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We revisit an argument proposed by Hardy concerning local realistic theories, but in terms of probability currents in standard quantum mechanics and of the trajectories obtained from its flux lines. We emphasize surprising properties of the trajectories in configuration space, in particular their (quasi) discontinuous variations when the context (the experimental setup) is changed. This occurs in both Galilean and Einsteinian relativity. In the latter case, discontinuous variations also appear without changing the setup, when the Lorentzian reference frame is changed., Comment: 10 pages 4 figures

We discuss a model of spontaneous collapse of the quantum state that does not require adding any stochastic processes to the standard dynamics. The additional ingredient with respect to the wave function is a position in the configuration space, which drives the collapse in a completely deterministic way. This new variable is equivalent to a set of positions of all the particles, i.e. a set of Bohmian positions, which obey the usual guiding equation of Bohmian theory. Any superposition of quantum states of a macroscopic object occupying different regions of space is projected by a localization process onto the region occupied by the positions. Since the Bohmian positions are well defined in a single realization of the experiment, a space localization into one region is produced. The mechanism is based on the correlations between these positions arising from the cohesive forces inside macroscopic objects. The model introduces two collapse parameters, which play a very similar role to those of the GRW and CSL theories. With appropriate values of these parameters, we check that the corresponding dynamics rapidly projects superpositions of macroscopic states localized in different regions of space into a single region, while is keeps a negligible effect in all situations where the predictions of standard quantum dynamics are known to be correct. The possible relations with gravity are briefly speculated. We then study the evolution of the density operator and a mean-field approximation of the dynamical equations of this model, as well as the change of the evolution of the momentum introduced by the localization process. Possible theoretical interpretations are finally discussed. Generally speaking, this model introduces a sharper border between the quantum and classical world than the GRW and CSL theories, and leaves a broader range of acceptable values for the parameters., Comment: 21 pages, 45 refs

The linear Schr\"{o}dinger equation does not predict that macroscopic bodies should be located at one place only. Quantum mechanics textbooks generally solve the problem by introducing the projection postulate, which forces definite values to emerge during position measurements; many other interpretations have also been proposed.\ Here, in the same spirit as the GRW and CSL theories, we modify the Schr\"{o}dinger equation in a way that efficiently cancels macroscopic density fluctuations in space.\ Instead of introducing the stochastic dynamics of GRW or CSL, we assume a deterministic dynamics that includes an attraction term towards the density in space of the de Broglie-Bohm position of particles. This automatically ensures macroscopic uniqueness, so that the state vector can be considered as a direct representation of physical reality., Comment: 14 pages, no figure. This is the version accepted by the European Physical Journal, with a few additions in the text and a few more references. A typo has been corrected in Eq (4)

{The Continuous Spontaneous Localization (CSL) theory alters the Schr\"odinger equation. It describes wave function collapse as a dynamical process instead of an ill-defined postulate, thereby providing macroscopic uniqueness and solving the so-called measurement problem of standard quantum theory. CSL contains a parameter $\lambda$ giving the collapse rate of an isolated nucleon in a superposition of two spatially separated states and, more generally, characterizing the collapse time for any physical situation. CSL is experimentally testable, since it predicts some behavior different from that predicted by standard quantum theory. One example is the narrowing of wave functions, which results in energy imparted to particles. Here we consider energy given to trapped ultra-cold atoms. Since these are the coldest samples under experimental investigation, it is worth inquiring how they are affected by the CSL heating mechanism. We examine the CSL heating of a BEC in contact with its thermal cloud. Of course, other mechanisms also provide heat and also particle loss. From varied data on optically trapped cesium BEC's, we present an energy audit for known heating and loss mechanisms. The result provides an upper limit on CSL heating and thereby an upper limit on the parameter $\lambda$. We obtain $\lambda\lesssim 1(\pm1)\times 10^{-7}$sec$^{-1}$.}, Comment: 36 pages; 5 figures, 3 tables

The tone hole geometry of a clarinet is optimized numerically. The instrument is modeled as a network of one dimensional transmission line elements. For each (non-fork) fingering, we first calculate the resonance frequencies of the input impedance peaks, and compare them with the frequencies of a mathematically even chromatic scale (equal temperament). A least square algorithm is then used to minimize the differences and to derive the geometry of the instrument. Various situations are studied, with and without dedicated register hole and/or enlargement of the bore. With a dedicated register hole, the differences can remain less than 10 musical cents throughout the whole usual range of a clarinet. The positions, diameters and lengths of the chimneys vary regularly over the whole length of the instrument, in contrast with usual clarinets. Nevertheless, we recover one usual feature of instruments, namely that gradually larger tone holes occur when the distance to the reed increases. A fully chromatic prototype instrument has been built to check these calculations, and tested experimentally with an artificial blowing machine, providing good agreement with the numerical predictions.

