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arXiv:quant-ph/0307118 · Journal of Optics B Quantum and Semiclassical Optics

Atomic motion in tilted optical lattices: an analytical approach

Quentin Thommen, Jean Claude Garreau, Véronique Zehnlé

Published May 8, 2004• 19 citations
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Abstract

This paper presents a formalism describing the dynamics of a quantum particle in a one-dimensional, time-dependent, tilted lattice. The formalism uses the Wannier-Stark states, which are localized in each site of the lattice, and provides a simple framework allowing fully-analytical developments. Analytic solutions describing the particle motion are explicit derived, and the resulting dynamics is studied.

DOI
10.1088/1464-4266/6/7/007

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This paper presents a formalism describing the dynamics of a quantum particle in a one-dimensional, time-dependent, tilted lattice. The formalism uses the Wannier-Stark states, which are localized in each site of the lattice, and provides a simple framework allowing fully-analytical developments. Analytic solutions describing the particle motion are explicit derived, and the resulting dynamics is studied.
The dynamics of cold Bose atoms in driven tilted optical lattices is analyzed focusing on destruction of Wannier-Stark localization and the phenomenon of band collapse. It is argued that an understanding of the experimental results requires thorough account for interaction effects. These are suppression of the ballistic spreading of atoms for resonant driving (a multiple of the driving frequency coincides with the Bloch frequency) and unbounded sub-diffusive spreading of atoms for off-resonant driving.
Recent work in atom optics has led to enormous progress in the study of quantum chaos and has addressed a broad range of problems in quantum transport, traditionally studied in the context of condensed matter physics. This issue brings together the various researchers working in the border domain between atom optics and solid state physics and focuses on atomic motion in light fields in a regime that is dominated by quantum effects. The topics discussed in this issue include: • quantum effects of atomic motion in light fields; • quantum chaos in time dependent lattices; • tunnelling in stationary or time-dependent lattices; • Wannier-Stark ladder and Bloch oscillations; • atomic band structures; • many-body effects on transport in optical lattices; • effects of decoherence on quantum transport; • weak and dynamical localization. At this point we take the opportunity to express our gratitude to the authors of the papers of this issue and the reviewers for their efforts in preparing and ensuring the high quality of the state of the art presentation.
We investigate the resonantly enhanced tunneling dynamics of ultracold bosons loaded on a tilted one-dimensional optical lattice, which can be used to simulate a chain of Ising spins and associated quantum phase transitions. The center-of-mass motion after a sudden tilt both at commensurate and incommensurate fillings is obtained via analytic, time-dependent exact diagonalization and density-matrix renormalization-group methods. We identify a maximum in the amplitude of the center-of-mass oscillations at the quantum critical point of the effective spin system. For the dynamics of incommensurate systems, which cannot be mapped to a spin model, we develop an analytical approach in which the time evolution is obtained by projecting onto resonant families of small clusters. We compare the results of this approach at low fillings to the exact time evolution and find good agreement even at filling factors as large as 2/3. Using this projection onto small clusters, we propose a controllable transport scheme applicable in the context of Atomtronic devices on optical lattices (``slinky scheme'').