Bose–Einstein condensation in random potentials

We present a rigorous study of the perfect Bose-gas in the presence of a homogeneous ergodic random potential. It is demonstrated that the Lifshitz tail behaviour of the one-particle spectrum reduces the critical dimensionality of the (generalized) Bose–Einstein Condensation (BEC) to d=1. To tackle the Off-Diagonal Long-Range Order (ODLRO) we introduce the space average one-body reduced density matrix. For a one-dimensional Poisson-type random potential we prove that randomness enhances the exponential decay of this matrix in domain free of the BEC. To cite this article: O. Lenoble et al., C. R. Physique 5 (2004).     

Bose–Einstein condensation and superfluidity in trapped atomic gases

Bose–Einstein condensates confined in traps exhibit unique features which have been the object of extensive experimental and theoretical studies in the last few years. In this paper I will discuss some issues concerning the behaviour of the order parameter and the dynamic and superfluid effects exhibited by such systems.     

Quantum degeneracy and Bose–Einstein condensation in low-dimensional trapped gases

At present, there are significant efforts to create 2D or 1D trapped gases by (tightly) confining the particle motion to zero point oscillations in one or two directions. The goal of this article is to show that the reduction of the spatial dimensionality in trapped Bose gases drastically changes the nature of the Bose-condensed state. In 2D and 1D gases, one can get a peculiar Bose-condensed state (quasicondensate) where the density fluctuations are suppressed, but the phase still fluctuates. The quasicondensate has the same density profile and local correlation properties as true condensates. However, it is very different with regard to phase coherence properties. We discuss how the phase coherence can be studied in experiments with 2D and 1D trapped gases.     

Bose–Einstein condensation of atomic hydrogen

The recent creation of a Bose–Einstein condensate of atomic hydrogen has added a new system to this exciting field. The differences between hydrogen and the alkali metal atoms require other techniques for the initial trapping and cooling of the atoms and the subsequent detection of the condensate. The use of a cryogenic loading technique results in a larger number of trapped atoms. Spectroscopic detection is well suited to measuring the temperature and density of the sample in situ. The transition was observed at a temperature of 50 μK and a density of 2×10¹⁴ cm^-3. The number of condensed atoms is about 10⁹ at a condensate fraction of a few percent. A peak condensate density of 4.8×10¹⁵ cm^-3 has been observed. Received: 22 June 1999 / Published online: 3 November 1999     

Bose–Einstein condensation of magnons in ferromagnetic thin films

Experimental evidence for Bose–Einstein condensation (BEC) of magnons at room temperature in a thin film of yttrium iron garnet (YIG) excited by parallel pumping is already available and different features of the experimental results have been explained qualitatively [Nature 443, 430 (2006)]. In the present work, we explain quantitatively different aspects of this experimental observation through spin wave treatment. In the case of parallel pumping field, we have developed a formula for the time required for the formation of magnon BEC in a thin film of ferromagnetic material. This relation is found to be in good agreement with known experimental results. In a similar treatment we predict the condition for the formation of BEC of magnons in the case of perpendicular pumping.     

Bose–Einstein condensation of a relativistic Bose gas in a harmonic potential

Using semiclassical method, Bose–Einstein condensation (BEC) of a relativistic ideal Bose gas (RIBG) with and without antibosons in the three-dimensional (3D) harmonic potential is investigated. Analytical expressions for the BEC transition temperature, condensate fraction, specific heat and entropy of the system are obtained. Relativistic effects on the properties of the system are discussed and it is found that the relativistic effect decreases the transition temperature T_c but enlarges the gap of specific heat at T_c. We also study the influence of antibosons on a RIBG. Comparing with the system without antibosons, the system with antibosons has a higher transition temperature and a lower Helmholtz free energy. It implies that the system with antibosons is more stable.     

On Bose–Einstein condensation in Josephson junctions star graph arrays

We report on the evidence of anomalous currents in graph-shaped arrays of Josephson junctions along peculiar branches of the networks. The specific case of a star-shaped array is considered and the evidence of the anomalies is achieved by comparing the current-voltage characteristics of the arrays embedded in the star structure with those of “reference” arrays which are fabricated by-side the network structure and are dc-isolated from these. The experimental data are consistent with the results of a theoretical model predicting gradients of the populations of Cooper pairs on the islands situated in proximity of the central superconductive island as a result of a Bose–Einstein condensation process.     

