Generalized Strong Curvature Singularities and Cosmic Censorship

A new definition of a strong curvature singularity is proposed. This definition is motivated by the definitions given by Tipler and Krolak, but is significantly different and more general. All causal geodesics terminating at these new singularities, which we call generalized strong curvature singularities, are classified into three possible types; the classification is based on certain relations between the curvature strength of the singularities and the causal structure in their neighborhood. A cosmic censorship theorem is formulated and proved which shows that only one class of generalized strong curvature singularities, corresponding to a single type of geodesics according to our classification, can be naked. Implications of this result for the cosmic censorship hypothesis are indicated.Comment: LaTeX, 11 pages, no figures, to appear in Mod. Phys. Lett.

Mutual Unbiasedness in Coarse-grained Continuous Variables

The notion of mutual unbiasedness for coarse-grained measurements of quantum continuous variable systems is considered. It is shown that while the procedure of "standard" coarse graining breaks the mutual unbiasedness between conjugate variables, this desired feature can be theoretically established and experimentally observed in periodic coarse graining. We illustrate our results in an optics experiment implementing Fraunhofer diffraction through a periodic diffraction grating, finding excellent agreement with the derived theory. Our results are an important step in developing a formal connection between discrete and continuous variable quantum mechanics.Comment: 5 pages, 3 figures + Supplemental Material (1 page) v2: Introduction expanded, minor typos correcte

Circularly polarized microwaves for magnetic resonance study in the GHz range: application to nitrogen-vacancy in diamonds

The ability to create time-dependent magnetic fields of controlled polarization is essential for many experiments with magnetic resonance. We describe a microstrip circuit that allows us to generate strong magnetic field at microwave frequencies with arbitrary adjusted polarization. The circuit performance is demonstrated by applying it to an optically detected magnetic resonance and Rabi nutation experiments in nitrogen-vacancy color centers in diamond. Thanks to high efficiency of the proposed microstrip circuit and degree of circular polarization of 85% it is possible to address the specific spin states of a diamond sample using a low power microwave generator.Comment: 4 pages, 7 figures, nitrogen-vacancy, microwave circular polarization, spin-state addressin

Time evolution of the QED vacuum in a uniform electric Field: Complete analytic solution by spinorial decomposition

Exact analytical solutions are presented for the time evolution of the density of pairs produced in the QED vacuum by a time-independent, uniform electric field. The mathematical tool used here to describe the pair production is the Dirac-Heisenberg-Wigner function introduced before [Phys. Rev. D 44, 1825 (1991)]. The initial value problem for this function is solved by decomposing the solution into a product of spinors. The equations for spinors are much simpler and are solved analytically. These calculations are nonperturbative since pair production is due to quantum-mechanical tunneling and the explicit solutions clearly exhibit their nonanalytic behavior.Comment: 6 pages, 1 figur

Coherent population oscillations with nitrogen-vacancy color centers in diamond

We present results of our research on two-field (two-frequency) microwave spectroscopy in nitrogen-vacancy (NV-) color centers in a diamond. Both fields are tuned to transitions between the spin sublevels of the NV- ensemble in the 3A2 ground state (one field has a fixed frequency while the second one is scanned). Particular attention is focused on the case where two microwaves fields drive the same transition between two NV- ground state sublevels (ms=0 -> ms=+1). In this case, the observed spectra exhibit a complex narrow structure composed of three Lorentzian resonances positioned at the pump-field frequency. The resonance widths and amplitudes depend on the lifetimes of the levels involved in the transition. We attribute the spectra to coherent population oscillations induced by the two nearly degenerate microwave fields, which we have also observed in real time. The observations agree well with a theoretical model and can be useful for investigation of the NV relaxation mechanisms.Comment: 17 page

Testing for entanglement with periodic coarse-graining

Continuous variables systems find valuable applications in quantum information processing. To deal with an infinite-dimensional Hilbert space, one in general has to handle large numbers of discretized measurements in tasks such as entanglement detection. Here we employ the continuous transverse spatial variables of photon pairs to experimentally demonstrate novel entanglement criteria based on a periodic structure of coarse-grained measurements. The periodization of the measurements allows for an efficient evaluation of entanglement using spatial masks acting as mode analyzers over the entire transverse field distribution of the photons and without the need to reconstruct the probability densities of the conjugate continuous variables. Our experimental results demonstrate the utility of the derived criteria with a success rate in entanglement detection of $\sim60\%$ relative to $7344$ studied cases.Comment: V1: revtex4, 10 pages, 4 figures + supp. material (4 pages, 1 figure) V2: Substantial revisions implemented both in theory and experimental data analysi

Microwave saturation spectroscopy of nitrogen-vacancy ensembles in diamond

Negatively-charged nitrogen-vacancy (NV$^-$) centers in diamond have generated much recent interest for their use in sensing. The sensitivity improves when the NV ground-state microwave transitions are narrow, but these transitions suffer from inhomogeneous broadening, especially in high-density NV ensembles. To better understand and remove the sources of broadening, we demonstrate room-temperature spectral "hole burning" of the NV ground-state transitions. We find that hole burning removes the broadening caused by magnetic fields from $^{13}$C nuclei and demonstrate that it can be used for magnetic-field-insensitive thermometry.Comment: Main text: 5 pages, 4 figures. Supplement: 6 pages, 3 figure