15 research outputs found
Digital control of force microscope cantilevers using a field programmable gate array
This report describes a cantilever controller for magnetic resonance force
microscopy (MRFM) based on a field programmable gate array (FPGA), along with
the hardware and software used to integrate the controller into an experiment.
The controller is assembled from a low-cost commercially available software
defined radio (SDR) device and libraries of open-source software. The
controller includes a digital filter comprising two cascaded second-order
sections ("biquads"), which together can implement transfer functions for
optimal cantilever controllers. An appendix in this report shows how to
calculate filter coefficients for an optimal controller from measured
cantilever characteristics. The controller also includes an input multiplexer
and adder used in calibration protocols. Filter coefficients and multiplexer
settings can be set and adjusted by control software while an experiment is
running. The input is sampled at 64 MHz; the sampling frequency in the filters
can be divided down under software control to achieve a good match with filter
characterisics. Data reported here were sampled at 500 kHz, chosen for acoustic
cantilevers with resonant frequencies near 8 kHz. Inputs are digitized with 12
bits resolution, outputs with 14 bits. The experiment software is organized as
a client and server to make it easy to adapt the controller to different
experiments. The server encapusulates the details of controller hardware
organization, connection technology, filter architecture, and number
representation. The same server could be used in any experiment, while a
different client encodes the particulars of each experiment.Comment: submitted to Review of Scientific Instrument
Practical recipes for the model order reduction, dynamical simulation, and compressive sampling of large-scale open quantum systems
This article presents numerical recipes for simulating high-temperature and
non-equilibrium quantum spin systems that are continuously measured and
controlled. The notion of a spin system is broadly conceived, in order to
encompass macroscopic test masses as the limiting case of large-j spins. The
simulation technique has three stages: first the deliberate introduction of
noise into the simulation, then the conversion of that noise into an equivalent
continuous measurement and control process, and finally, projection of the
trajectory onto a state-space manifold having reduced dimensionality and
possessing a Kahler potential of multi-linear form. The resulting simulation
formalism is used to construct a positive P-representation for the thermal
density matrix. Single-spin detection by magnetic resonance force microscopy
(MRFM) is simulated, and the data statistics are shown to be those of a random
telegraph signal with additive white noise. Larger-scale spin-dust models are
simulated, having no spatial symmetry and no spatial ordering; the
high-fidelity projection of numerically computed quantum trajectories onto
low-dimensionality Kahler state-space manifolds is demonstrated. The
reconstruction of quantum trajectories from sparse random projections is
demonstrated, the onset of Donoho-Stodden breakdown at the Candes-Tao sparsity
limit is observed, a deterministic construction for sampling matrices is given,
and methods for quantum state optimization by Dantzig selection are given.Comment: 104 pages, 13 figures, 2 table
Upper limit map of a background of gravitational waves
We searched for an anisotropic background of gravitational waves using data
from the LIGO S4 science run and a method that is optimized for point sources.
This is appropriate if, for example, the gravitational wave background is
dominated by a small number of distinct astrophysical sources. No signal was
seen. Upper limit maps were produced assuming two different power laws for the
source strain power spectrum. For an f^-3 power law and using the 50 Hz to 1.8
kHz band the upper limits on the source strain power spectrum vary between
1.2e-48 Hz^-1 (100 Hz/f)^3 and 1.2e-47 Hz^-1 (100 Hz /f)^3, depending on the
position in the sky. Similarly, in the case of constant strain power spectrum,
the upper limits vary between 8.5e-49 Hz^-1 and 6.1e-48 Hz^-1.
As a side product a limit on an isotropic background of gravitational waves
was also obtained. All limits are at the 90% confidence level. Finally, as an
application, we focused on the direction of Sco-X1, the closest low-mass X-ray
binary. We compare the upper limit on strain amplitude obtained by this method
to expectations based on the X-ray luminosity of Sco-X1.Comment: 11 pages, 9 figures, 2 table
Upper limit map of a background of gravitational waves
We searched for an anisotropic background of gravitational waves using data
from the LIGO S4 science run and a method that is optimized for point sources.
This is appropriate if, for example, the gravitational wave background is
dominated by a small number of distinct astrophysical sources. No signal was
seen. Upper limit maps were produced assuming two different power laws for the
source strain power spectrum. For an f^-3 power law and using the 50 Hz to 1.8
kHz band the upper limits on the source strain power spectrum vary between
1.2e-48 Hz^-1 (100 Hz/f)^3 and 1.2e-47 Hz^-1 (100 Hz /f)^3, depending on the
position in the sky. Similarly, in the case of constant strain power spectrum,
the upper limits vary between 8.5e-49 Hz^-1 and 6.1e-48 Hz^-1.
As a side product a limit on an isotropic background of gravitational waves
was also obtained. All limits are at the 90% confidence level. Finally, as an
application, we focused on the direction of Sco-X1, the closest low-mass X-ray
binary. We compare the upper limit on strain amplitude obtained by this method
to expectations based on the X-ray luminosity of Sco-X1.Comment: 11 pages, 9 figures, 2 table