. (2011) New Journal of Physics, 13, Article ID: 023020.
http://dx.doi.org/10.1088/1367-2630/13/2/023020
[22] Lucioni, E., Deissler, B., Tanzi, L., Roati, G., Zaccanti, M., Modugno, M., Larcher, M., Dalfovo, F., Inguscio, M. and Modugno, G. (2011) Physical Review Letters, 106, Article ID: 230403.
http://dx.doi.org/10.1103/PhysRevLett.106.230403
[23] Gadway, B., Pertot, D., Reeves, J., Vogt, M. and Schneble, D. (2011) Physical Review Letters, 107, Article ID: 145306.
http://dx.doi.org/10.1103/PhysRevLett.107.145306
[24] Anderson, P.W. (1958) Absence of Diffusion in Certain Random Lattices. Physical Review, 109, 1492-1505.
(For a review, see Kramer, B. and MacKinnon, A. (1993) Localization: Theory and experiment. Reports on Progress in Physics, 56, 1469.)
http://dx.doi.org/10.1088/0034-4885/56/12/001
[25] Aubry, S. and André, G. (1980) Annals of the Israel Physical Society, 3, 133.
[26] Harper, P.G. (1955) Proceedings of the Physical Society. Section A, 68, 874.
http://dx.doi.org/10.1088/0370-1298/68/10/304
[27] Grempel, D.R., Fishman, S. and Prange, R.E. (1982) Physical Review Letters, 49, 833-836.
http://dx.doi.org/10.1103/PhysRevLett.49.833
[28] Kohmoto, M. (1983) Physical Review Letters, 51, 1198-1201. http://dx.doi.org/10.1103/PhysRevLett.51.1198
[29] Diener, R.B., Georgakis, G.A., Zhong, J., Raizen, M. and Niu, Q. (2001) Physical Review A, 64, Article ID: 033416.
http://dx.doi.org/10.1103/PhysRevA.64.033416
[30] Ingold, G.L., Wobst, A., Aulbach, Ch. and Hanggi, P. (2002) European Physical Journal B, 30, 175-179.
http://dx.doi.org/10.1140/epjb/e2002-00372-9
[31] Boers, D.J., Goedeke, B., Hinrichs, D. and Holthaus, M. (2007) Physical Review A, 75, Article ID: 063404.
http://dx.doi.org/10.1103/PhysRevA.75.063404
[32] Biddle, J. and Sarma, S.D. (2010) Physical Review Letters, 104, Article ID: 070601.
http://dx.doi.org/10.1103/PhysRevLett.104.070601
[33] Larcher, M., Modugno, M. and Dalfovo, F. (2011) Physical Review A, 83, Article ID: 013624.
http://dx.doi.org/10.1103/PhysRevA.83.013624
[34] Larcher, M., Dalfovo, F. and Modugno, M. (2009) Physical Review A, 80, Article ID: 053606.
http://dx.doi.org/10.1103/PhysRevA.80.053606
[35] Zhang, Z., Tong, P., Gong, J. and Li, B. (2011) Physical Review E, 83, Article ID: 056205.
http://dx.doi.org/10.1103/PhysRevE.83.056205
[36] Adhikari, S.K. and Salasnich, L. (2009) Physical Review A, 80, Article ID: 023606.
http://dx.doi.org/10.1103/PhysRevA.80.023606
[37] Sanchez-Palencia, L. and Santos, L. (2005) Physical Review A, 72, Article ID: 053607.
http://dx.doi.org/10.1103/PhysRevA.72.053607
[38] Cetoli, A. and Lundh, E. (2010) Physical Review A, 81, Article ID: 063635.
http://dx.doi.org/10.1103/PhysRevA.81.063635
[39] Shrestha, U. and Modugno, M. (2010) Physical Review A, 82, Article ID: 033604.