A set of 55 clarinet reeds is observed by holography, collecting 2 series of measurements made under 2 different moisture contents, from which the resonance frequencies of the 15 first modes are deduced. A statistical analysis of the results reveals good correlations, but also significant differences between both series. Within a given series, flexural modes are not strongly correlated. A Principal Component Analysis (PCA) shows that the measurements of each series can be described with 3 factors capturing more than $90\%$ of the variance: the first is linked with transverse modes, the second with flexural modes of high order and the third with the first flexural mode. A forth factor is necessary to take into account the individual sensitivity to moisture content. Numerical 3D simulations are conducted by Finite Element Method, based on a given reed shape and an orthotropic model. A sensitivity analysis revels that, besides the density, the theoretical frequencies depend mainly on 2 parameters: $E_L$ and $G_{LT}$. An approximate analytical formula is proposed to calculate the resonance frequencies as a function of these 2 parameters. The discrepancy between the observed frequencies and those calculated with the analytical formula suggests that the elastic moduli of the measured reeds are frequency dependent. A viscoelastic model is then developed, whose parameters are computed as a linear combination from 4 orthogonal components, using a standard least squares fitting procedure and leading to an objective characterization of the material properties of the cane \textit{Arundo donax}.

In the measurement of the amplitude of vibration of objects, holographic imaging techniques usually involve fringe counting; due to the limited resolution of images, measurements of large amplitudes are not accessible. We demonstrate a technique that suppresses the necessity of fringe counting: frequency sideband imaging, where the order of the sideband is considered as a marker of the amplitude. The measurement is completely local: no comparison with another reference point on the object is necessary. It involves a sharp variation of a signal, which makes it robust against perturbations. The method is demonstrated in an experiment made with a vibrating clarinet reed; phase modulations as large as 1000 radians have been measured.

We perform Ramsey spectroscopy on the ground state of ultra-cold 87Rb atoms magnetically trapped on a chip in the Knudsen regime. Field inhomogeneities over the sample should limit the 1/e contrast decay time to about 3 s, while decay times of 58 s are actually observed. We explain this surprising result by a spin self-rephasing mechanism induced by the identical spin rotation effect originating from particle indistinguishability. We propose a theory of this synchronization mechanism and obtain good agreement with the experimental observations. The effect is general and susceptible to appear in other physical systems., Comment: Revised version; improved description of the theoretical treatment

The dynamical equations of clarinet-like systems are known to be reducible to a non-linear iterated map within reasonable approximations. This leads to time oscillations that are represented by square signals, analogous to the Raman regime for string instruments. In this article, we study in more detail the properties of the corresponding non-linear iterations, with emphasis on the geometrical constructions that can be used to classify the various solutions (for instance with or without reed beating) as well as on the periodicity windows that occur within the chaotic region. In particular, we find a regime where period tripling occurs and examine the conditions for intermittency. We also show that, while the direct observation of the iteration function does not reveal much on the oscillation regime of the instrument, the graph of the high order iterates directly gives visible information on the oscillation regime (characterization of the number of period doubligs, chaotic behaviour, etc.).

When independent Bose-Einstein condensates (BEC), described quantum mechanically by Fock (number) states, are sent into interferometers, the measurement of the output port at which the particles are detected provides a binary measurement, with two possible results $\pm1$. With two interferometers and two BEC's, the parity (product of all results obtained at each interferometer) has all the features of an Einstein-Podolsky-Rosen quantity, with perfect correlations predicted by quantum mechanics when the settings (phase shifts of the interferometers) are the same. When they are different, significant violations of Bell inequalities are obtained. These violations do not tend to zero when the number $N$ of particles increases, and can therefore be obtained with arbitrarily large systems, but a condition is that all particles should be detected. We discuss the general experimental requirements for observing such effects, the necessary detection of all particles in correlation, the role of the pixels of the CCD detectors, and that of the alignments of the interferometers in terms of matching of the wave fronts of the sources in the detection regions. Another scheme involving three interferometers and three BEC's is discussed; it leads to Greenberger Horne Zeilinger (GHZ) sign contradictions, as in the usual GHZ case with three particles, but for an arbitrarily large number of them. Finally, generalizations of the Hardy impossibilities to an arbitrarily large number of particles are introduced. BEC's provide a large versality for observing violations of local realism in a variety of experimental arrangements., Comment: appendix added

