Signatures of inter-band transitions on dynamical localization
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THE EUROPEAN PHYSICAL JOURNAL D
Regular Article
Signatures of inter-band transitions on dynamical localization Sara Medhet1 , Tomotake Yamakoshi2 , Muhammad Ayub1 , Farhan Saif1,a , and Shinichi Watanabe3 1 2 3
Department of Electronics, Quaid-i-Azam University, 45320 Islamabad, Pakistan Institute for Laser Science, University of Electro-Communications, 1-5-1 Chofugaoka, Chofu-shi, Tokyo 182-8585, Japan Department of Engineering Science, University of Electro-Communications, 1-5-1 Chofugaoka, Chofu-shi, Tokyo 182-8585, Japan Received 3 October 2019 / Received in final form 12 May 2020 Published online 25 August 2020 c EDP Sciences / Societ`
a Italiana di Fisica / Springer-Verlag GmbH Germany, part of Springer Nature, 2020 Abstract. We explain the dynamics of ultracold atoms in amplitude modulated optical lattice with harmonic confinement. We show the existence of dynamical localization that manifests itself as the cold atoms exhibit quantum suppression of classical chaos in the dynamical system. The exponential localization takes place both in momentum as well as in coordinate space within certain windows on modulation amplitude. We show that inter-band transitions, taking place due to the amplitude modulation in optical lattice, play an important role in controlling the dynamical localization of matter waves. Our obtained results can be generalized to other dynamical systems and are experimentally realizable as we consider the values of parameters from the present-day available experiments.
1 Introduction Ultracold atoms in optical lattices simulate electron dynamics in ideal solid state crystals with advantages, that are, no defects and no impurities. In the presence of high degree of experimental control [1–4] the atoms are loaded efficiently in bands formed by optical lattice in the presence of magnetic trap [5,6]. The inter-band transitions of cold atoms in modulated potentials are subject of interest as a resource for quantum simulations [7–9] that provide a useful way to understand complicated condensed matter systems, such as simulation of photoconductivity [10]. Atomic wave packets are coherently de-excited into lattice-bands by lattice intensity modulation [11,12]. In this contribution we show that the phenomenon of inter-band transitions plays a crucial role in exhibiting dynamical localization [13–15] of the cold atoms in modulated optical lattice – that is an analogue of Anderson localization of electron in a disordered lattice. The dynamics of ultracold atoms in amplitude modulated and phase modulated 1D, 2D, and 3D optical lattices is an analogue of an electron dynamics in a crystal under the influence of AC electric field. The ultra-cold atoms in optical lattice in the presence of a modulating force experience another degree of freedom leading to nonlinear dynamical characteristics [16]. Such optical lattice systems in the presence of phase modulation have been the subject of interest to observe quantum chaos [17], photon assisted tunnelling [18], control of Mott insulator transitions [19], qua
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