Tunnelling rates for the nonlinear Wannier-Stark problem

[en] We present a method to numerically compute accurate tunnelling rates for a Bose-Einstein condensate which is described by the nonlinear Gross-Pitaevskii equation. Our method is based on a sophisticated real-time integration of the complex-scaled Gross-Pitaevskii equation, and it is capable of finding the stationary eigenvalues for the Wannier-Stark problem. We show that even weak nonlinearities have significant effects in the vicinity of very sensitive resonant tunnelling peaks, which occur in the rates as a function of the Stark field amplitude. The mean-field interaction induces a broadening and a shift of the peaks, and the latter is explained by an analytic perturbation theory.

Disciplines :

Physics

Author, co-author :

Wimberger, S.

Schlagheck, Peter ; Université de Liège - ULiège > Département de physique > Physique quantique statistique

Mannella, R.

Language :

English

Title :

Tunnelling rates for the nonlinear Wannier-Stark problem

Publication date :

2006

Journal title :

Journal of Physics : B Atomic Molecular and Optical Physics

ISSN :

0953-4075

eISSN :

1361-6455

Publisher :

Institute of Physics, Bristol, United Kingdom

Volume :

Issue :

Pages :

729-740

Peer reviewed :

Peer Reviewed verified by ORBi

Available on ORBi :

since 05 November 2010

Statistics

Number of views

43 (1 by ULiège)

Number of downloads

1 (1 by ULiège)

More statistics

Scopus citations^®

Scopus citations^®
without self-citations

OpenCitations

OpenAlex citations

Bibliography

Kittel C 1996 Introduction to Solid State Physics (New York: Wiley)
Nenciu G 1991 Rev. Mod. Phys. 63 91
Grecchi V and Sacchetti A 1997 Phys. Rev. Lett. 78 4474
Holthaus M 2000 J. Opt. B 2 589
Glück M, Kolovsky A R and Korsch H J 2002 Phys. Rep. 366 103
Kolovsky A R and Korsch H J 2004 Int. J. Mod. Phys. B 18 1235
Cristiani M, Morsch O, Müller J H, Ciampini D and Arimondo E 2002 Phys. Rev. A 66 021601
Morsch O, Müller J H, Cristiani M, Ciampini D and Arimondo E 2001 Phys. Rev. Lett. 87 140402
Glück M, Kolovsky A R and Korsch H J 1999 Phys. Rev. Lett. 83 891
Glutsch S 2004 Phys. Rev. B 89 235317
Steck D A, Oskay W H and Raizen M G 2001 Science 293 274
Hensinger W K et al 2001 Nature 412 52
Averbukh V, Osovski S and Moiseyev N 2002 Phys. Rev. Lett. 89 253201
Greiner M, Mandel O, Esslinger T, Hänsch T W and Bloch I 2002 Nature 415 39
Anderson B P and Kasevich M A 1998 Science 282 1686
Jona-Lasinio M, Morsch O, Cristiani M, Malossi N, Müller J H, Courtade E, Anderlini M and Arimondo E 2003 Phys. Rev. Lett. 91 230406
Jona-Lasinio M, Morsch O, Cristiani M, Arimondo E and Menotti C 2005 Preprint cond-mat/0501572
Roati G, de Mirandes E, Ferlaino F, Ott H, Modugno G and Inguscio M 2004 Phys. Rev. Lett. 92 230402
Pethick C J and Smith H 2002 Bose-Einstein Condensation in Dilute Gases (Cambridge: Cambridge University Press)
Pitaevskii L and Stringari S 2003 Bose-Einstein Condensation (Oxford: Oxford University Press)
Wimberger S, Mannella R, Morsch O, Arimondo E, Kolovsky A R and Buchleitner A 2005 Phys. Rev. A 72 063610
Gemelke N, Sarajlic E, Bidel Y, Hong S and Chu S 2005 Preprint cond-mat/0504311
Schlagheck P and Paul T 2004 Preprint cond-mat/0402089 (Phys. Rev. A, submitted)
Olshanii M 1998 Phys. Rev. Lett. 81 938
Krämer M, Mennoti C, Pitaevskii L and Stringari S 2003 Eur. Phys. J D 27 247
Paul T, Richter K and Schlagheck P 2005 Phys. Rev. Lett. 94 020404
Gustavson T L, Chikkatur A P, Leanhardt A E, Görlitz A, Gupta S, Pritchard D E and Ketterle W 2002 Phys. Rev. Lett. 88 020401
Hänsel W, Reichel J, Hommelhoff P and Hänsch T W 2001 Phys. Rev. Lett. 86 608
Folman R, Krüger O, Schiedmayer J, Denschlag J and Henkel C 2003 Adv. At. Mol. Opt. Phys. 48 263
Carr L D, Holland M J and Malomed B A 2005 J. Phys. B: At. Mol. Opt. Phys. 38 3217
Baslev E and Combes J M 1971 Math. Phys. 22 280
Kukulin V I, Krasnopo'sky V M and Horáček J 1989 Theory of Resonances (Dordrecht: Kluwer)
Moiseyev N 1998 Phys. Rep. 302 211
Moiseyev N and Cederbaum L S 2005 Phys. Rev. A 72 033605
Maquet A, Chu S I and Reinhardt W P 1983 Phys. Rev. A 27 2946
Buchleitner A, Gremaud B and Delande D 1994 J. Phys. B: At. Mol. Opt. Phys. 27 2663
Press W H, Flannery B P, Teukolsky S A and Vettering W T 1989 Numerical Recipes (Cambridge: Cambridge University Press)
Robkerts J L, Claussen N R, Cornish S L, Donley E A, Cornell E A and Wieman C E 2001 Phys. Rev. Lett. 86 4211
Thommen Q, Garreau J C and Zehnlé V 2003 Phys. Rev. Lett. 91 210405
Moiseyev N, Carr L D, Malomed B A and Band Y B 2004 J. Phys. B: At. Mol. Opt. Phys. 37 L193
Adhikari S K 2005 J. Phys. B: At. Mol. Opt. Phys. 38 579
Witthaut D, Mossmann S and Korsch H J 2005 J. Phys. A: Math. Gen. 38 1777
Choi DI and Niu Q 1999 Phys. Rev. Lett. 82 2022
Zobay O and Garraway B M 2000 Phys. Rev. A 61 033603
Wu B and Niu Q 2000 Phys. Rev. A 61 23402
Wu B and Niu Q 2000 New J. Phys. 5 104
Konotop V V, Kevrekidis P G and Salerno M 2005 Phys. Rev. A 72 023611