We obtain quantitative measurements of the oscillation amplitude of vibrating objects by using sideband digital holography. The frequency sidebands on the light scattered by the object, shifted by n times the vibration frequency, are selectively detected by heterodyne holography, and images of the object are calculated for different orders n. Orders up to n=120 have been observed, allowing the measurement of amplitudes of oscillation that are significantly larger than the optical wavelength. Using the positions of the zeros of intensity for each value of n, we reconstruct the shape of vibration the object., Comment: 6 pages

Quantum systems in Fock states do not have a phase. When two or more Bose-Einstein condensates are sent into interferometers, they nevertheless acquire a relative phase under the effect of quantum measurements. The usual explanation relies on spontaneous symmetry breaking, where phases are ascribed to all condensates and treated as unknown classical quantities. However, this image is not always sufficient: when all particles are measured, quantum mechanics predicts probabilities that are sometimes in contradiction with it, as illustrated by quantum violations of local realism. In this letter, we show that interferometers can be used to demonstrate a large variety of violations with an arbitrarily large number of particles. With two independent condensates, we find violations of the BCHSH inequalities, as well as new N-body Hardy impossibilities. With three condensates, we obtain new GHZ (Greenberger, Horne and Zeilinger) type contradictions., Comment: version published in Phys Rev

We discuss the properties of two Bose-Einstein condensates in different spin states, represented quantum mechanically by a double Fock state. Individual measurements of the spins of the particles are performed in transverse directions (perpendicular to the spin quantization axis), giving access to the relative phase of the two macroscopically occupied states. Before the first spin measurement, the phase is completely undetermined; after a few measurements, a more and more precise knowledge of its value emerges under the effect of the quantum measurement process. This naturally leads to the usual notion of a quasi-classical phase (Anderson phase) and to an interesting transposition of the EPR (Einstein-Podolsky-Rosen) argument to macroscopic physical quantities. The purpose of this article is to discuss this transposition, as well as situations where the notion of a quasi-classical phase is no longer sufficient to account for the quantum results, and where significant violations of Bell type inequalities are predicted., Comment: a few misprints corrected, a reference added. This is the published version

We study theoretically the properties of two Bose-Einstein condensates in different spin states, represented by a double Fock state. Individual measurements of the spins of the particles are performed in transverse directions, giving access to the relative phase of the condensates. Initially, this phase is completely undefined, and the first measurements provide random results. But a fixed value of this phase rapidly emerges under the effect of the successive quantum measurements, giving rise to a quasi-classical situation where all spins have parallel transverse orientations. If the number of measurements reaches its maximum (the number of particles), quantum effects show up again, giving rise to violations of Bell type inequalities. The violation of BCHSH inequalities with an arbitrarily large number of spins may be comparable (or even equal) to that obtained with two spins., Comment: version published, with a shorter abstract to fit into the 9 lines of PRL, one more reference, and minor changes

The EPR argument points to the existence of additional variables that are necessary to complete standard quantum theory. It was dismissed by Bohr because it attributes physical reality to isolated microscopic systems, independently of the macroscopic measurement apparatus. Here, we transpose the EPR argument to macroscopic systems, assuming that they are in spatially extended Fock spin states and subject to spin measurements in remote regions of space. Bohr's refutation of the EPR argument does not seem to apply in this case, since the difference of scale between the microscopic measured system and the macroscopic measuring apparatus can no longer be invoked., Comment: contribution to the workshop "Beyond que quantum", at the Lorentz Institute (Leiden, Netherlands) in may 2006

