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Conference on Lasers and Electro-Optics Europe & European Quantum Electronics Conference (CLEO/Europe-EQEC)

Bloch oscillations of neutral atoms adsorbed on crystalline surfaces

Thierry Passerat de Silans, Martine Chevrollier, Marcos Oriá

Published Jun 1, 2007• 0 citations
Publisher

Abstract

In the present work we theoretically develop a new system to explore the BO phenomena using neutral atoms trapped in accelerated adsorption potentials. We show that particles bound to a surface by the surface-normal van der Waals potential and having energy bands due to the 2D-periodic potential related to the corrugation of the surface, fulfill the requirements for one to explore behaviours of quantum transport, probing Bloch oscillations or doing Wannier-Stark spectroscopy.

DOI
10.1109/cleoe-iqec.2007.4386749

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In the present work we theoretically develop a new system to explore the BO phenomena using neutral atoms trapped in accelerated adsorption potentials. We show that particles bound to a surface by the surface-normal van der Waals potential and having energy bands due to the 2D-periodic potential related to the corrugation of the surface, fulfill the requirements for one to explore behaviours of quantum transport, probing Bloch oscillations or doing Wannier-Stark spectroscopy.
The dipolar interaction between neutral atoms and non-resonant surfaces results in attractive potentials.We describe here techniques to probe these interactions, particulary focussing in mechanisms to selectively prepare adsorption quantum states. The control of the external degrees of freedom of atoms very close to a surface allows one, in the one hand, to get values for the parameters of the potentials between neutral atoms and solid surfaces and, on the other hand, to develop schemes to explore matter behavior at low dimensionality. As an application for the 2D confined atomic matter-wave we consider Bloch oscillation for atoms in a periodic surface potential.
A quantum particle subjected to a constant force undergoes an accelerated motion following a parabolic path, which differs from the classical motion just because of wave packet spreading (quantum diffusion). However, when a periodic potential is added (such as in a crystal) the particle undergoes Bragg scattering and an oscillatory (rather than accelerated) motion is found, corresponding to the famous Bloch oscillations (BOs). Here, we introduce an exactly-solvable quantum Hamiltonian model, corresponding to a generalized Wannier–Stark Hamiltonian [Formula: see text], in which a quantum particle shows an intermediate dynamical behavior, namely an oscillatory motion superimposed to an accelerated one. Such a novel dynamical behavior is referred to as accelerated BOs. Analytical expressions of the spectrum, improper eigenfunctions and propagator of the generalized Wannier–Stark Hamiltonian [Formula: see text] are derived. Finally, it is shown that acceleration and quantum diffusion in the generalized Wannier–Stark Hamiltonian are prevented for Airy wave packets, which undergo a periodic breathing dynamics that can be referred to as Airy–Bloch oscillations.
We study the energy spectrum of atoms trapped in a vertical one-dimensional optical lattice in close proximity to a reflective surface. We propose an effective model to describe the interaction between the atoms and the surface at any distance. Our model includes the long-range Casimir-Polder potential together with a short-range Lennard-Jones potential, which are considered nonperturbatively with respect to the optical lattice potential. We find an intricate energy spectrum which contains a pair of loosely bound states localized close to the surface in addition to a surface-modified Wannier-Stark ladder at long distances. Atomic interferometry involving those loosely bound atom-surface states is proposed to probe the adsorption dynamics of atoms on mirrors.
Bloch oscillation (BO), i.e., the oscillatory motion of a quantum particle in a periodic potential, is one of the most striking effects of coherent quantum transport in matter. In the semiclassical picture, it is well known that BOs can be explained owing to the periodic band structure of the crystal and the so-called acceleration theorem: since in the momentum space the particle wave packet drifts with a constant speed without being distorted, in real space the probability distribution of the particle undergoes a periodic motion following a trajectory which exactly reproduces the shape of the lattice band. In non-Hermitian lattices with a complex (i.e., not real) energy band, extension of the semiclassical model is not intuitive. Here we show that the acceleration theorem holds for non-Hermitian lattices with a complex energy band only on average, and that the periodic wave-packet motion of the particle in real space is described by a trajectory in the complex plane, i.e., it generally corresponds to reshaping and breathing of the wave packet in addition to a transverse oscillatory motion. The concept of BOs involving complex trajectories is exemplified by considering two examples of non-Hermitian lattices with a complex band dispersion relation, including the Hatano-Nelson tight-binding Hamiltonian describing the hopping motion of a quantum particle on a linear lattice with an imaginary vector potential and a tight-binding lattice with imaginary hopping rates.
This work is devoted to Bloch oscillations (BO) of cold neutral atoms in optical lattices. After a general introduction to the phenomenon of BO and its realization in optical lattices, we study different extentions of this problem, which account for recent developments in this field. These are two-dimensional BO, decoherence of BO, and BO in correlated systems. Although these problems are discussed in relation to the system of cold atoms in optical lattices, many of the results are of general validity and can be well applied to other systems showing the phenomenon of BO.
This work is devoted to Bloch oscillations (BO) of cold neutral atoms in optical lattices. After a general introduction to the phenomenon of BO and its realization in optical lattices, we study different extentions of this problem, which account for recent developments in this field. These are two-dimensional BO, decoherence of BO, and BO in correlated systems. Although these problems are discussed in relation to the system of cold atoms in optical lattices, many of the results are of general validity and can be well applied to other systems showing the phenomenon of BO.