Narrow Results

In this paper, we consider the effect of an aperiodic hopping distribution on a single electron. The aperiodic sequence of hopping energies was generated by using a sinusoidal function whose phase ϕ varies as a power-law, ϕ ∝ n^ν, where n labels the positions along the chain. The exponent ν controls the degree of aperiodicity in the sequence hopping terms. Using the transfer matrix method, we compute the localization length within the band of allowed energies. Our numerical calculations indicate that, for an aperiodic sequence of hopping energies with ν < 1, a new phase of extended states appears in this model. For a pseudorandom hopping distribution with ν > 1, all eigenstates remain localized. In addition, we study the electronic dynamics subjected to an electric field. Our numerical calculations reveals perfect Bloch oscillations for ν < 1. The typical frequency of these oscillations agree with the semiclassical predictions.

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.

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.

Motivated by a recent experiment on Bloch oscillation of Bose–Einstein condensates (BEC) in accelerated optical lattices, we consider the Josephson dynamics of a BEC in an accelerated double-well potential. We show that acceleration suppresses coherent population / phase oscillation between the two wells. Accelerating the double-well renders the Josephson coupling energy E_J time-dependent and this emerges as a source of dissipation. This dissipative mechanism helps to stabilize the system. The results are used to interpret a recent experimental result (M. Jona-Lasinio, O. Morsh, M. Cristiani E. Arimonod and C. Menotti, cond-mat / 0501572).

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 $Ĥ$, 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 $Ĥ$ 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 consider the dynamics of electrons in semiconductor superlattices in intense multifrequency electric fields. We examine the conditions for dynamic localization and electromagnetic transparency. We investigate processes of formation, destruction, and stabilization of electromagnetic transparency in biharmonic field. The stable states with static fields are determined.

The following sections are included:

• Introduction

• Atom Interferometry with 24-Photon-Momentum-Transfer Bragg Beam Splitters

• Noise-Immune, Recoil-Sensitive, Large-Area Atom Interferometers

• Very large area atom interferometers by differential optical acceleration

• Towards fundamental physics measurements by atom interferometry
  • Detection of gravitational waves

• References

We use Bloch oscillations to coherently transfer many photon momenta to atoms. Then we can measure accurately the recoil velocity ħk/m and deduce the fine structure constant α. The velocity variation due to Bloch oscillations is measured using atom interferometry. This method yields a value of the fine structure constant α^-1 = 137.035 999 45 (62) with a relative uncertainty of about 4.5 × 10^-9.