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Register a new userBloch oscillations in an aperiodic one-dimensional potential
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We study the dynamics of an electron subjected to a static uniform electric field within a one-dimensional tight-binding model with a slowly varying aperiodic potential. The unbiased model is known to support phases of localized and extended one-electron states separated by two mobility edges. We show that the electric field promotes sustained Bloch oscillations of an initial Gaussian wave packet whose amplitude reflects the band width of extended states. The frequency of these oscillations exhibit unique features, such as a sensitivity to the initial wave packet position and a multimode structure for weak fields, originating from the characteristics of the underlying aperiodic potential.
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We study the dynamics of an electron subjected to a uniform electric field within a tight-binding model with long-range-correlated diagonal disorder. The random distribution of site energies is assumed to have a power spectrum $S(k) sim 1/k^{alpha}$ with $alpha > 0$. Moura and Lyra [Phys. Rev. Lett. {bf 81}, 3735 (1998)] predicted that this model supports a phase of delocalized states at the band center, separated from localized states by two mobility edges, provided $alpha > 2$. We find clear signatures of Bloch-like oscillations of an initial Gaussian wave packet between the two mobility edges and determine the bandwidth of extended states, in perfect agreement with the zero-field prediction.
We use a neural network approach to explore the inverse problem of Bloch oscillations in a monoatomic linear chain: given a signal describing the path of oscillations of electrons as a function of time, we determine the strength of the applied field along the direction of motion or, equivalently, the lattice spacing. We find that the proposed approach has more than 80% of accuracy classifying the studied physical parameters.
We examine bosons hopping on a one-dimensional lattice in the presence of a random potential at zero temperature. Bogoliubov excitations of the Bose-Einstein condensate formed under such conditions are localized, with the localization length diverging at low frequency as $ell(omega)sim 1/omega^alpha$. We show that the well known result $alpha=2$ applies only for sufficiently weak random potential. As the random potential is increased beyond a certain strength, $alpha$ starts decreasing. At a critical strength of the potential, when the system of bosons is at the transition from a superfluid to an insulator, $alpha=1$. This result is relevant for understanding the behavior of the atomic Bose-Einstein condensates in the presence of random potential, and of the disordered Josephson junction arrays.
In the conventional theory of hopping transport the positions of localized electronic states are assumed to be fixed, and thermal fluctuations of atoms enter the theory only through the notion of phonons. On the other hand, in 1D and 2D lattices, where fluctuations prevent formation of long-range order, the motion of atoms has the character of the large scale diffusion. In this case the picture of static localized sites may be inadequate. We argue that for a certain range of parameters, hopping of charge carriers among localization sites in a network of 1D chains is a much slower process than diffusion of the sites themselves. Then the carriers move through the network transported along the chains by mobile localization sites jumping occasionally between the chains. This mechanism may result in temperature independent mobility and frequency dependence similar to that for conventional hopping.
We investigate both experimentally and theoretically disorder induced damping of Bloch oscillations of Bose-Einstein condensates in optical lattices. The spatially inhomogeneous force responsible for the damping is realised by a combination of a disordered optical and a magnetic gradient potential. We show that the inhomogeneity of this force results in a broadening of the quasimomentum spectrum, which in turn causes damping of the centre-of-mass oscillation. We quantitatively compare the obtained damping rates to the simulations using the Gross-Pitaevskii equation. Our results are relevant for high precision experiments on very small forces, which require the observation of a large number of oscillation cycles.
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