Nonlinear coherent destruction of tunneling

We study theoretically two coupled periodically-curved optical waveguides with Kerr nonlinearity. We find that the tunneling between the waveguides can be suppressed in a wide range of parameters due to nonlinearity. Such suppression of tunneling is different from the coherent destruction of tunneling in a linear medium, which occurs only at the isolated degeneracy point of the quasienergies. We call this novel suppression nonlinear coherent destruction of tunneling.Comment: 4 pages,5 figure

Quasi-energies and Floquet states of two weakly coupled Bose-Einstein condensates under periodic driving

We investigate the quasi-energies and Floquet states of two weakly coupled Bose-Einstein condensates driven by a periodic force. The quasi-energies and Floquet states of this system are computed within two different theoretical frameworks: the mean-field model and the second-quantized model. The mean-field approach reveals a triangular structure in the quasi-energy band. Our analysis of the corresponding Floquet states shows that this triangle signals the onset of a localization phenomenon, which can be regarded as a generalization of the well-known phenomenon called coherent destruction of tunneling. With the second quantized model, we find also a triangular structure in the quantum quasi-energy band, which is enveloped by the mean-field triangle. The close relation between these two sets of quasi-energies is further explored by a semi-classical method. With a Sommerfeld rule generalized to time-dependent systems, the quantum quasi-energies are computed by quantizing semiclassically the mean-field model and they are found to agree very well with the results obtained directly with the second-quantized model.Comment: 8pages,12figure

Investigation of the Impact of Mixing Intensity on Dissolved Oxygen Half Velocity Constants in a Sidestream Deammonification Environment

The liquid waste (centrate) from the dewatering stage in the solids treatment stream (sidestream) of a wastewater treatment plant is typically rich in ammonium. If this centrate is recycled to the wastewater treatment stream (mainstream), the aeration requirements in the mainstream bioreactor will increase. A new technology, sidestream deammonification, has been developed to reduce the loading of ammonium from the sidestream to the mainstream. However, this and similar technologies require delicate control of the dissolved oxygen (DO) in the bulk liquid. Therefore, improved knowledge of factors influencing the DO half-velocity constants (K_O2) of the functional organisms in the sidestream treatment will enhance the control of the growth of these organisms and ultimately nitrogen removal efficiency. The impact of mixing conditions on K_O2 values was investigated in this study. Experiments were conducted in a quasi-sequencing batch reactor (SBR) to reproduce a sidestream deammonification environment treating dewatering centrate. Once steady-state conditions were established, the mixer speed was changed from the initial setting of an average velocity gradient of 15/s at 8.0 L to 5.3/s at 8.0 L (from 150 rpm to 75 rpm) while maintaining other parameters constant. The objective of this study was to demonstrate the impact of mixing intensity on the estimated K_O2 values of ammonium oxidizing bacteria (AOB) and anaerobic ammonium oxidizing (Anammox) bacteria. The effect of mixing intensity was assessed in terms of overall nitrogen removal efficiency in the SBR and by examining the magnitude of K_O2 values of AOB (K_O2^AOB) and Anammox bacteria (K_O2^Anammox) that were determined in activity tests. Nitrogen removal efficiency during steady-state conditions increased from 62% to 84%; and the value of estimated K_O2^Anammox increased statistically significantly for the lower mixing intensity condition. However, the value of the estimated K_O2^AOB remained statistically the same. In conclusion, this research showed that mixing intensity had an impact on the estimated K_O2^Anammox value and nitrogen removal in the SBR

The Landau Level of Fragile Topology

We study the Hofstadter butterfly and Landau levels of the twisted bilayer graphene (TBG). We show that the nontrivial fragile topology of the lowest two bands near the charge neutral point makes their Hofstadter butterfly generically connected with higher bands, closing the gap between the first and second conduction (valence) bands at a certain magnetic flux per unit cell. We also develop a momentum space method for calculating the TBG Hofstadter butterfly, from which we identify three phases where the Hofstadter butterflies of the lowest two bands and the higher bands are connected in different ways. We show this leads to a crossing between the $\nu=4$ Landau fan from the charge neutral point and the zero field band gap at one flux per Moir\'e unit cell, which corresponds to a magnetic field $25\theta^2$T (twist angle $\theta$ in degrees). This provides an experimentally testable feature of the fragile topology. In general, we expect it to be a generic feature that the Hofstadter butterfly of topological bands are connected with the Hofstadter spectra of other bands. We further show the TBG band theory with Zeeman splitting being the most sizable splitting could result in Landau fans at the charge neutral point and half fillings near the magic angle, and we predict their variations under an in-plane magnetic field.Comment: 7+33 pages, 4+23 figure

Topology-Bounded Superfluid Weight In Twisted Bilayer Graphene

While regular flat bands are good for enhancing the density of states and hence the gap, they are detrimental to the superfluid weight. We show that the predicted nontrivial topology of the two lowest flat bands of twisted bilayer graphene plays an important role in the enhancement of the superfluid weight and hence of superconductivity. We derive the superfluid weight (phase stiffness) of the TBLG superconducting flat bands with a uniform pairing, and show that it can be expressed as an integral of the Fubini-Study metric of the flat bands. This mirrors results already obtained for nonzero Chern number bands even though the TBLG flat bands have zero Chern number. We further show the metric integral is lower bounded by the topological $C_{2z}T$ Wilson loop winding number of the TBLG flat bands, which renders the superfluid weight has a topological lower bound proportional to the pairing gap. In contrast, trivial flat bands have a zero superfluid weight. The superfluid weight is crucial in determining the BKT transition temperature of the superconductor. Based on the transition temperature measured in TBLG experiments, we estimate the topological contribution of the superfluid weight in TBLG.Comment: 7+22 pages, 4 figure