We derive the scaling structure of the Kosterlitz-Thouless-Berezinskii (KTB) transition temperature of a homogeneous Bose gas in two dimensions within diagrammatic perturbation theory. Approaching the system from above the transition, we calculate the critical temperature, $T_{KT}$, and show how the superfluid mass density emerges from Josephson's relation as an interplay between the condensate density in a finite size system, and the infrared structure of the single particle Green's function. We then discuss the trapped two-dimensional Bose gas, where the interaction changes the transition qualitatively from Bose-Einstein in an ideal gas to a KTB transition in the thermodynamic limit. We show that the transition temperature lies below the ideal Bose-Einstein transition temperature, and calculate the first correction in terms of the interparticle interactions. The jump of the total superfluid mass at the transition is suppressed in a trapped system., Comment: 7 pages

We propose to store non-classical states of light into the macroscopic collective nuclear spin ($10^{18}$ atoms) of a $^3$He vapor, using metastability exchange collisions. These collisions, commonly used to transfer orientation from the metastable state $2^{3}S\_1$ to the ground state state of $^3$He, can also transfer quantum correlations. This gives a possible experimental scheme to map a squeezed vacuum field state onto a nuclear spin state with very long storage times (hours)., Comment: 4 pages

We revisit the question of how a definite phase between Bose-Einstein condensates can spontaneously appear under the effect of measurements. We first consider a system that is the juxtaposition of two subsystems in Fock states with high populations, and assume that successive individual position measurements are performed. Initially, the relative phase is totally undefined, and no interference effect takes place in the first position measurement. But, while successive measurements are accumulated, the relative phase becomes better and better known, and a clear interference pattern emerges. It turns out that all observed results can be interpreted in terms of a pre-existing, but totally unknown, relative phase, which remains exactly constant during the experiment. We then generalize the results to more condensates. We also consider other initial quantum states than pure Fock states, and distinguish between intrinsic phase of a quantum state and phase induced by measurements. Finally, we examine the case of multiple condensates of spin states. We discuss a curious quantum effect, where the measurement of the spin angular momentum of a small number of particles can induce a big angular momentum in a much larger assembly of particles, even at an arbitrary distance. This spin observable can be macroscopic, assimilable to the pointer of a measurement apparatus, which illustrates the non-locality of quantum mechanics with particular clarity., Comment: a factor 1/2 added in equation (9); reference (30) completed, DOI added

We discuss certain specific features of the calculation of the critical temperature of a dilute repulsive Bose gas. Interactions modify the critical temperature in two different ways. First, for gases in traps, temperature shifts are introduced by a change of the density profile, arising itself from a modification of the equation of state of the gas (reduced compressibility); these shifts can be calculated simply within mean field theory. Second, even in the absence of a trapping potential (homogeneous gas in a box), temperature shifts are introduced by the interactions; they arise from the correlations introduced in the gas, and thus lie inherently beyond mean field theory - in fact, their evaluation requires more elaborate, non-perturbative, calculations. One illustration of this non-perturbative character is provided by the solution of self-consistent equations, which relate together non-linearly the various energy shifts of the single particle levels k. These equations predict that repulsive interactions shift the critical temperature (at constant density) by an amount which is positive, and simply proportional to the scattering length a; nevertheless, the numerical coefficient is difficult to compute. Physically, the increase of the temperature can be interpreted in terms of the reduced density fluctuations introduced by the repulsive interactions, which facilitate the propagation of large exchange cycles across the sample., Comment: two minor corrections, two refs added

Even if the tuning between the first and second register of a clarinet has been optimized by instrument makers, the lowest twelfths remain slightly too large (inharmonicity). In this article, we study the problem from two different points of view. First, we systematically review various physical reasons why this inharmonicity may take place, and the effect of different bore perturbations inserted in cylindrical instruments. Applications to a real clarinet resonator and comparisons with impedance measurements are then presented. A commonly accepted idea is that the register hole is the dominant cause for this inharmonicity: it is natural to expect that opening this hole will raise the resonance frequencies of the instrument, except for the note for which the hole is at the pressure node. We show that the real situation is actually more complicated because other effects, such as open holes or bore taper and bell, introduce resonance shifts that are comparable but with opposite sign, so that a relatively good overall compensation takes place. The origin of the observed inharmonicity in playing frequencies is therefore different. In a second part, we use an elementary model of the clarinet in order to isolate the effect of the register hole: a perfect cylindrical tube without closed holes. Optimization techniques are then used to calculate an optimum location for the register hole; the result turns out to be close to the location chosen by clarinet makers. Finally, attempts are made numerically to improve the situation by introducing small perturbations in the higher part of the cylindrical resonator, but no satisfactory improvement is obtained., Comment: 28 June 2004 (submitted to Applied Acoustics)