http://dx.doi.org/10.1103/PhysRevA.82.033604
[40] Roscilde, T. (2008) Physical Review A, 77, Article ID: 063605. http://dx.doi.org/10.1103/PhysRevA.77.063605
[41] Schmitt, F., Hild, M. and Roth, R. (2009) Physical Review A, 80, Article ID: 023621.
http://dx.doi.org/10.1103/PhysRevA.80.023621
[42] Deng, X., Citro, R., Minguzzi, A. and Orignac, E. (2008) Physical Review A, 78, Article ID: 013625.
http://dx.doi.org/10.1103/PhysRevA.78.013625
[43] Roux, G., Barthel, T., McCulloch, I.P., Kollath, C., Schollwock, U. and Giamarchi, T. (2008) Physical Review A, 78, Article ID: 023628.
http://dx.doi.org/10.1103/PhysRevA.78.023628
[44] Deng, X., Citro, R., Orignac, E. and Minguzzi, A. (2009) European Physical Journal B, 68, 435-443.
http://dx.doi.org/10.1140/epjb/e2009-00069-7
[45] Rey, A.M., Satija, I.I. and Clark, C.W. (2006) Physical Review A, 73, Article ID: 063610.
http://dx.doi.org/10.1103/PhysRevA.73.063610
[46] Cai, X., Chen, S. and Wang, Y. (2010) Superfluid-to-Bose-glass transition of hard-core bosons in a one-dimensional incommensurate optical lattice. Physical Review A, 81, Article ID: 023626.
[47] Cai, X., Chen, S. and Wang, Y. (2010) Ground-state and dynamical properties of hard-core bosons in one-dimensional incommensurate optical lattices with a harmonic trap. Physical Review A, 81, Article ID: 053629.
[48] Towers, J., Cormack, S.C. and Hutchinson, D.A.W. (2013) Physical Review A, 88, Article ID: 043625.
http://dx.doi.org/10.1103/PhysRevA.88.043625
[49] Jachymski, K. and Idziaszek, Z. (2012) Physical Review A, 86, Article ID: 023607.
http://dx.doi.org/10.1103/PhysRevA.86.023607
[50] Pethick, C.J. and Smith, H. (2002) Bose-Einstein Condensation in Dilute Gases. Cambridge University Press, Cambridge.
[51] Griffin, A. (1996) Physical Review B, 53, 9341-9347.
http://dx.doi.org/10.1103/PhysRevB.53.9341
[52] Hutchinson, D.A.W., Zaremba, E. and Griffin, A. (1997) Physical Review Letters, 78, 1842-1845.
http://dx.doi.org/10.1103/PhysRevLett.78.1842
[53] Hutchinson, D.A.W., Burnett, K., Dodd, R.J., Morgan, S.A., Rusch, M., Zaremba, E., Proukakis, N.P., Edwards, M. and Clark, C.W. (2000) Journal of Physics B, 33, 3825.
http://dx.doi.org/10.1088/0953-4075/33/19/302
[54] Wild, B.G., Blakie, P.B. and Hutchinson, D.A.W. (2006) Physical Review A, 73, Article ID: 023604.
http://dx.doi.org/10.1103/PhysRevA.73.023604
[55] Rey, A.M., Burnett, K., Roth, R., Edwards, M., Williams, C.J. and Clark, C.W. (2003) Journal of Physics B, 36, 825.
http://dx.doi.org/10.1088/0953-4075/36/5/304
[56] van Oosten, D., van der Straten, P. and Stoof, H.T.C. (2001) Physical Review A, 63, Article ID: 053601.
http://dx.doi.org/10.1103/PhysRevA.63.053601
[57] Lieb, E.H., Seiringer, R. and Yngvason, J. (2002) Physical Review B, 66, Article ID: 134529.
http://dx.doi.org/10.1103/PhysRevB.66.134529
[58] Batrouni, G.G. and Scallettar, R.T. (1992) Physical Review B, 46, 9051-9062.
http://dx.doi.org/10.1103/PhysRevB.46.9051

  
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