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

Efficient Dynamic Unstructured Methods and Applications for Transonic Flows and Hypersonic Stage Separation

Relative-moving boundary problems have a wide variety of applications. They appear in staging during a launch process, store separation from a military aircraft, rotor-stator interaction in turbomachinery, and dynamic aeroelasticity. The dynamic unstructured technology (DUT) is potentially a strong approach to simulate unsteady flows around relative-moving bodies, by solving time-dependent governing equations. The dual-time stepping scheme is implemented to improve its efficiency while not compromising the accuracy of solutions. The validation of the implicit scheme is performed on a pitching NACA0012 airfoil and a rectangular wing with low reduced frequencies in transonic flows. All the matured accelerating techniques, including the implicit residual smoothing, the local time stepping, and the Full-Approximate-Scheme (FAS) multigrid method, are resorted once a dynamic problem is transformed into a series of “static” problems. Even with rather coarse Euler-type meshes, one order of CPU time savings is achieved without losing the accuracy of solutions in comparison to the popular Runge-Kutta scheme. More orders of CPU time savings are expected in real engineering applications where highly stretched viscous-type meshes are needed. The applicability of DUT is also extended from transonic/supersonic flows to hypersonic flows through special measures in spatial discretization to simulate the staging of a hypersonic vehicle. First, the simulations in Mach 5 and Mach 10 flights are performed on the longitudinal symmetry plane. A network of strong shocks and expansion waves are captured. A prescribed two-degrees-of-freedom motion is imposed on the booster and the adapter to mimic the staging. Then, a 3-D static Euler solver with an efficient edge-based data structure is modified for time-accurate flows. The overall history of aerodynamic interference during the staging in Mach 5 flight is obtained by an animation method, consisting of six static solutions along the assumed stage path. From the animation method, the following conclusions are made. After the booster and the adapter move away from the research vehicle by 60% vehicle length, their effects on the research vehicle are confined to the wake flow of the research vehicle. The aerodynamic forces on the research vehicle converge to the values in free flight when the booster is away from the research vehicle by 1.77 times vehicle length. The aerodynamic interference is a highly nonlinear function in terms of the distance between the vehicle, the booster, and the adapter. Finally, two dynamic computations are performed when the booster and the adapter are extremely close to the research vehicle. It is observed from these 3-D dynamic computations that as the stage separation advances, the aerodynamic interference becomes less sensitive to further relative motions

Coherent Destruction of Tunneling and Dark Floquet State

We study a system of three coherently coupled states, where one state is shifted periodically against the other two. We discover such a system possesses a dark Floquet state at zero quasienergy and always with negligible population at the intermediate state. This dark Floquet state manifests itself dynamically in terms of the suppression of inter-state tunneling, a phenomenon known as coherent destruction of tunneling. We suggest to call it dark coherent destruction of tunneling (DCDT). At high frequency limit for the periodic driving, this Floquet state reduces to the well-known dark state widely used for STIRAP. Our results can be generalized to systems with more states and can be verified with easily implemented experiments within current technologies.Comment: 5 pages, 3 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