Self-trapped nonlinear matter waves in periodic potentials

We demonstrate that the recent observation of nonlinear self-trapping of matter waves in one-dimensional optical lattices [Th. Anker, Phys. Rev. Lett. 94, 020403 (2005)10.1103/PhysRevLett.94.020403] can be associated with a novel type of broad nonlinear state existing in the gaps of the matter-wave band-gap spectrum. We find these self-trapped localized modes in one-, two-, and three-dimensional periodic potentials, and demonstrate that such novel gap states can be generated experimentally in any dimension.     

Nonlinear self-trapping of matter waves in periodic potentials

We report the first experimental observation of nonlinear self-trapping of Bose-condensed 87Rb atoms in a one-dimensional waveguide with a superimposed deep periodic potential . The trapping effect is confirmed directly by imaging the atomic spatial distribution. Increasing the nonlinearity we move the system from the diffusive regime, characterized by an expansion of the condensate, to the nonlinearity dominated self-trapping regime, where the initial expansion stops and the width remains finite. The data are in quantitative agreement with the solutions of the corresponding discrete nonlinear equation. Our results reveal that the effect of nonlinear self-trapping is of local nature, and is closely related to the macroscopic self-trapping phenomenon already predicted for double-well systems.     

Interaction-induced decoherence of atomic BLOCH oscillations

We show that the energy spectrum of the Bose-Hubbard model amended by a static field exhibits Wigner-Dyson level statistics. In itself a characteristic signature of quantum chaos, this induces the irreversible decay of Bloch oscillations of cold, interacting atoms loaded into an optical lattice, and provides a Hamiltonian model for interaction-induced decoherence.     

Localization of matter waves in two-dimensional disordered optical potentials

We consider ultracold atoms in 2D disordered optical potentials and calculate microscopic quantities characterizing matter wave quantum transport in the noninteracting regime. We derive the diffusion constant as a function of all relevant microscopic parameters and show that coherent multiple scattering induces significant weak localization effects. In particular, we find that even the strong localization regime is accessible with current experimental techniques and calculate the corresponding localization length.     

Glory oscillations in the index of refraction for matter waves

We have measured the index of refraction for sodium de Broglie waves in gases of Ar, Kr, Xe, and N2 over a wide range of sodium velocities. We observe glory oscillations--a velocity-dependent oscillation in the forward scattering amplitude. An atom interferometer was used to observe glory oscillations in the phase shift caused by the collision, which are larger than glory oscillations observed in the cross section. The glory oscillations depend sensitively on the shape of the interatomic potential, allowing us to discriminate among various predictions for these potentials, none of which completely agrees with our measurements.     

Photon BLOCH oscillations in porous silicon optical superlattices

We report the first observation of oscillations of the electromagnetic field in an optical superlattice based on porous silicon. These oscillations are an optical equivalent of well-known electronic Bloch oscillations in crystals. Elementary cells of our structure are composed by microcavities whose coupling gives rise to the extended collective modes forming optical minigaps and minibands. By varying thicknesses of the cavities along the structure axis, we have created an effective electric field for photons. A very high quality factor of the confined optical state of the Wannier-Stark ladder may allow lasing in porous silicon-based superlattices.     

Quantum diffusion of matter waves in 2D speckle potentials

This paper investigates quantum diffusion of matter waves in two-dimensional random potentials, focussing on expanding Bose-Einstein condensates in spatially correlated optical speckle potentials. Special care is taken to describe the effect of dephasing, finite system size, and an initial momentum distribution. We derive general expressions for the interference-renormalized diffusion constant, the disorder-averaged probability density distribution, the variance of the expanding atomic cloud, and the localized fraction of atoms. These quantities are studied in detail for the special case of an inverted-parabola momentum distribution as obtained from an expanding condensate in the Thomas-Fermi regime. Lastly, we derive quantitative criteria for the unambiguous observation of localization effects in a possible 2D experiment.     

