Graphene with time-dependent spin-orbit coupling: Truncated Magnus expansion approach

We analyze the role of ac-driven Rashba spin-orbit coupling in monolayer graphene including a spin-dependent mass term. Using the Magnus expansion as a semi-analytical approximation scheme a full account of the quasienergie spectrum of spin states is given. We discuss the subtleties arising in correctly applying the Magnus expansion technique in order to determine the quasienergy spectrum. Comparison to the exact numerical solution gives appropriate boundaries to the validity of the Magnus expansion solution.Comment: 8 pages, 4 figure

Floquet spin states in graphene under ac driven spin-orbit interaction

We study the role of periodically driven time-dependent Rashba spin-orbit coupling (RSOC) on a monolayer graphene sample. After recasting the originally $4\times 4$ system of dynamical equations as two time-reversal related two-level problems, the quasi-energy spectrum and the related dynamics are investigated via various techniques and approximations. In the static case the system is a gapped at the Dirac point. The rotating wave approximation (RWA) applied to the driven system unphysically preserves this feature, while the Magnus-Floquet approach as well as a numerically exact evaluation of the Floquet equation show that this gap is dynamically closed. In addition, a sizable oscillating pattern of the out-of-plane spin polarization is found in the driven case for states which completely unpolarized in the static limit. Evaluation of the autocorrelation function shows that the original uniform interference pattern corresponding to time-independent RSOC gets distorted. The resulting structure can be qualitatively explained as a consequence of the transitions induced by the ac driving among the static eigenstates, i.e., these transitions modulate the relative phases that add up to give the quantum revivals of the autocorrelation function. Contrary to the static case, in the driven scenario, quantum revivals (suppresions) are correlated to spin up (down) phases.Comment: 10 pages, 8 figures. Typos corrected. Accepted for publication in PR

Temporal and diffraction effects in entanglement creation in an optical cavity

A practical scheme for entanglement creation between distant atoms located inside a single-mode optical cavity is discussed. We show that the degree of entanglement and the time it takes for the entanglement to reach its optimum value is a sensitive function the initial conditions and the position of the atoms inside the cavity mode. It is found that the entangled properties of the two atoms can readily be extracted from dynamics of a simple two-level system. Effectively, we engineer two coupled qubits whose the dynamics are analogous to that of a driven single two-level system. It is found that spatial variations of the coupling constants actually help to create transient entanglement which may appear on the time scale much longer than that predicted for the case of equal coupling constants. When the atoms are initially prepared in an entangled state, they may remain entangled for all times. We also find that the entanglement exhibits an interesting phenomenon of diffraction when the the atoms are located between the nodes and antinodes of the cavity mode. The diffraction pattern of the entanglement varies with time and we explain this effect in terms of the quantum property of complementarity, which is manifested as a tradeoff between the knowledge of energy of the exchanged photon versus the evolution time of the system.Comment: Phys. Rev. A75, 042307 (2007

Hydraulic brake safety valve

Safety device, consisting of three separate fluid chambers, insures that two wheels of a brake system continue to function if a failure occurs

Cover protects critical electrical connectors against damage during handling

Split-half cover eliminates the surface marring and dirt penetration problems previously encountered during handling and cable assembly. Metal retaining ring slips over the two plastic halves to hold them in place