Amplitude Spectroscopy of a Solid-State Artificial Atom

The energy-level structure of a quantum system plays a fundamental role in determining its behavior and manifests itself in a discrete absorption and emission spectrum. Conventionally, spectra are probed via frequency spectroscopy whereby the frequency \nu of a harmonic driving field is varied to fulfill the conditions \Delta E = h \nu, where the driving field is resonant with the level separation \Delta E (h is Planck's constant). Although this technique has been successfully employed in a variety of physical systems, including natural and artificial atoms and molecules, its application is not universally straightforward, and becomes extremely challenging for frequencies in the range of 10's and 100's of gigahertz. Here we demonstrate an alternative approach, whereby a harmonic driving field sweeps the atom through its energy-level avoided crossings at a fixed frequency, surmounting many of the limitations of the conventional approach. Spectroscopic information is obtained from the amplitude dependence of the system response. The resulting ``spectroscopy diamonds'' contain interference patterns and population inversion that serve as a fingerprint of the atom's spectrum. By analyzing these features, we determine the energy spectrum of a manifold of states with energies from 0.01 to 120 GHz \times h in a superconducting artificial atom, using a driving frequency near 0.1 GHz. This approach provides a means to manipulate and characterize systems over a broad bandwidth, using only a single driving frequency that may be orders of magnitude smaller than the energy scales being probed.Comment: 12 pages, 13 figure

Government failure: Four types

Economists tend to see the market as a default option for social order and a role for government only when markets fail. Developing a convincing analysis of the role of government in economic processes, however, needs to start by considering government failure in its own terms. Drawing on insights from institutional economics, law and economics and the philosophy of law, emphasizing the necessity of rules for the economy, this paper develops the concept of government failure. The paper identifies and develops four different types of government failure. Government can set rules for economic processes and actors that are (1) too specific, (2) too broad, (3) that are arbitrary, or (4) that conflict with other rules it has set out to address other, related issues (possibly primarily noneconomic). Government failure is illustrated in the context of Intellectual Property Right (IPR) law as it relates to Anti-Trust law