Boyle, Spinoza and Glauber: On the Philosophical Redintegration of Saltpeter A Reply to Antonio Clericuzio

Traditionally, the so-called ‘redintegration experiment’ is at the center of the comments on the supposed Boyle/Spinoza correspondence. A. Clericuzio argued (refuting the interpretation by R.A. & M.B. Hall) in his influential publications that, in De nitro, Boyle accounted for the ‘redintegration’ of saltpeter on the grounds of the chemical properties of corpuscles and did not make any attempt to deduce them from the mechanical principles. By contrast, this paper claims that with his De nitro Boyle wanted to illustrate and promote precisely his new Corpuscular or Mechanical Philosophy, and that he did significant attempts to explain the phenomena in terms of mechanical qualities. Boyle had borrowed the ‘redintegration experiment’ from R. Glauber and used it as a tool to prove that his philosophy was the right alternative for the Peripatetic and Paracelsian theory of qualities of bodies. Consequently, Clericuzio’s characterization of the Boyle/Spinoza controversy as a discussion between a strict mechanical philosopher and a chemist is problematic and should be revised

Stroboscopic high-order nonlinearity for quantum optomechanics

High-order quantum nonlinearity is an important prerequisite for the advanced quantum technology leading to universal quantum processing with large information capacity of continuous variables. Levitated optomechanics, a field where motion of dielectric particles is driven by precisely controlled tweezer beams, is capable of attaining the required nonlinearity via engineered potential landscapes of mechanical motion. Importantly, to achieve nonlinear quantum effects, the evolution caused by the free motion of mechanics and thermal decoherence have to be suppressed. For this purpose, we devise a method of stroboscopic application of a highly nonlinear potential to a mechanical oscillator that leads to the motional quantum non-Gaussian states exhibiting nonclassical negative Wigner function and squeezing of a nonlinear combination of mechanical quadratures. We test the method numerically by analysing highly instable cubic potential with relevant experimental parameters of the levitated optomechanics, prove its feasibility within reach, and propose an experimental test. The method paves a road for unique experiments instantaneously transforming a ground state of mechanical oscillators to applicable nonclassical states by nonlinear optical force.Comment: 13+8 pages, 2+3 figures. Close to the published versio

Geometry of entanglement witnesses for two qutrits

We characterize a convex subset of entanglement witnesses for two qutrits. Equivalently, we provide a characterization of the set of positive maps in the matrix algebra of 3 x 3 complex matrices. It turns out that boundary of this set displays elegant representation in terms of SO(2) rotations. We conjecture that maps parameterized by rotations are optimal, i.e. they provide the strongest tool for detecting quantum entanglement. As a byproduct we found a new class of decomposable entanglement witnesses parameterized by improper rotations from the orthogonal group O(2).Comment: 9 page