An empirical modification of the force field approach to describe the modulation of galactic cosmic rays close to Earth in a broad range of rigidities

On their way through the heliosphere, Galactic Cosmic Rays (GCRs) are modulated by various effects before they can be detected at Earth. This process can be described by the Parker equation, which calculates the phase space distribution of GCRs depending on the main modulation processes: convection, drifts, diffusion and adiabatic energy changes. A first order approximation of this equation is the force field approach, reducing it to a one-parameter dependency, the solar modulation potential $\phi$. Utilizing this approach, it is possible to reconstruct $\phi$ from ground based and spacecraft measurements. However, it has been shown previously that $\phi$ depends not only on the Local Interstellar Spectrum (LIS) but also on the energy range of interest. We have investigated this energy dependence further, using published proton intensity spectra obtained by PAMELA as well as heavier nuclei measurements from IMP-8 and ACE/CRIS. Our results show severe limitations at lower energies including a strong dependence on the solar magnetic epoch. Based on these findings, we will outline a new tool to describe GCR proton spectra in the energy range from a few hundred MeV to tens of GeV over the last solar cycles. In order to show the importance of our modification, we calculate the global production rates of the cosmogenic radionuclide $^{10}$Be which is a proxy for the solar activity ranging back thousands of years

Spatial gradients of GCR protons in the inner heliosphere derived from Ulysses COSPIN/KET and PAMELA measurements

During the transition from solar cycle 23 to 24 from 2006 to 2009, the Sun was in an unusual solar minimum with very low activity over a long period. These exceptional conditions included a very low interplanetary magnetic field (IMF) strength and a high tilt angle, which both play an important role in the modulation of galactic cosmic rays (GCR) in the heliosphere. Thus, the radial and latitudinal gradients of GCRs are very much expected to depend not only on the solar magnetic epoch, but also on the overall modulation level. We determine the non-local radial and the latitudinal gradients of protons in the rigidity range from ~0.45 to 2 GV. This was accomplished by using data from the satellite-borne experiment Payload for Antimatter Matter Exploration and Light-nuclei Astrophysics (PAMELA) at Earth and the Kiel Electron Telescope (KET) onboard Ulysses on its highly inclined Keplerian orbit around the Sun with the aphelion at Jupiter's orbit. In comparison to the previous A>0 solar magnetic epoch, we find that the absolute value of the latitudinal gradient is lower at higher and higher at lower rigidities. This energy dependence is therefore a crucial test for models that describe the cosmic ray transport in the inner heliosphere

A levitated nanoparticle as a classical two-level atom

The center-of-mass motion of a single optically levitated nanoparticle resembles three uncoupled harmonic oscillators. We show how a suitable modulation of the optical trapping potential can give rise to a coupling between two of these oscillators, such that their dynamics are governed by a classical equation of motion that resembles the Schr\"odinger equation for a two-level system. Based on experimental data, we illustrate the dynamics of this parametrically coupled system both in the frequency and in the time domain. We discuss the limitations and differences of the mechanical analogue in comparison to a true quantum mechanical system

Non-equilibrium steady state of a driven levitated particle with feedback cooling

Laser trapped nanoparticles have been recently used as model systems to study fundamental relations holding far from equilibrium. Here we study, both experimentally and theoretically, a nanoscale silica sphere levitated by a laser in a low density gas. The center of mass motion of the particle is subjected, at the same time, to feedback cooling and a parametric modulation driving the system into a non-equilibrium steady state. Based on the Langevin equation of motion of the particle, we derive an analytical expression for the energy distribution of this steady state showing that the average and variance of the energy distribution can be controlled separately by appropriate choice of the friction, cooling and modulation parameters. Energy distributions determined in computer simulations and measured in a laboratory experiment agree well with the analytical predictions. We analyse the particle motion also in terms of the quadratures and find thermal squeezing depending on the degree of detuning.Comment: Submitted to the New Journal of Physic

Nonlinear mode-coupling and synchronization of a vacuum-trapped nanoparticle

We study the dynamics of a laser-trapped nanoparticle in high vacuum. Using parametric coupling to an external excitation source, the linewidth of the nanoparticle's oscillation can be reduced by three orders of magnitude. We show that the oscillation of the nanoparticle and the excitation source are synchronized, exhibiting a well-defined phase relationship. Furthermore, the external source can be used to controllably drive the nanoparticle into the nonlinear regime, thereby generating strong coupling between the different translational modes of the nanoparticle. Our work contributes to the understanding of the nonlinear dynamics of levitated nanoparticles in high vacuum and paves the way for studies of pattern formation, chaos, and stochastic resonance.Comment: 5 pages, 3 figure

Long distance manipulation of a levitated nanoparticle in high vacuum

Accurate delivery of small targets in high vacuum is a pivotal task in many branches of science and technology. Beyond the different strategies developed for atoms, proteins, macroscopic clusters and pellets, the manipulation of neutral particles over macroscopic distances still poses a formidable challenge. Here we report a novel approach based on a mobile optical trap operated under feedback control that enables long range 3D manipulation of a silica nanoparticle in high vacuum. We apply this technique to load a single nanoparticle into a high-finesse optical cavity through a load-lock vacuum system. We foresee our scheme to benefit the field of optomechanics with levitating nano-objects as well as ultrasensitive detection and monitoring.Comment: 12 pages 5 figure

Observation of nitrogen vacancy photoluminescence from an optically levitated nanodiamond

We present the first evidence of nitrogen vacancy (NV) photoluminescence from a nanodiamond suspended in a free-space optical dipole trap at atmospheric pressure. The photoluminescence rates are shown to decrease with increasing trap laser power, but are inconsistent with a thermal quenching process. For a continuous-wave trap, the neutral charge state (NV$^0$) appears to be suppressed. Chopping the trap laser yields higher total count rates and results in a mixture of both NV$^0$ and the negative charge state (NV$^-$).Comment: Updated to published version appearing in Optics Letter