This article presents a general discussion of several aspects of our present understanding of quantum mechanics. The emphasis is put on the very special correlations that this theory makes possible: they are forbidden by very general arguments based on realism and local causality. In fact, these correlations are completely impossible in any circumstance, except the very special situations designed by physicists especially to observe these purely quantum effects. Another general point that is emphasized is the necessity for the theory to predict the emergence of a single result in a single realization of an experiment. For this purpose, orthodox quantum mechanics introduces a special postulate: the reduction of the state vector, which comes in addition to the Schrodinger evolution postulate. Nevertheless, the presence in parallel of two evolution processes of the same object (the state vector) maybe a potential source for conflicts; various attitudes that are possible to avoid this problem are discussed in this text. After a brief historical introduction, recalling how the very special status of the state vector has emerged in quantum mechanics, various conceptual difficulties are introduced and discussed. The Einstein Podolsky Rosen (EPR) theorem is presented with the help of a botanical parable, in a way that emphasizes how deeply the EPR reasoning is rooted into what is often called "scientific method''. In another section the GHZ argument, the Hardy impossibilities, as well as the BKS theorem are introduced in simple terms., Comment: texte soumis un an apres sa parution; quelques erreurs de detail corrigees

We study the effects of repulsive interactions on the critical density for the Bose-Einstein transition in a homogeneous dilute gas of bosons. First, we point out that the simple mean field approximation produces no change in the critical density, or critical temperature, and discuss the inadequacies of various contradictory results in the literature. Then, both within the frameworks of Ursell operators and of Green's functions, we derive self-consistent equations that include the dynamic correlations in the system and predict the change of the critical density. We argue that the dominant contribution to this change can be obtained within classical field theory and show that the lowest order correction introduced by interactions is linear in the scattering length, $a$, with a positive coefficient. Finally, we calculate this coefficient within various approximations, and compare with various recent numerical estimates., Comment: 25 pages, 6 figures, 2 ref. added, minor changes in introduction and conclusion, to appear in EJP B

We show that the shift in the transition temperature of the dilute homogeneous Bose gas is non-analytic in the scattering amplitude, $a$. The first correction beyond the positive linear shift in $a$ is negative and of order $a^2\ln a$. This non-universal non-analytic structure indicates how the discrepancies between numerical calculations at finite $a$ can be reconciled with calculations of the limit $a \to0$, since the linearity is apparent only for anomalously small $a$., Comment: 4 pages, 1 figure, to appear in Phys. Rev. Lett

The Bogoliubov transformation is generally derived in the context of identical bosons with the use of ``second quantized'' a and $a^{\dagger}$ operators (or, equivalently, in field theory). Here, we show that the transformation, together with its characteristic energy spectrum, can also be derived within the Hilbert space of distinguishable particles, obeying Boltzmann statistics; in this derivation, ordinary dyadic operators play the role usually played by the a and $a^{\dagger}$ operators; therefore, breaking the symmetry of particle conservation is not necessary.

We show that the critical temperature of a uniform dilute Bose gas must increase linearly with the s-wave scattering length describing the repulsion between the particles. Because of infrared divergences, the magnitude of the shift cannot be obtained from perturbation theory, even in the weak coupling regime; rather, it is proportional to the size of the critical region in momentum space. By means of a self-consistent calculation of the quasiparticle spectrum at low momenta at the transition, we find an estimate of the effect in reasonable agreement with numerical simulations., Comment: 4 pages, Revtex, to be published in Physical Review Letters

We determine the critical temperature of a 3-d homogeneous system of hard-sphere Bosons by path-integral Monte Carlo simulations and finite-size scaling. At low densities, we find that the critical temperature is increased by the repulsive interactions, in the form of a power law in density with exponent 1/3: $\Delta T_C/T_0\sim (na^3)^{1/3}$. At high densities the result for liquid helium, namely a lower critical temperature than in the non-interacting case, is recovered. We give a microscopic explanation for the observed behavior., Comment: 4 pages, 4 figures;; replacement with minor corrections: p.1 (after Eq.1), p.2 (after Eq. 4), x-axis label in Fig. 2