Relevance of the weak equivalence principle and experiments to test it: lessons from the past and improvements expected in space

Tests of the Weak Equivalence Principle (WEP) probe the foundations of physics. Ever since Galileo in the early 1600s, WEP tests have attracted some of the best experimentalists of any time. Progress has come in bursts, each stimulated by the introduction of a new technique: the torsion balance, signal modulation by Earth rotation, the rotating torsion balance. Tests for various materials in the field of the Earth and the Sun have found no violation to the level of about 1 part in 1e13. A different technique, Lunar Laser Ranging (LLR), has reached comparable precision. Today, both laboratory tests and LLR have reached a point when improving by a factor of 10 is extremely hard. The promise of another quantum leap in precision rests on experiments performed in low Earth orbit. The Microscope satellite, launched in April 2016 and currently taking data, aims to test WEP in the field of Earth to 1e-15, a 100-fold improvement possible thanks to a driving signal in orbit almost 500 times stronger than for torsion balances on ground. The `Galileo Galilei' (GG) experiment, by combining the advantages of space with those of the rotating torsion balance, aims at a WEP test 100 times more precise than Microscope, to 1e-17. A quantitative comparison of the key issues in the two experiments is presented, along with recent experimental measurements relevant for GG. Early results from Microscope, reported at a conference in March 2017, show measurement performance close to the expectations and confirm the key role of rotation with the advantage (unique to space) of rotating the whole spacecraft. Any non-null result from Microscope would be a major discovery and call for urgent confirmation; with 100 times better precision GG could settle the matter and provide a deeper probe of the foundations of physics.Comment: To appear: Physics Letters A, special issue in memory of Professor Vladimir Braginsky, 2017. Available online: http://dx.doi.org/10.1016/j.physleta.2017.09.02

Generation of 87^{87}Rb-resonant bright two-mode squeezed light with four-wave mixing

Squeezed states of light have found their way into a number of applications in quantum-enhanced metrology due to their reduced noise properties. In order to extend such an enhancement to metrology experiments based on atomic ensembles, an efficient light-atom interaction is required. Thus, there is a particular interest in generating narrow-band squeezed light that is on atomic resonance. This will make it possible not only to enhance the sensitivity of atomic based sensors, but also to deterministically entangle two distant atomic ensembles. We generate bright two-mode squeezed states of light, or twin beams, with a non-degenerate four-wave mixing (FWM) process in hot $^{85}$Rb in a double-lambda configuration. Given the proximity of the energy levels in the D1 line of $^{85}$Rb and $^{87}$Rb, we are able to operate the FWM in $^{85}$Rb in a regime that generates two-mode squeezed states in which both modes are simultaneously on resonance with transitions in the D1 line of $^{87}$Rb, one mode with the $F=2$ to $F'=2$ transition and the other one with the $F=1$ to $F'=1$ transition. For this configuration, we obtain an intensity difference squeezing level of $-3.5$ dB. Moreover, the intensity difference squeezing increases to $-5.4$ dB and $-5.0$ dB when only one of the modes of the squeezed state is resonant with the D1 $F=2$ to $F'=2$ or $F=1$ to $F'=1$ transition of $^{87}$Rb, respectively

Infinite chain of N different deltas: a simple model for a Quantum Wire

We present the exact diagonalization of the Schrodinger operator corresponding to a periodic potential with N deltas of different couplings, for arbitrary N. This basic structure can repeat itself an infinite number of times. Calculations of band structure can be performed with a high degree of accuracy for an infinite chain and of the correspondent eigenlevels in the case of a random chain. The main physical motivation is to modelate quantum wire band structure and the calculation of the associated density of states. These quantities show the fundamental properties we expect for periodic structures although for low energy the band gaps follow unpredictable patterns. In the case of random chains we find Anderson localization; we analize also the role of the eigenstates in the localization patterns and find clear signals of fractality in the conductance. In spite of the simplicity of the model many of the salient features expected in a quantum wire are well reproduced.Comment: 28 pages, LaTeX, 13 eps figures (3 color

Screening of point charges in Si quantum dots

The screening of point charges in hydrogenated Si quantum dots ranging in diameter from 10 A to 26 A has been studied using first-principles density-functional methods. We find that the main contribution to the screening function originates from the electrostatic field set up by the polarization charges at the surface of the nanocrystals. This contribution is well described by a classical electrostatics model of dielectric screening

Rejoinder to "Support Vector Machines with Applications"

Rejoinder to ``Support Vector Machines with Applications'' [math.ST/0612817]Comment: Published at http://dx.doi.org/10.1214/088342306000000501 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Simple model for a Quantum Wire II. Correlations

In a previous paper (Eur. Phys. J. B 30, 239-251 (2002)) we have presented the main features and properties of a simple model which -in spite of its simplicity- describes quite accurately the qualitative behaviour of a quantum wire. The model was composed of N distinct deltas each one carrying a different coupling. We were able to diagonalize the Hamiltonian in the periodic case and yield a complete and analytic description of the subsequent band structure. Furthermore the random case was also analyzed and we were able to describe Anderson localization and fractal structure of the conductance. In the present paper we go one step further and show how to introduce correlations among the sites of the wire. The presence of a correlated disorder manifests itself by altering the distribution of states and the localization of the electrons within the systemComment: RevTex, 7 pages, 9 figures (3 greyscale, 6 coloured