Nanoantennas: new prospects in light-matter-interactions

The possibilities of nanoantennas for an enhanced interaction of light with quantum systems is theoretically investigated. A versatile framework is introduced to describe this interaction. A classical electrodynamics description of nanoantennas enables to freely design and tune them for specific means. But this approach leads to a semiclassical description of the entire system. We introduce a quantization scheme for nanoantennas based on their quasinormal modes, which enables a fully quantum treatment of the hybrid system. We show how nanoantennas can be designed to enhance the rates of so-called dipole-forbidden transitions of quantum systems, since the electromagnetic fields in the vicinity of a nanoantenna may vary much stronger than for plane waves. Specifically, an electric quadrupole excitation rate can be enhanced in the gap of a dimer nanoantenna. In regard to the specifics of an assumed quantum system, this excitation can cause a luminescence enhancement.We suggest using a hybrid quantum system consisting of a nanoantenna and a quantum system as an ultra-bright single-photon source. Due to its interaction with a nanoantenna, a quantum system can spontaneously emit radiation at higher rates when compared to free space. But this enhancement is not the only important figure of merit for single-photon sources. A trade-off between emission rate and nonclassicality of the emitted light is found as well. We investigate how quantum systems may be strongly coupled to nanoantennas. Fundamental trade-offs may set ultimate limits for achievable coupling-to-loss-ratios. To realize the strong coupling regime, nanoantennas have to be sufficiently small, which causes comparably low efficiencies. If a strongly coupled hybrid system is pumped, its dynamics and spectral response depends considerably on the excitation strength. The effects of strong coupling are most pronounced for weak excitations

Equivalence Relations on Stonian Spaces

AbstractQuotient spaces of locally compact Stonian spaces which generalize in some sense the concept of Stone representation space of a Boolean algebra are investigated emphasizing the measure theoretical point of view, and a representation theorem for finitely additive measures is proved

Executive Powers: The Role of the Supreme Court in an Expanding Presidency

In the Pacificus-Helvidius debate of 1793, Alexander Hamilton locked horns with James Madison in a classic exchange of broadsides on the issue of express versus inherent executive powers. In his interpretation of presidential powers, Hamilton sows the seeds for an argument which justifies the exercise of executive powers in combating situations of domestic emergency and in matters concerning the general welfare or public interest. The seeds of this theory took firm root more than sixty years later in the administration of Abraham Lincoln. Subsequently, the growth of these roots was stimulated by the Supreme Court\u27s decisions in the famous cases of in re Neagle (1890), In re Debs (1895), and United States v. Midwest Oil Co. (1915) and has blossomed into a full blown, if not overblown, succession of strong Presidents during the last seventy years. Along with the spiraling development of executive power, volumes of critical material gushed forth in response to both the growth of presidential powers and its budding textbook Presidency rationale; however, the impact of this response has been slight, and as one author of the late 1950\u27s put it, the President of today is a creature of custom. Given the above introduction, the purpose of this paper is to discuss the role of the Supreme Court in an expanding Presidency by focusing on its decisions in Youngstown Sheet and Tube Co. v. Sawyer (1952), New York Times Co. v. United States (1971), and United States v. Nixon (1974). It is believed that the various opinions found in the three cases mirror the ever-increasing debate which surrounds the growth of executive powers. As rulings, the decisions not only provide the Supreme Court\u27s views on the scope of inherent executive powers, but also provide a means with which to analyze the role of the Court in the expanding Presidency. Since each of the decisions turned on the special circumstances of the case, it is suggested that none of the rulings can be read as imposing any serious limitations on inherent executive powers. On the contrary, the burden and thesis of this paper is that the Court, in each of the three cases, paved the way for future presidential claims of implied powers