Defining Agency and Its Scope (II)

Fiduciary law necessarily raises issues of delineation and demarcation, which this paper demonstrates through examples involving common-law agents. Serving as an agent, and thus as a fiduciary, does not necessarily mean that agency law prescribes all duties that the agent owes the principal. The agent may have rights external to the relationship that the agent may exercise, distinct from the duty of loyalty owed the principal. When an agent acts outside the bounds of an agency relationship, the principal’s consent is not requisite to conduct that would constitute disloyalty within the bounds of the agency relationship. The paper illustrates the significance of this point through a series of examples drawn from a range of contexts, including auctions of art objects. Prior scholarship neglects the implications of demarcations that define the scope of an agency relationship and of fiduciary relationships more generically. More generally or theoretically, the paper examines the qualities of fiduciary duty as a default rule, arguing that the relative “stickiness” of the default varies. Agency law contains two different kinds of altering rules—necessary and sufficient conditions to vary a default rule—consisting of agreements that define the scope of the agent’s representative role on behalf of the principal, and consent by the principal to actions by the agent within that scope that relieve the agent of liability for breach of fiduciary duty, which impose significantly different requisites. The basic distinction between agreement and consent has parallels elsewhere in agency law; for example, ratification, like consent, requires specificity because to be legally effective ratification requires that the principal know, as a matter of historical fact, what the agent has done. Agreement, on the other hand, requires less specificity, comparable to manifestations that confer actual authority on an agent which necessarily does not require that the principal foresee all actions that the agent may take that fall within the scope of the grant of authority. And ratification, like effective consent, is a matter of historical fact, not hypothesis. These implications follow because agency law, by positioning an agent as the principal’s representative for purposes of legally-salient interactions with third parties and facts about the world, frames the agent as an extension of the principal, not the principal’s substitute

Sensing electrochemical signals using a nitrogen-vacancy center in diamond

Chemical sensors with high sensitivity that can be used in extreme conditions and can be miniaturized are of high interest in science and industry. The Nitrogen-vacancy (NV) center in diamond is an ideal candidate as a nanosensor due to the long coherence time of its electron spin and its optical accessibility. In this theoretical work, we propose to use an NV center to detect electrochemical signals emerging from an electrolyte solution, thus obtaining a concentration sensor. For this purpose, we propose to use the inhomogeneous dephasing rate of the electron spin of the NV center ($1/T^*_2$) as a signal. We show that for a range of mean ionic concentrations in the bulk of the electrolyte solution, the electric field fluctuations produced by the diffusional fluctuations in the local concentration of ions, result in dephasing rates which can be inferred from free induction decay measurements. Moreover, we show that for a range of concentrations, the electric field generated at the position of the NV center can also be used to estimate the concentration of ions.Comment: 17 pages, 7 figures, comments are welcom

Bayesian estimation for quantum sensing in the absence of single-shot detection

Quantum information protocols, such as quantum error correction and quantum phase estimation, have been widely used to enhance the performance of quantum sensors. While these protocols have relied on single-shot detection, in most practical applications only an averaged readout is available, as in the case of room-temperature sensing with the electron spin associated with a nitrogen-vacancy center in diamond. Here, we theoretically investigate the application of the quantum phase estimation algorithm for high dynamic-range magnetometry, in the case where single-shot readout is not available. We show that, even in this case, Bayesian estimation provides a natural way to use the available information in an efficient way. We apply Bayesian analysis to achieve an optimized sensing protocol for estimating a time-independent magnetic field with a single electron spin associated to a nitrogen-vacancy center at room temperature and show that this protocol improves the sensitivity over previous protocols by more than a factor of 3. Moreover, we show that an extra enhancement can be achieved by considering the timing information in the detector clicks.Comment: 7 pages + 2 pages supplementary, 5 figures, In the updated version we have added updating the probability after every single measurement. Comments are welcom

Temperature Dependent Photophysics of Single NV Centers in Diamond

We present a comprehensive study of the temperature and magnetic-field dependent photoluminescence (PL) of individual NV centers in diamond, spanning the temperature-range from cryogenic to ambient conditions. We directly observe the emergence of the NV's room-temperature effective excited state structure and provide a clear explanation for a previously poorly understood broad quenching of NV PL at intermediate temperatures around 50 K. We develop a model that quantitatively explains all of our findings, including the strong impact that strain has on the temperaturedependence of the NV's PL. These results complete our understanding of orbital averaging in the NV excited state and have significant implications for the fundamental understanding of the NV center and its applications in quantum sensing.Comment: 5 pages, 4 figures plus Supplementary Material. Questions and comments are welcome. arXiv admin note: text overlap with arXiv:2105.0807

A Diamond Nanowire Single Photon Antenna

The development of a robust light source that emits one photon at a time is an outstanding challenge in quantum science and technology. Here, at the transition from many to single photon optical communication systems, fully quantum mechanical effects may be utilized to achieve new capabilities, most notably perfectly secure communication via quantum cryptography. Practical implementations place stringent requirements on the device properties, including stable photon generation, room temperature operation, and efficient extraction of many photons. Single photon light emitting devices based on fluorescent dye molecules, quantum dots, and carbon nanotube material systems have all been explored, but none have simultaneously demonstrated all criteria. Here, we describe the design, fabrication, and characterization of a bright source of single photons consisting of an individual Nitrogen-vacancy color center (NV center) in a diamond nanowire operating in ambient conditions. The nanowire plays a positive role in increasing the number of single photons collected from the NV center by an order of magnitude over devices based on bulk diamond crystals, and allows operation at an order of magnitude lower power levels. This result enables a new class of nanostructured diamond devices for room temperature photonic and quantum information processing applications, and will also impact fields as diverse as biological and chemical sensing, opto-mechanics, and scanning-probe microscopy.Comment: 16 pages, 4 figures, v2: Includes improved reference list; modified figure 1 to show a large array of NW and FDTD simulation of field profile; direct experimental comparsion of several bulk/NW devices in figure