Finite normal subgroups of strongly verbally closed groups

In the recent paper by A. A. Klyachko, V. Yu. Miroshnichenko, and A. Yu. Olshanskii, it is proven that the center of any finite strongly verbally closed group is its direct factor. One of the results of the current paper is the generalization of this nontrivial fact to the case of finite normal subgroups of any strongly verbally closed groups. It follows from this generalization that finitely generated nilpotent groups with nonabelian torsion subgroups are not strongly verbally closed.Comment: 11 pages. V2: Proposition concerning the center of a strong retract is added, and minor errors are correcte

The centre of a finitely generated strongly verbally closed group is almost always pure

The assertion in the title implies that many interesting groups (e.g., all non-abelian braid groups or ${\bf SL}_{100}(\mathbb Z)$) are not strongly verbally closed, i.e., they embed into some finitely generated groups as verbally closed subgroups, which are not retracts.Comment: 5 pages. A Russian version of this paper is at http://halgebra.math.msu.su/staff/klyachko/papers.ht

Driving Rydberg-Rydberg transitions from a co-planar microwave waveguide

The coherent interaction between ensembles of helium Rydberg atoms and microwave fields in the vicinity of a solid-state co-planar waveguide is reported. Rydberg-Rydberg transitions, at frequencies between 25 GHz and 38 GHz, have been studied for states with principal quantum numbers in the range 30 - 35 by selective electric-field ionization. An experimental apparatus cooled to 100 K was used to reduce effects of blackbody radiation. Inhomogeneous, stray electric fields emanating from the surface of the waveguide have been characterized in frequency- and time-resolved measurements and coherence times of the Rydberg atoms on the order of 250 ns have been determined.Comment: 5 pages, 5 figure

Off-diagonal geometric phase for mixed states

We extend the off-diagonal geometric phase [Phys. Rev. Lett. {\bf 85}, 3067 (2000)] to mixed quantal states. The nodal structure of this phase in the qubit (two-level) case is compared with that of the diagonal mixed state geometric phase [Phys. Rev. Lett. {\bf 85}, 2845 (2000)]. Extension to higher dimensional Hilbert spaces is delineated. A physical scenario for the off-diagonal mixed state geometric phase in polarization-entangled two-photon interferometry is proposed.Comment: small corrections; journal reference adde

Kinematic approach to off-diagonal geometric phases of nondegenerate and degenerate mixed states

Off-diagonal geometric phases have been developed in order to provide information of the geometry of paths that connect noninterfering quantal states. We propose a kinematic approach to off-diagonal geometric phases for pure and mixed states. We further extend the mixed state concept proposed in [Phys. Rev. Lett. {\bf 90}, 050403 (2003)] to degenerate density operators. The first and second order off-diagonal geometric phases are analyzed for unitarily evolving pairs of pseudopure states.Comment: New section IV, new figure, journal ref adde

Photon State Tomography for Two-Mode Correlated Itinerant Microwave Fields

Continuous variable entanglement between two modes of a radiation field is usually studied at optical frequencies. As an important step towards the observation of entanglement between propagating microwave photons we demonstrate the experimental state reconstruction of two field modes in the microwave domain. In particular, we generate two-mode correlated states with a Josephson parametric amplifier and detect all four quadrature components simultaneously in a two-channel heterodyne setup using amplitude detectors. Analyzing two-dimensional phase space histograms for all possible pairs of quadratures allows us to determine the full covariance matrix and reconstruct the four-dimensional Wigner function. We demonstrate strong correlations between the quadrature amplitude noise in the two modes. Under ideal conditions two-mode squeezing below the standard quantum limit should be observable in future experiments.Comment: 4 pages, 4 figure

Preparation of Subradiant States using Local Qubit Control in Circuit QED

Transitions between quantum states by photon absorption or emission are intimately related to symmetries of the system which lead to selection rules and the formation of dark states. In a circuit quantum electrodynamics setup, in which two resonant superconducting qubits are coupled through an on-chip cavity and driven via the common cavity field, one single-excitation state remains dark. Here, we demonstrate that this dark state can be excited using local phase control of individual qubit drives to change the symmetry of the driving field. We observe that the dark state decay via spontaneous emission into the cavity is suppressed, a characteristic signature of subradiance. This local control technique could be used to prepare and study highly correlated quantum states of cavity-coupled qubits.Comment: 5 pages, 4 figure

Benchmarking the noise sensitivity of different parametric two-qubit gates in a single superconducting quantum computing platform

The possibility to utilize different types of two-qubit gates on a single quantum computing platform adds flexibility in the decomposition of quantum algorithms. A larger hardware-native gate set may decrease the number of required gates, provided that all gates are realized with high fidelity. Here, we benchmark both controlled-Z (CZ) and exchange-type (iSWAP) gates using a parametrically driven tunable coupler that mediates the interaction between two superconducting qubits. Using randomized benchmarking protocols we estimate an error per gate of $0.9\pm0.03\%$ and $1.3\pm0.4\%$ fidelity for the CZ and the iSWAP gate, respectively. We argue that spurious $ZZ$-type couplings are the dominant error source for the iSWAP gate, and that phase stability of all microwave drives is of utmost importance. Such differences in the achievable fidelities for different two-qubit gates have to be taken into account when mapping quantum algorithms to real hardware.Comment: 24 pages, including supplementary informatio

Suitability of Different PCR-DGGE Primer Sets for the Monitoring of Lactic Acid Bacteria in Wine

Lactic acid bacteria (LAB) play a dual role in winemaking as they are the main effectors of malolactic fermentation, but some members can also cause wine spoilage. PCR-DGGE has proved to be a quick tool to study the LAB community and their fluctuation in wine. For detecting wine-associated LAB by PCR-DGGE, the primer sets WLAB1/WLAB2GC, WBAC1/WBAC2GC, Lac1/Lac1o/Lac2GC, 341fGC/518r and rpoB1/rpoB1o/rpoB2GC were tested and evaluated in this study. The primer systems were assessed by the separation of LAB reference strains on DGGE gels and by attributing the resulting amplicons to defined species. Subsequently, the detection of LAB in wine samples and enrichments thereof was compared. While the primer systems WBAC1/WBAC2GC and 341fGC/518r were not appropriate, the Lac1/Lac1o/Lac2GC primer set performed well. However, multiple bands complicated the evaluation. The rpoB1/rpoB1o/rpoB2GC set seemed to be promising for the detection of LAB in wine, although further improvements in terms of the detection limit need to be done. Due to the pronounced sensitivity and the sufficient discrimination of LAB at species level, the WLAB1/WLAB2GC primer system was found to be most suitable for studying the occurrence of LAB in wine