Abstract
We study Anderson localization of single particles in continuous, correlated, one-dimensional disordered potentials. We show that tailored correlations can completely change the energy-dependence of the localization length. By considering two suitable models of disorder, we explicitly show that disorder correlations can lead to a nonmonotonic behavior of the localization length versus energy. Numerical calculations performed within the transfer-matrix approach and analytical calculations performed within the phase formalism up to order three show excellent agreement and demonstrate the effect. We finally show how the nonmonotonic behavior of the localization length with energy can be observed using expanding ultracold-atom gases.
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References
P.W. Anderson, Phys. Rev. 109, 1492 (1958)
J.-L. Basdevant, J. Dalibard, Quantum Mechanics (Springer, Berlin, 2005)
V.L. Berezinskii, Sov. Phys. JETP 38, 620 (1974)
A. Bernard, W. Guerin, J. Billy, F. Jendrzejewski, P. Cheinet, A. Aspect, V. Josse, P. Bouyer, New J. Phys. 13, 065015 (2011)
J. Billy, V. Josse, Z. Zuo, A. Bernard, B. Hambrecht, P. Lugan, D. Clément, L. Sanchez-Palencia, P. Bouyer, A. Aspect, Nature (London) 453, 891 (2008)
Y. Castin, R. Dum, Phys. Rev. Lett. 77, 5315 (1996)
Y.P. Chen, J. Hitchcock, D. Dries, M. Junker, C. Welford, R.G. Hulet, Phys. Rev. A 77, 033632 (2008)
D. Clément, P. Bouyer, A. Aspect, L. Sanchez-Palencia, Phys. Rev. A 77, 033631 (2008)
D. Clément, A.F. Varón, J.A. Retter, L. Sanchez-Palencia, A. Aspect, P. Bouyer, New J. Phys. 8, 165 (2006)
P.-G. de Gennes, Superconductivity of Metals and Alloys (Addison-Wesley, 1995)
D. Dries, S.E. Pollack, J.M. Hitchcock, R.G. Hulet, Phys. Rev. A 82, 033603 (2010)
A.M. García-García, E. Cuevas, Phys. Rev. B 79, 073104 (2009)
A.A. Gogolin, Sov. Phys. JETP 44, 1003 (1976)
A.A. Gogolin, V.I. Mel’nikov, E.I. Rashba, Sov. Phys. JETP 42, 168 (1976)
J.W. Goodman, Speckle Phenomena in Optics: Theory and Applications (Roberts and Co, Englewood, 2007)
W. Guerin, J.-F. Riou, J.P. Gaebler, V. Josse, P. Bouyer, A. Aspect, Phys. Rev. Lett. 97, 200402 (2006)
E. Gurevich, O. Kenneth, Phys. Rev. A 79, 063617 (2009)
H. Hu, A. Strybulevych, J.H. Page, S.E. Skipetrov, B.A. van Tiggelen, Nature Phys. 4, 845 (2008)
F.M. Izrailev, A.A. Krokhin, Phys. Rev. Lett. 82, 4062 (1999)
M. Janssen, Phys. Rep. 295, 1 (1998)
F. Jendrzejewski, A. Bernard, K. Müller, P. Cheinet, V. Josse, M. Piraud, L. Pezzé, L. Sanchez-Palencia, A. Aspect, P. Bouyer, Nature Phys. 8, 398 (2012)
S. John, Phys. Rev. Lett. 53, 2169 (1984)
Yu. Kagan, E.L. Surkov, G.V. Shlyapnikov, Phys. Rev. A 54, R1753 (1996)
S.S. Kondov, W.R. McGehee, J.J. Zirbel, B. DeMarco, Science 334, 66 (2011)
S. Kotani, S. Taniguchi, Proc. Int. Symp. Kyoto (Mathematical Library, vol. 32, North-Holland, Amsterdam, 1984), p. 225
U. Kuhl, F.M. Izrailev, A.A. Krokhin, Phys. Rev. Lett. 100, 126402 (2008)
U. Kuhl, F.M. Izrailev, A.A. Krokhin, H.-J. Stöckmann, Appl. Phys. Lett. 77, 633 (2000)
Y. Lahini, A. Avidan, F. Pozzi, M. Sorel, R. Morandotti, D.N. Christodoulides, Y. Silberberg, Phys. Rev. Lett. 100, 013906 (2008)
P.A. Lee, T.V. Ramakrishnan, Rev. Mod. Phys. 57, 287 (1985)
I.M. Lifshits, S.A. Gredeskul, L.A. Pastur, Introduction to the Theory of Disordered Systems (Wiley, New York, 1988)
P. Lugan, A. Aspect, L. Sanchez-Palencia, D. Delande, B. Grémaud, C.A. Müller, C. Miniatura, Phys. Rev. A 80, 023605 (2009)
C.A. Müller, D. Delande, Ultracold Gases and Quantum Information, edited by C. Miniatura et al., Lecture Notes of the Les Houches Summer School in Singapore 2009: vol. XCI, chapter Disorder and interference: localization phenomena (Oxford University Press, Oxford, 2011)
M. Piraud, P. Lugan, P. Bouyer, A. Aspect, L. Sanchez-Palencia, Phys. Rev. A 83, 031603 (2011)
M. Piraud, A. Aspect, L. Sanchez-Palencia, Phys. Rev. A 85, 063611 (2012)
M. Piraud, L. Pezzé, L. Sanchez-Palencia, Europhys. Lett. 99, 50003 (2012)
M. Piraud, L. Pezzé, L. Sanchez-Palencia, Quantum transport of atomic matterwaves in anisotropic 2d and 3d disorder [arXiv:1211.5872, 2012]
M. Płodzień, S. Krzvsztof, Phys. Rev. A 84, 023624 (2011)
J.D. Reppy, J. Low Temp. Phys. 87, 205 (1992)
G. Roati, C. D’Errico, L. Fallani, M. Fattori, C. Fort, M. Zaccanti, G. Modugno, M. Modugno, M. Inguscio, Nature (London) 453, 895 (2008)
N.P. Robins, C. Figl, S.A. Haine, A.K. Morrison, M. Jeppesen, J.J. Hope, J.D. Close, Phys. Rev. Lett. 96, 140403 (2006)
L. Sanchez-Palencia, D. Clément, P. Lugan, P. Bouyer, A. Aspect, New J. Phys. 10, 045019 (2008)
L. Sanchez-Palencia, D. Clément, P. Lugan, P. Bouyer, G.V. Shlyapnikov, A. Aspect, Phys. Rev. Lett. 98, 210401 (2007)
L. Sanchez-Palencia, M. Lewenstein, Nature Phys. 6, 87 (2010)
T. Schwartz, G. Bartal, S. Fishman, M. Segev, Nature (London) 446, 52 (2007)
T.A. Sedrakyan, J.P. Kestner, S. Das Sarma, Phys. Rev. A 84, 053621 (2011)
T. Sedrakyan, Phys. Rev. B 69, 085109 (2004)
B. Shapiro, J. Phys. A: Math. Theor. 45, 143001 (2012)
M. Störzer, P. Gross, C.M. Aegerter, G. Maret, Phys. Rev. Lett. 96, 063904 (2006)
D.S. Wiersma, P. Bartolini, A. Lagendijk, R. Righini, Nature (London) 390, 671 (1997)
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Piraud, M., Sanchez-Palencia, L. Tailoring Anderson localization by disorder correlations in 1D speckle potentials. Eur. Phys. J. Spec. Top. 217, 91–102 (2013). https://doi.org/10.1140/epjst/e2013-01758-6
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DOI: https://doi.org/10.1140/epjst/e2013-01758-6