Validity of the Hohenberg Theorem for a Generalized Bose-Einstein Condensation in Two Dimensions

Several authors have considered the possibility of a generalized Bose-Einstein condensation (BEC) in which a band of low states is occupied so that the total occupation number is macroscopic, even if the occupation number of each state is not extensive. The Hohenberg theorem (HT) states that there is no BEC into a single state in 2D; we consider its validity for the case of a generalized condensation and find that, under certain conditions, the HT does not forbid a BEC in 2D. We discuss whether this situation actually occurs in any theoretical model system.Comment: 6 pages, Latex, JLTP class, accepted by Jour. Low Temp. Phys., Quantum Fluids and Solids Conference QFS200

Ursell operators in statistical physics of dense systems: the role of high order operators and of exchange cycles

The purpose of this article is to discuss cluster expansions in dense quantum systems as well as their interconnection with exchange cycles. We show in general how the Ursell operators of order 3 or more contribute to an exponential which corresponds to a mean-field energy involving the second operator U2, instead of the potential itself as usual. In a first part, we consider classical statistical mechanics and recall the relation between the reducible part of the classical cluster integrals and the mean-field; we introduce an alternative method to obtain the linear density contribution to the mean-field, which is based on the notion of tree-diagrams and provides a preview of the subsequent quantum calculations. We then proceed to study quantum particles with Boltzmann statistics (distinguishable particles) and show that each Ursell operator Un with n greater or equal to 3 contains a ``tree-reducible part'', which groups naturally with U2 through a linear chain of binary interactions; this part contributes to the associated mean-field experienced by particles in the fluid. The irreducible part, on the other hand, corresponds to the effects associated with three (or more) particles interacting all together at the same time. We then show that the same algebra holds in the case of Fermi or Bose particles, and discuss physically the role of the exchange cycles, combined with interactions. Bose condensed systems are not considered at this stage. The similarities and differences between Boltzmann and quantum statistics are illustrated by this approach, in contrast with field theoretical or Green's functions methods, which do not allow a separate study of the role of quantum statistics and dynamics.Comment: 31 pages, 7 figure

Large amplitude spin waves in ultra-cold gases

We discuss the theory of spin waves in non-degenerate ultra-cold gases, and compare various methods which can be used to obtain appropriate kinetic equations. We then study non-hydrodynamic situations, where the amplitude of spin waves is sufficiently large to bring the system far from local equilibrium. In the first part of the article, we compare two general methods which can be used to derive a kinetic equation for a dilute gas of atoms (bosons or fermions) with two internal states (treated as a pseudo-spin 1/2). The collisional methods are in the spirit of Boltzmann's original derivation of his kinetic equation where, at each point of space, the effects of all sorts of possible binary collisions are added. We discuss two different versions of collisional methods, the Yvon-Snider approach and the S matrix approach. The second method uses the notion of mean field, which modifies the drift term of the kinetic equation, in the line of the Landau theory of transport in quantum liquids. For a dilute cold gas, it turns out that all these derivations lead to the same drift terms in the transport equation, but differ in the precise expression of the collision integral and in higher order gradient terms. In the second part of the article, the kinetic equation is applied to spin waves in trapped ultra-cold gases. Numerical simulations are used to illustrate the strongly non-hydrodynamic character of the spin waves recently observed with trapped Rb87 atoms. The decay of the phenomenon, which takes place when the system relaxes back towards equilibrium, is also discussed, with a short comment on decoherence.Comment: To appear in Eur. Phys. J.

Evolution of additional (hidden) quantum variables in the interference of Bose-Einstein condensates

Additional variables (also often called “hidden variables”) are sometimes added to standard quantum mechanics in order to remove its indeterminism or “incompleteness” and to make the measurement process look more classical. Here we discuss a case in which an additional variable arises almost spontaneously from the quantum formalism: the emergence of a relative phase between two highly populated Fock-state Bose-Einstein condensates. The model simulated here involves the interference of two Bose condensates, one with all up spins and the other with down spins, along a z axis. With the clouds overlapping, we consider the results of measuring spins in a transverse plane (the general direction is studied in an appendix). The determination of the previously “hidden” phase becomes progressively more definite as additional measurements are made. We also provide an analysis of a recent and closely related experiment

Conditionnal squeezing of an atomic alignement

We investigate the possibility to perform a Quantum Non Demolition measurement of the collective alignment of an atomic ensemble in the case of a $F\geq 1$ spin. We compare the case of purely vectorial and purely tensorial Hamiltonians and show how to achieve conditional squeezing or entanglement of atomic alignment components.Comment: 7 pages, 2 figure

Bose-Einstein transition temperature in a dilute repulsive gas

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 adde

Photons uncertainty solves Einstein-Podolsky-Rosen paradox

Einstein, Podolsky and Rosen (EPR) pointed out that the quantum-mechanical description of "physical reality" implied an unphysical, instantaneous action between distant measurements. To avoid such an action at a distance, EPR concluded that Quantum Mechanics had to be incomplete. However, its extensions involving additional "hidden variables", allowing for the recovery of determinism and locality, have been disproved experimentally (Bell's theorem). Here, I present an opposite solution of the paradox based on the greater indeterminism of the modern Quantum Field Theory (QFT) description of Particle Physics, that prevents the preparation of any state having a definite number of particles. The resulting uncertainty in photons radiation has interesting consequences in Quantum Information Theory (e.g. cryptography and teleportation). Moreover, since it allows for less elements of EPR physical reality than the old non-relativistic Quantum Mechanics, QFT satisfies the EPR condition of completeness without the need of hidden variables. The residual physical reality does never violate locality, thus the unique objective proof of "quantum nonlocality" is removed in an interpretation-independent way. On the other hand, the supposed nonlocality of the EPR correlations turns out to be a problem of the interpretation of the theory. If we do not rely on hidden variables or new physics beyond QFT, the unique viable interpretation is a minimal statistical one, that preserves locality and Lorentz symmetry.Comment: Published version, with updated referenc