Bowen Measure From Heteroclinic Points

We present a new construction of the entropy-maximizing, invariant probability measure on a Smale space (the Bowen measure). Our construction is based on points that are unstably equivalent to one given point, and stably equivalent to another: heteroclinic points. The spirit of the construction is similar to Bowen's construction from periodic points, though the techniques are very different. We also prove results about the growth rate of certain sets of heteroclinic points, and about the stable and unstable components of the Bowen measure. The approach we take is to prove results through direct computation for the case of a Shift of Finite type, and then use resolving factor maps to extend the results to more general Smale spaces

The series spectra of the stripped boron atom (BIII)

In a preceding article [1], we have brought forward evidence that in "hot spark" spectra the strongest lines generally correspond to atoms from which the valence electrons have all been stripped off, so that the resulting spectrum is hydrogen-like, i.e., is due to one single electron moving between the series of levels characteristic of a simple nucleus-electron system. For such a nucleus-electron system the Bohr theory in its elementary form [2] which dealt only with circular orbits, i.e., with variations in azimuthal quantum numbers, the radial being always zero, yielded at once the result that the energies corresponding to a given quantum state, e.g., quantum number 1, increased in the ratio 1, 4, 9, 16, etc., as the nuclear charged increased in the ratio 1, 2, 3, 4, etc. This meant physically that the frequencies corresponding to jumps from infinity to an orbit of given quantum number, technically called term-values, when divided by the square of the nuclear charge should come out a constant; otherwise stated that the constant term in the Rydberg formula should become N, 4N, 9N, 16N

Feedback Enhanced Sensitivity in Optomechanics: Surpassing the Parametric Instability Barrier

The intracavity power, and hence sensitivity, of optomechanical sensors is commonly limited by parametric instability. Here we characterize the parametric instability induced sensitivity degradation in a micron scale cavity optomechanical system. Feedback via optomechanical transduction and electrical gradient force actuation is applied to suppress the parametric instability. As a result a 5.4 fold increase in mechanical motion transduction sensitivity is achieved to a final value of $1.9\times 10^{-18}\rm m Hz^{-1/2}$.Comment: 4 pages, 4 figure

Laser cooling and control of excitations in superfluid helium

Superfluidity is an emergent quantum phenomenon which arises due to strong interactions between elementary excitations in liquid helium. These excitations have been probed with great success using techniques such as neutron and light scattering. However measurements to-date have been limited, quite generally, to average properties of bulk superfluid or the driven response far out of thermal equilibrium. Here, we use cavity optomechanics to probe the thermodynamics of superfluid excitations in real-time. Furthermore, strong light-matter interactions allow both laser cooling and amplification of the thermal motion. This provides a new tool to understand and control the microscopic behaviour of superfluids, including phonon-phonon interactions, quantised vortices and two-dimensional quantum phenomena such as the Berezinskii-Kosterlitz-Thouless transition. The third sound modes studied here also offer a pathway towards quantum optomechanics with thin superfluid films, including femtogram effective masses, high mechanical quality factors, strong phonon-phonon and phonon-vortex interactions, and self-assembly into complex geometries with sub-nanometre feature size.Comment: 6 pages, 4 figures. Supplementary information attache

Minimum requirements for feedback enhanced force sensing

The problem of estimating an unknown force driving a linear oscillator is revisited. When using linear measurement, feedback is often cited as a mechanism to enhance bandwidth or sensitivity. We show that as long as the oscillator dynamics are known, there exists a real-time estimation strategy that reproduces the same measurement record as any arbitrary feedback protocol. Consequently some form of nonlinearity is required to gain any advantage beyond estimation alone. This result holds true in both quantum and classical systems, with non-stationary forces and feedback, and in the general case of non-Gaussian and correlated noise. Recently, feedback enhanced incoherent force sensing has been demonstrated [Nat. Nano. \textbf{7}, 509 (2012)], with the enhancement attributed to a feedback induced modification of the mechanical susceptibility. As a proof-of-principle we experimentally reproduce this result through straightforward filtering.Comment: 5 pages + 2 pages of Supplementary Informatio

Thin film superfluid optomechanics

Excitations in superfluid helium represent attractive mechanical degrees of freedom for cavity optomechanics schemes. Here we numerically and analytically investigate the properties of optomechanical resonators formed by thin films of superfluid $^4$He covering micrometer-scale whispering gallery mode cavities. We predict that through proper optimization of the interaction between film and optical field, large optomechanical coupling rates $g_0>2\pi \times 100$ kHz and single photon cooperativities $C_0>10$ are achievable. Our analytical model reveals the unconventional behaviour of these thin films, such as thicker and heavier films exhibiting smaller effective mass and larger zero point motion. The optomechanical system outlined here provides access to unusual regimes such as $g_0>\Omega_M$ and opens the prospect of laser cooling a liquid into its quantum ground state.Comment: 18 pages, 6 figure

Series spectra of two-valence-electron atoms of boron (BII) and carbon (CIII)

Series spectra of BII and CIII.—By methods previously reported in the identification of lines in the extreme ultraviolet, 13 lines in addition to the pp′ group of BII have been identified, completing the classification of all lines known to be due to BII. Taking the 4f level as 27800 (probably correct to within 200 frequency units), the following term values were obtained for BII: 3s, 72930.8; 4s, 36655.5; 2p1, 165343.9; 2p2,3, 165362.7; 3p1, 59006.5; 3p2,3, 59010.0; 3d, 52054.2; 4d, 28640.4; 5f, 17795.7; 2S, 194325.9; 3S, 66665.1; 2P, 120929.4; 3D, 48410.3. In the case of CIII, 8 lines in addition to the pp′ group were identified, and taking the 4f level as 62600, the following term values were obtained for CIII: 3s, 146197.2; 2p, 331939.2; 3p1, 124685.8; 3p2, 124698.6; 3p3, 124704.1; 3d, 114387.2; 2S, 375463.1; 2P, 273111.0. Progression of frequency separations and of screening constants for regular doublets for Li to O is shown in Table VI, for one to six valence electrons. The separation (2p2-2p1) or (2p3-2p1) regularly decreases and the constant s regularly increases, for a given element, with the number of valence electrons, irrespective of the fact that both doublets and triplets are involved

High frequency rays of cosmic origin I. Sounding balloon observations at extreme altitudes

Discharge rate of an electroscope at altitudes from 5 to 15.5 km.—Four specially designed instruments, each comprising a recording electroscope, thermometer and barometer and each weighing but 190 gr were sent up with sounding balloons from Kelly Field, Texas. Three were recovered and of these two had satisfactory records of their flight during which they reached altitudes of 11.2 and 15.5 km, respectively. A comparison of the recorded electroscope reading at the 5 km level during ascent with the reading at the same level during descent shows that the average discharge rate of the electroscopes while above the 5 km level was about three times their discharge rates at the surface of the earth, and corresponded to an average rate of production of ions of 46.2 ions per cc per sec. This is only 25 percent of the value to be expected from the observations of Hess and of Kolhörster and constitutes definite proof that there exists no penetrating radiation of cosmic origin having an absorption coefficient as large as 0.57 per meter of water