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arXiv:1006.4067 · Physical Review A

Driven optical lattices as strong-field simulators

Stephan Arlinghaus, Martin Holthaus

Published Jun 8, 2010• 25 citations
arXivHTMLPDF

Abstract

We argue that ultracold atoms in strongly shaken optical lattices can be subjected to conditions similar to those experienced by electrons in laser-irradiated crystalline solids, but without introducing secondary polarization effects. As a consequence, one can induce nonperturbative multiphoton-like resonances due to the mutual penetration of ac-Stark-shifted Bloch bands. These phenomena can be detected with a combination of currently available laboratory techniques.

DOI
10.1103/physreva.81.063612

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We argue that ultracold atoms in strongly shaken optical lattices can be subjected to conditions similar to those experienced by electrons in laser-irradiated crystalline solids, but without introducing secondary polarization effects. As a consequence, one can induce nonperturbative multiphoton-like resonances due to the mutual penetration of ac-Stark-shifted Bloch bands. These phenomena can be detected with a combination of currently available laboratory techniques.
We suggest that Bose-Einstein condensates in optical lattices subjected to ac forcing with a smooth envelope may provide detailed experimental access to multiphotonlike transitions between ac-Stark-shifted Bloch bands. Such transitions correspond to resonances described theoretically by avoided quasienergy crossings. We show that the width of such anticrossings can be inferred from measurements involving asymmetric pulses. We also introduce a pulse tracking strategy for locating the particular driving amplitudes for which resonances occur. Our numerical calculations refer to a currently existing experimental setup [E. Haller, R. Hart, M. J. Mark, J. G. Danzl, L. Reichs\"ollner, and H.-C. N\"agerl, Phys. Rev. Lett. 104, 200403 (2010)].
The present thesis is devoted to quantum simulation of strongly interacting systems of ultra-cold atoms in optical lattices. It is a theoretical work which focuses on the possibility to employ strong time-periodic forcing for the coherent control of these system. This form of quantum engineering is called Floquet engineering. Experimentally, time-periodic forcing has been successfully applied to realize a variety of physical models and phenomena, especially in the regime of weak interactions. We describe two novel proposals for interesting phenomena in the regime of strong interactions that rely on lattice shaking: melting of a Mott-insulator into an excited-state superfluid via coherent coupling of Bloch bands and the creation of 1D lattice anyons. Furthermore, the role of multiphoton excitations in a driven lattice is analyzed since these processes can lead to unwanted heating and thereby impeding of successful Floquet engineering in the experiment. The introductory Chapter 1 gives an overview over the field of quantum simulations with ultra-cold atoms in optical lattices and describes the experimental progress that has been made in the recent years. In Chapter 2, Floquet theory is reviewed, which provides an excellent framework to deal with time-periodic Hamiltonians and which is the basis of the analysis presented in the following chapters. Chapter 3 deals with the proposal of coherently coupling Bloch bands of an optical lattice via resonant lattice shaking. In particular, the orbital-driven phase transition from a Mott insulating to a superfluid ground state is described in detail. In Chapter 4, a proposal of realizing 1D lattice anyons from strongly interacting bosons in a shaken and tilted lattice is worked out. Furthermore, Friedel oscillations are proposed to provide a measurable real-space signature for the anyonization. Finally, in Chapter 5 multiphoton excitations to higher Bloch bands are analyzed for the cases of a shaken and an amplitude-modulated lattice. The strength and the location of resonances, which are associated with heating, are described theoretically and numerically.
Motivated by recent experimental progress achieved with ultracold atoms in kilohertz-driven optical lattices, we provide a theoretical discussion of mechanisms governing the response of a particle in a cosine lattice potential to strong forcing pulses with smooth envelope. Such pulses effectuate adiabatic motion of a wave packet's momentum distribution on quasienergy surfaces created by spatiotemporal Bloch waves. Deviations from adiabaticity can then be deliberately exploited for exerting coherent control and for reaching target states which may not be accessible by other means. As one particular example, we consider an analog of the $\ensuremath{\pi}$ pulses known from optical resonance. We also suggest adapting further techniques previously developed for controlling atomic and molecular dynamics by laser pulses to the coherent control of matter waves in shaken optical lattices.
Ultracold atoms in specifically designed optical lattices can be used to mimic the many-particle Hamiltonian (whose effective parameters can be tuned in a wide range) describing electrons and positrons in an external electric field. This analogy facilitates the experimental simulation of (so far unobserved) fundamental quantum phenomena such as the Schwinger effect, i.e., spontaneous electron-positron pair creation out of the vacuum by a strong electric field. Such an experiment would also test nonperturbative aspects of these lattice systems.
The scope of the present publication-based thesis on periodically forced optical lattices is twofold: In the first part, the reader is introduced to the main concepts required to formulate the central results of this thesis, and a review is given of landmark papers on coherently controlling ultracold atoms by subjecting them to periodic forces. The second part provides the author's own results of original research on the subject and consists of four publications and a preprint. It is shown how ultracold atoms in optical lattices can be used as strong-field simulators, dynamic localization in optical lattices are described in detail, and multiphoton-like processes are studied. A generalized acceleration theorem for spatiotemporal Bloch waves is developed and used to enable a controlled wave-packet manipulation in optical lattices.
Summary form only given. The AC-Stark shift of a set of interfering laser beams together with the Zeeman interaction with external magnetic fields provide flexible mechanisms for coherently controlling atomic wave packets. When detuned far from atomic resonance, these optical lattices can trap cold atoms with minimal dissipation and thus provide an ideal environment for observing quantum coherent phenomena. We consider a one dimensional lattice of double wells produced by counterpropagating linearly polarized laser beams and a static magnetic field transverse to the laser wave vectors.