Commuting symmetry operators of the Dirac equation, Killing-Yano and Schouten-Nijenhuis brackets

In this paper we derive the most general first-order symmetry operator commuting with the Dirac operator in all dimensions and signatures. Such an operator splits into Clifford even and Clifford odd parts which are given in terms of odd Killing-Yano and even closed conformal Killing-Yano inhomogeneous forms respectively. We study commutators of these symmetry operators and give necessary and sufficient conditions under which they remain of the first-order. In this specific setting we can introduce a Killing-Yano bracket, a bilinear operation acting on odd Killing-Yano and even closed conformal Killing-Yano forms, and demonstrate that it is closely related to the Schouten-Nijenhuis bracket. An important non-trivial example of vanishing Killing-Yano brackets is given by Dirac symmetry operators generated from the principal conformal Killing-Yano tensor [hep-th/0612029]. We show that among these operators one can find a complete subset of mutually commuting operators. These operators underlie separability of the Dirac equation in Kerr-NUT-(A)dS spacetimes in all dimensions [arXiv:0711.0078].Comment: 37 pages, no figure

Nondestructive readout for a superconducting flux qubit

We present a new readout method for a superconducting flux qubit, based on the measurement of the Josephson inductance of a superconducting quantum interference device that is inductively coupled to the qubit. The intrinsic flux detection efficiency and back-action are suitable for a fast and nondestructive determination of the quantum state of the qubit, as needed for readout of multiple qubits in a quantum computer. We performed spectroscopy of a flux qubit and we measured relaxation times of the order of 80 $\mu s$.Comment: 4 pages, 4 figures; modified content, figures and references; accepted for publication in Phys. Rev. Let

QND measurement of a superconducting qubit in the weakly projective regime

Quantum state detectors based on switching of hysteretic Josephson junctions biased close to their critical current are simple to use but have strong back-action. We show that the back-action of a DC-switching detector can be considerably reduced by limiting the switching voltage and using a fast cryogenic amplifier, such that a single readout can be completed within 25 ns at a repetition rate of 1 MHz without loss of contrast. Based on a sequence of two successive readouts we show that the measurement has a clear quantum non-demolition character, with a QND fidelity of 75 %.Comment: submitted to PR

Nonlinear stability of pulse solutions for the discrete FitzHugh-Nagumo equation with infinite-range interactions

We establish the existence and nonlinear stability of travelling pulse solutions for the discrete FitzHugh-Nagumo equation with infinite-range interactions close to the continuum limit. For the verification of the spectral properties, we need to study a functional differential equation of mixed type (MFDE) with unbounded shifts. We avoid the use of exponential dichotomies and phase spaces, by building on a technique developed by Bates, Chen and Chmaj for the discrete Nagumo equation. This allows us to transfer several crucial Fredholm properties from the PDE setting to our discrete setting

Josephson squelch filter for quantum nanocircuits

We fabricated and tested a squelch circuit consisting of a copper powder filter with an embedded Josephson junction connected to ground. For small signals (squelch-ON), the small junction inductance attenuates strongly from DC to at least 1 GHz, while for higher frequencies dissipation in the copper powder increases the attenuation exponentially with frequency. For large signals (squelch-OFF) the circuit behaves as a regular metal powder filter. The measured ON/OFF ratio is larger than 50dB up to 50 MHz. This squelch can be applied in low temperature measurement and control circuitry for quantum nanostructures such as superconducting qubits and quantum dots.Comment: Corrected and completed references 6,7,8. Updated some minor details in figure

Soil biological quality of grassland fertilized with adjusted cattle manure slurries in comparison with organic and inorganic fertilizers

We studied the effect of five fertilizers (including two adjusted manure slurries) and an untreated control on soil biota and explored the effect on the ecosystem services they provided. Our results suggest that the available N (NO3- and NH4+) in the soil plays a central role in the effect of fertilizers on nematodes and microorganisms. Microorganisms are affected directly through nutrient availability and indirectly through grass root mass. Nematodes are affected indirectly through microbial biomass and grass root mass. A lower amount of available N in the treatment with inorganic fertilizer was linked to a higher root mass and a higher abundance and proportion of herbivorous nematodes. A higher amount of available N in the organic fertilizer treatments resulted in a twofold higher bacterial activity (measured as bacterial growth rate, viz. thymidine incorporation), a higher proportion of bacterivorous nematodes, a 30% higher potential N mineralization (aerobic incubation), and 25–50% more potentially mineralizable N (anaerobic incubation). Compared to inorganic fertilizer, organic fertilization increased the C total, the N total, the activity of decomposers, and the supply of nutrients via the soil food web. Within the group of organic fertilizers, there was no significant difference in C total, abundances of soil biota, and the potential N mineralization rate. There were no indications that farmyard manure or the adjusted manure slurries provided the ecosystem service “supply of nutrients” better than normal manure slurry. Normal manure slurry provided the highest bacterial activity and the highest amount of mineralizable N and it was the only fertilizer resulting in a positive trend in grass yield over the years 2000–2005. The number of earthworm burrows was higher in the treatments with organic fertilizers compared to the one with the inorganic fertilizer, which suggests that organic fertilizers stimulate the ecosystem service of water regulation more than inorganic fertilizer. The trend towards higher epigeic earthworm numbers with application of farmyard manure and one of the adjusted manure slurries, combined with the negative relation between epigeic earthworms and bulk density and a significantly lower penetration resistance in the same fertilizer types, is preliminary evidence that these two organic fertilizer types contribute more to the service of soil structure maintenance than inorganic fertilize

Low-crosstalk bifurcation detectors for coupled flux qubits

We present experimental results on the crosstalk between two AC-operated dispersive bifurcation detectors, implemented in a circuit for high-fidelity readout of two strongly coupled flux qubits. Both phase-dependent and phase-independent contributions to the crosstalk are analyzed. For proper tuning of the phase the measured crosstalk is 0.1 % and the correlation between the measurement outcomes is less than 0.05 %. These results show that bifurcative readout provides a reliable and generic approach for multi-partite correlation experiments.Comment: Copyright 2010 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Applied Physics Letters and may be found at http://link.aip.org/link/?apl/96/12350