Dynamic Polarization Effects in Ion Channeling Through Single-Well Carbon Nanotubs

Ion channeling through a single-wall carbon nanotube is simulated by solving Newton’s equations for ion motion at intermediate energies, under the action of both the surface-atom repulsive forces and the polarization forces due to the dynamic perturbation of the nanotube electrons. The atomic repulsion is described by a continuum potential based on the Thomas-Fermi-Moliere model, whereas the dynamic polarization of the nanotube electrons is described by a two-dimensional hydrodynamic model, giving rise to the transverse dynamic image force and the longitudinal stopping force. In the absence of centrifugal forces, a balance between the image force and the atomic repulsion is found to give rise to ion trajectories which oscillate over peripheral radial regions in the nanotube, provided the ion impact position is not too close to the nanotube wall, the impact angle is sufficiently small, and the incident speed is not too high. Otherwise, the ion is found to oscillate between the nanotube walls, passing over a local maximum of the potential in the center of the nanotube, which results from the image interaction. The full statistical analysis of 103 ion trajectories has been made to further demonstrate the actual effect of dynamic polarization on the ion channeling

Controllable coupling between a nanomechanical resonator and a coplanar-waveguide resonator via a superconducting flux qubit

We study a tripartite quantum system consisting of a coplanar-waveguide (CPW) resonator and a nanomechanical resonator (NAMR) connected by a flux qubit, where the flux qubit has a large detuning from both resonators. By a unitray transformation and a second-order approximation, we obtain a strong and controllable (i.e., magnetic-field-dependent) effective coupling between the NAMR and the CPW resonator. Due to the strong coupling, vacuum Rabi splitting can be observed from the voltage-fluctuation spectrum of the CPW resonator. We further study the properties of single photon transport as inferred from the reflectance or equivalently the transmittance. We show that the reflectance and the corresponding phase shift spectra both exhibit doublet of narrow spectral features due to vacuum Rabi splitting. By tuning the external magnetic field, the reflectance and the phase shift can be varied from 0 to 1 and $-\pi$ to $\pi$, respectively. The results indicate that this hybrid quantum system can act as a quantum router.Comment: 8 pages, 6 figure

A Pure Quantum Approximate Optimization Algorithm Based on CNR Operation

By introducing the "comparison and replacement" (CNR) operation, we propose a general-purpose pure quantum approximate optimization algorithm and derive its core optimization mechanism quantitatively. The algorithm is constructed to a $p$-level divide-and-conquer structure based on the CNR operations. The quality of approximate optimization improves with the increase of $p$. For sufficiently general optimization problems, the algorithm can work and produce the near-optimal solutions as expected with considerably high probability. Moreover, we demonstrate that the algorithm is scalable to be applied to large size problems. Our algorithm is applied to two optimization problems with significantly different degeneracy, the Gaussian weighted 2-edge graph and MAX-2-XOR, and then we show the algorithm performance in detail when the required qubits number of the two optimization problems is 10

Higher-order solutions to non-Markovian quantum dynamics via hierarchical functional derivative

Solving realistic quantum systems coupled to an environment is a challenging task. Here we develop a hierarchical functional derivative (HFD) approach for efficiently solving the non-Markovian quantum trajectories of an open quantum system embedded in a bosonic bath. An explicit expression for arbitrary order HFD equation is derived systematically. Moreover, it is found that for an analytically solvable model, this hierarchical equation naturally terminates at a given order and thus becomes exactly solvable. This HFD approach provides a systematic method to study the non-Markovian quantum dynamics of an open system coupled to a bosonic environment.Comment: 5 pages, 2 figure