Photon condensation: A new paradigm for Bose–Einstein condensation

Bose–Einstein condensation is a state of matter known to be responsible for peculiar properties exhibited by superfluid Helium-4 and superconductors. Bose–Einstein condensate (BEC) in its pure form is realizable with alkali atoms under ultra-cold temperatures. In this paper, we review the experimental scheme that demonstrates the atomic Bose–Einstein condensate. We also elaborate on the theoretical framework for atomic Bose–Einstein condensation, which includes statistical mechanics and the Gross–Pitaevskii equation. As an extension, we discuss Bose–Einstein condensation of photons realized in a fluorescent dye filled optical microcavity. We analyze this phenomenon based on the generalized Planck’s law in statistical mechanics. Further, a comparison is made between photon condensate and laser. We describe how photon condensate may be a possible alternative for lasers since it does not require an energy consuming population inversion process.     

Generalized Beth–Uhlenbeck approach to mesons and diquarks in hot,dense quark matter

An important first step in the program of hadronization of chiral quark models is the bosonization in meson and diquark channels. This procedure is presented at finite temperatures and chemical potentials for the SU(2) flavor case of the NJL model with special emphasis on the mixing between scalar meson and scalar diquark modes which occurs in the 2SC color superconducting phase. The thermodynamic potential is obtained in the Gaussian approximation for the meson and diquark fields and it is given in the Beth–Uhlenbeck form. This allows a detailed discussion of bound state dissociation in hot, dense matter (Mott effect) in terms of the in-medium scattering phase shift of two-particle correlations. It is shown for the case without meson–diquark mixing that the phase shift can be separated into a continuum and a resonance part. In the latter, the Mott transition manifests itself by a change of the phase shift at threshold by π$\pi$ in accordance with Levinson’s theorem, when a bound state transforms to a resonance in the scattering continuum. The consequences for the contribution of pionic correlations to the pressure are discussed by evaluating the Beth–Uhlenbeck equation of state in different approximations. A similar discussion is performed for the scalar diquark channel in the normal phase. Further developments and applications of the developed approach are outlined.     

Bose–Einstein condensation in the three-sphere and in the infinite slab: Analytical results

We study the finite size effects on Bose–Einstein condensation (BEC) of an ideal non-relativistic Bose gas in the three-sphere (spatial section of the Einstein universe) and in a partially finite box which is infinite in two of the spatial directions (infinite slab). Using the framework of grand-canonical statistics, we consider the number of particles, the condensate fraction and the specific heat. After obtaining asymptotic expansions for large system size, which are valid throughout the BEC regime, we describe analytically how the thermodynamic limit behaviour is approached. In particular, in the critical region of the BEC transition, we express the chemical potential and the specific heat as simple explicit functions of the temperature, highlighting the effects of finite size. These effects are seen to be different for the two different geometries. We also consider the Bose gas in a one-dimensional box, a system which does not possess BEC in the sense of a phase transition even in the infinite volume limit.     

Domain walls and their interactions in a two-component Bose–Einstein condensate

We investigate domain wall excitations in a two-component Bose–Einstein condensate with two-body interactions and pair-transition effects. It is shown that domain wall excitations can be described exactly by kink and anti-kink excitations in each component. The domain wall solutions are given analytically, which exist with different conditions compared with the domain wall reported before. Bubble-droplet structure can be also obtained from the fundamental domain wall, and their interactions are investigated analytically. Especially, domain wall interactions demonstrate some striking particle transition dynamics. These striking transition effects make the domain wall admit quite different collision behavior, in contrast to the collision between solitons or other nonlinear waves. The collisions between kinks induce some phase shift, which makes the domain wall change greatly. Their collisions can be elastic or inelastic with proper combination of fundamental domain walls. These characters can be used to manipulate one domain wall by interacting with other ones.     

Vacuum quark condensate,chiral Lagrangian,and Bose–Einstein statistics

In a series of articles it was recently claimed that the quantum chromodynamic (QCD) condensates are not the properties of the vacuum but of the hadrons and are confined inside them. We point out that this claim is incompatible with the chiral Lagrangian and Bose–Einstein statistics of the Goldstone bosons (pions) in chiral limit and conclude that the quark condensate must be the property of the QCD vacuum.     