Diffusion in periodic potentials

We discuss the static and dynamic phenomena connected with the Brownian motion of a particle in a periodic potential. Specifically we consider the dynamic mobility and the dynamic structure factor. We show with numerical examples how translational and oscillatory motion show up in these quantities. The calculations are done for the onedimensional case. A main tool is the continued fraction expansion of the relevant correlation functions. It enables us, for example, to obtain numerically accurate results for the mobility in a cosine potential. Possible applications of this model lie in the fields of superionic conductors and molecular crystals with rotational diffusion.     

Acoustic analogue of electronic BLOCH oscillations and resonant Zener tunneling in ultrasonic superlattices

We demonstrate the existence of Bloch oscillations of acoustic fields in sound propagation through a superlattice of water cavities and layers of methyl methacrylate. To obtain the acoustic equivalent of a Wannier-Stark ladder, we employ a set of cavities with different thicknesses. Bloch oscillations are observed as time-resolved oscillations of transmission in a direct analogy to electronic Bloch oscillations in biased semiconductor superlattices. Moreover, for a particular gradient of cavity thicknesses, an overlap of two acoustic minibands occurs, which results in resonant Zener-like transmission enhancement.     

Stochastic resonance in periodic potentials

We have studied the motion of a particle in a periodic potential plus a bias, driven by a noise and a coherent forcing. The response (power spectrum) of the particle at the driving forcing frequency is considered for different values of the noise intensity and of the bias. It is shown via direct simulation that the response displays the phenomenon of stochastic resonance, although the phenomenology is somehow different from the one observed in the standard bistable system.     

Diffusion in flashing periodic potentials

The one-dimensional overdamped Brownian motion in a symmetric periodic potential modulated by external time-reversible noise is analyzed. The calculation of the effective diffusion coefficient is reduced to the mean first passage time problem. We derive general equations to calculate the effective diffusion coefficient of Brownian particles moving in arbitrary supersymmetric potential modulated by: (i) an external white Gaussian noise and (ii) a Markovian dichotomous noise. For both cases the exact expressions for the effective diffusion coefficient are derived. We obtain acceleration of diffusion in comparison with the free diffusion case for fast fluctuating potentials with arbitrary profile and for sawtooth potential in case (ii). In this case the parameter region where this effect can be observed is given. We obtain also a finite net diffusion in the absence of thermal noise. For rectangular potential the diffusion slows down, for all parameters of noise and of potential, in comparison with the case when particles diffuse freely.     

Conduction bands in classical periodic potentials

The energy of a quantum particle cannot be determined exactly unless there is an infinite amount of time to perform the measurement. This paper considers the possibility that ΔE, the uncertainty in the energy, may be complex. To understand the effect of a particle having a complex energy, the behaviour of a classical particle in a one-dimensional periodic potential V(x) = −cos(x) is studied. On the basis of detailed numerical simulations it is shown that if the energy of such a particle is allowed to be complex, the classical motion of the particle can exhibit two qualitatively different behaviours: (i) The particle may hop from classically allowed site to nearest-neighbour classically allowed site in the potential, behaving as if it were a quantum particle in an energy gap and undergoing repeated tunnelling processes or (ii) the particle may behave as a quantum particle in a conduction band and drift at a constant average velocity through the potential as if it were undergoing resonant tunnelling. The classical conduction bands for this potential are determined numerically with high precision.     

Brownian motion in fluctuating periodic potentials

This work deals with the overdamped motion of a particle in a fluctuating one-dimensional periodic potential. If the potential has no inversion symmetry and its fluctuations are asymmetric and correlated in time, a net flow can be generated at finite temperatures. We present results for the stationary current for the case of a piecewise linear potential, especially for potentials being close to the case with inversion symmetry. The aim is to study the stationary current as a function of the potential. Depending on the form of the potential, the current changes sign once or even twice as a function of the correlation time of the potential fluctuations. To explain these current reversals, several mechanisms are proposed. Finally, we discuss to what extent the model is useful to understand the motion of biomolecular motors.