Bloch-Landau-Zener oscillations in a quasi-periodic potential

被引:5
作者
Prates, Henrique C. [1 ]
Konotop, Vladimir V.
机构
[1] Univ Lisbon, Fac Ciencias, Dept Fis, Edificio C8, P-1749016 Lisbon, Portugal
来源
PHYSICAL REVIEW RESEARCH | 2024年 / 6卷 / 02期
关键词
WANNIER-STARK LADDERS; SCHRODINGER-EQUATION; LOCALIZATION; RESONANCES; ELECTRONS; DYNAMICS; ATOMS;
D O I
10.1103/PhysRevResearch.6.L022011
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
Bloch oscillations and Landau-Zener tunneling are ubiquitous phenomena which are sustained by a band-gap spectrum of a periodic Hamiltonian and can be observed in dynamics of a quantum particle or a wavepacket in a periodic potential under action of a linear force. Such physical setting remains meaningful for aperiodic potentials too, although band-gap structure does not exist anymore. Here we consider the dynamics of noninteracting atoms and Bose-Einstein condensates in a quasiperiodic one-dimensional optical lattice subjected to a weak linear force. Excited states with energies below the mobility edge, and thus localized in space, are considered. We show that the observed oscillatory behavior is enabled by tunneling between the initial state and a state (or several states) located nearby in the coordinate-energy space. The states involved in such Bloch-Landau-Zener oscillations are determined by the selection rule consisting of the condition of their spatial proximity and condition of quasiresonances occurring at avoided crossings of the energy levels. The latter condition is formulated mathematically using the Gershgorin circle theorem. The effect of the inter-atomic interactions on the dynamics can also be predicted on the bases of the developed theory. The reported results can be observed in any physical system allowing for observation of the Bloch oscillations, upon introducing incommensurablity in the governing Hamiltonian.
引用
收藏
页数:6
相关论文
共 72 条
[1]   Macroscopic quantum interference from atomic tunnel arrays [J].
Anderson, BP ;
Kasevich, MA .
SCIENCE, 1998, 282 (5394) :1686-1689
[2]  
Aubry S., 1980, Annals of the Israel Physical Society, V3, P133
[3]   QUANTUM PARTICLE IN ONE-DIMENSIONAL POTENTIALS WITH INCOMMENSURATE PERIODS [J].
AZBEL, MY .
PHYSICAL REVIEW LETTERS, 1979, 43 (26) :1954-1957
[4]   Observation of atomic tunneling from an accelerating optical potential [J].
Bharucha, CF ;
Madison, KW ;
Morrow, PR ;
Wilkinson, SR ;
Sundaram, B ;
Raizen, MG .
PHYSICAL REVIEW A, 1997, 55 (02) :R857-R860
[5]   Localization in one-dimensional incommensurate lattices beyond the Aubry-Andre model [J].
Biddle, J. ;
Wang, B. ;
Priour, D. J., Jr. ;
Das Sarma, S. .
PHYSICAL REVIEW A, 2009, 80 (02)
[6]  
Bloch Felix., 1928, Z PHYS, V52, P555, DOI DOI 10.1007/BF01339455
[7]   Bloch oscillations in plasmonic waveguide arrays [J].
Block, A. ;
Etrich, C. ;
Limboeck, T. ;
Bleckmann, F. ;
Soergel, E. ;
Rockstuhl, C. ;
Linden, S. .
NATURE COMMUNICATIONS, 2014, 5
[8]   Mobility edges in bichromatic optical lattices [J].
Boers, Dave J. ;
Goedeke, Benjamin ;
Hinrichs, Dennis ;
Holthaus, Martin .
PHYSICAL REVIEW A, 2007, 75 (06)
[9]   Bloch-Zener oscillations [J].
Breid, B. M. ;
Witthaut, D. ;
Korsch, H. J. .
NEW JOURNAL OF PHYSICS, 2006, 8
[10]   Experimental properties of Bose-Einstein condensates in one-dimensional optical lattices: Bloch oscillations, Landau-Zener tunneling, and mean-field effects [J].
Cristiani, M. ;
Morsch, O. ;
Müller, J.H. ;
Ciampini, D. ;
Arimondo, E. .
Physical Review A - Atomic, Molecular, and Optical Physics, 2002, 65 (6 A) :636121-636121