26,056 research outputs found
Optimal Control Theory for Continuous Variable Quantum Gates
We apply the methodology of optimal control theory to the problem of
implementing quantum gates in continuous variable systems with quadratic
Hamiltonians. We demonstrate that it is possible to define a fidelity measure
for continuous variable (CV) gate optimization that is devoid of traps, such
that the search for optimal control fields using local algorithms will not be
hindered. The optimal control of several quantum computing gates, as well as
that of algorithms composed of these primitives, is investigated using several
typical physical models and compared for discrete and continuous quantum
systems. Numerical simulations indicate that the optimization of generic CV
quantum gates is inherently more expensive than that of generic discrete
variable quantum gates, and that the exact-time controllability of CV systems
plays an important role in determining the maximum achievable gate fidelity.
The resulting optimal control fields typically display more complicated Fourier
spectra that suggest a richer variety of possible control mechanisms. Moreover,
the ability to control interactions between qunits is important for delimiting
the total control fluence. The comparative ability of current experimental
protocols to implement such time-dependent controls may help determine which
physical incarnations of CV quantum information processing will be the easiest
to implement with optimal fidelity.Comment: 39 pages, 11 figure
The Casimir force on a surface with shallow nanoscale corrugations: Geometry and finite conductivity effects
We measure the Casimir force between a gold sphere and a silicon plate with
nanoscale, rectangular corrugations with depth comparable to the separation
between the surfaces. In the proximity force approximation (PFA), both the top
and bottom surfaces of the corrugations contribute to the force, leading to a
distance dependence that is distinct from a flat surface. The measured Casimir
force is found to deviate from the PFA by up to 15%, in good agreement with
calculations based on scattering theory that includes both geometry effects and
the optical properties of the material
Model of Thermal Wavefront Distortion in Interferometric Gravitational-Wave Detectors I: Thermal Focusing
We develop a steady-state analytical and numerical model of the optical
response of power-recycled Fabry-Perot Michelson laser gravitational-wave
detectors to thermal focusing in optical substrates. We assume that the thermal
distortions are small enough that we can represent the unperturbed intracavity
field anywhere in the detector as a linear combination of basis functions
related to the eigenmodes of one of the Fabry-Perot arm cavities, and we take
great care to preserve numerically the nearly ideal longitudinal phase
resonance conditions that would otherwise be provided by an external
servo-locking control system. We have included the effects of nonlinear thermal
focusing due to power absorption in both the substrates and coatings of the
mirrors and beamsplitter, the effects of a finite mismatch between the
curvatures of the laser wavefront and the mirror surface, and the diffraction
by the mirror aperture at each instance of reflection and transmission. We
demonstrate a detailed numerical example of this model using the MATLAB program
Melody for the initial LIGO detector in the Hermite-Gauss basis, and compare
the resulting computations of intracavity fields in two special cases with
those of a fast Fourier transform field propagation model. Additional
systematic perturbations (e.g., mirror tilt, thermoelastic surface
deformations, and other optical imperfections) can be included easily by
incorporating the appropriate operators into the transfer matrices describing
reflection and transmission for the mirrors and beamsplitter.Comment: 24 pages, 22 figures. Submitted to JOSA
- …