Investigation of classical and fractional Bose–Einstein condensation for harmonic potential

In this study, classical and fractional Gross–Pitaevskii (GP) equations were solved for harmonic potential and repulsive interactions between the boson particles using the Homotopy Perturbation Method (HPM) to investigate the ground state dynamics of Bose–Einstein Condensation (BEC). The purpose of writing fractional GP equations is to consider the system in a more realistic manner. The memory effects of non-Markovian processes involving long-range interactions between bosons with the restriction of the ergodic hypothesis and the effect of non-Gaussian distributions of bosons in the condensation can be taken into account with time fractional and space fractional GP equations, respectively. The obtained results of the fractional GP equations differ from the results of the classical one. While the Gauss distribution describing the homogeneous, reversible and unitary system is obtained from the classical GP equation, the probability density of the solution function of fractional GP equations is non-conserved. This situation describes the inhomogeneous, irreversible and non-unitary systems.     

Modulational instability and moving gap soliton in Bose–Einstein condensation with Feshbach resonance management

We investigate the modulational instability of symmetric and asymmetric continuous wave solutions in Bose–Einstein condensates in optical lattices with Feshbach resonance managed atomic scattering length. The model is based on a pair of averaged coupled mode Gross–Pitaevskii equations. We analyze the characteristics of the modulational instability in the form of typical dependence of the instability growth rate on the perturbation wavenumber and system’s parameters. We have numerically solved the coupled mode equations by using the split step Fourier method. Convincing agreement has been obtained between analytical and numerical results. Furthermore, the moving and stationary gap solitons in the first spectral gap of the optical lattices for the same amplitude but different phases in the presence and absence of the mean atomic scattering length under the Feshbach resonance management are also constructed.     

Landau damping in a dipolar Bose–Fermi mixture in the Bose–Einstein condensation(BEC) limit

By using a mean-field approximation which describes the coupled oscillations of condensate and noncondensate atoms in the collisionless regime, Landau damping in a dilute dipolar Bose–Fermi mixture in the BEC limit where Fermi superfluid is treated as tightly bounded molecules, is investigated. In the case of a uniform quasi-two-dimensional(2D)case, the results for the Landau damping due to the Bose–Fermi interaction are obtained at low and high temperatures. It is shown that at low temperatures, the Landau damping rate is exponentially suppressed. By increasing the strength of dipolar interaction, and the energy of boson quasiparticles, Landau damping is suppressed over a broader temperature range.     

Bose–Einstein condensation versus Dicke–Hepp–Lieb transition in an optical cavity

We provide an exact solution for the interplay between Bose–Einstein condensation and the Dicke–Hepp–Lieb self-organization transition of an ideal Bose gas trapped inside a single-mode optical cavity and subject to a transverse laser drive. Based on an effective action approach, we determine the full phase diagram at arbitrary temperature, which features a bi-critical point where the transitions cross. We calculate the dynamically generated band structure of the atoms and the associated suppression of the critical temperature for Bose–Einstein condensation in the phase with a spontaneous periodic density modulation. Moreover, we determine the evolution of the polariton spectrum due to the coupling of the cavity photons and the atomic field near the self-organization transition, which is quite different above or below the Bose–Einstein condensation temperature. At low temperatures, the critical value of the Dicke–Hepp–Lieb transition decreases with temperature and thus thermal fluctuations can enhance the tendency to a periodic arrangement of the atoms.     

Non-autonomous bright matter wave solitons in spinor Bose–Einstein condensates

We investigate the dynamics of bright matter wave solitons in spin-1 Bose–Einstein condensates with time modulated nonlinearities. We obtain soliton solutions of an integrable autonomous three-coupled Gross–Pitaevskii (3-GP) equations using Hirota?s method involving a non-standard bilinearization. The similarity transformations are developed to construct the soliton solutions of non-autonomous 3-GP system. The non-autonomous solitons admit different density profiles. An interesting phenomenon of soliton compression is identified for kink-like nonlinearity coefficient with Hermite–Gaussian-like potential strength. Our study shows that these non-autonomous solitons undergo non-trivial collisions involving condensate switching.     

Bose–Einstein condensates in concentrically coupled annular traps with spin–orbit coupling and rotation

We investigate Bose–Einstein condensates in concentrically coupled annular traps with spin–orbit coupling and rotation. The ground state wave functions are computed by minimizing the Gross–Pitaevskii energy functional, and the combined effects of system?s parameters, especially the spin–orbit coupling and rotating, are investigated. The results show that for a finite fixed spin–orbit coupling, with increasing the angular frequency of rotation, the system is always in phase coexistence. Moreover, phase transitions between different ground state phases can be induced not only by spin–orbit coupling, but also rotation, which resembles very much the one where the s-wave interactions are varied.