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).     

Bound diquarks and their Bose–Einstein condensation in strongly coupled quark matter

We explore the formation of diquark bound states and their Bose–Einstein condensation (BEC) in the phase diagram of three-flavor quark matter at nonzero temperature, T, and quark chemical potential, μ  . Using a quark model with a four-fermion interaction, we identify diquark excitations as poles of the microscopically computed diquark propagator. The quark masses are obtained by solving a dynamical equation for the chiral condensate and are found to determine the stability of the diquark excitations. The stability of diquark excitations is investigated in the T–μ$T\text{–}\mu$ plane for different values of the diquark coupling strength. We find that diquark bound states appear at small quark chemical potentials and at intermediate coupling strengths. Bose–Einstein condensation of non-strange diquark states occurs when the attractive interaction between quarks is sufficiently strong.     

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 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.     

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.     

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.     

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.     

Polaron in an electron–exciton structure under the conditions of the Bose–Einstein condensation

A polaron state of an electron in a hybrid system composed of a two-dimensional electron gas and a Bose–Einstein condensate of excitons situated in a quantum well coplanar with the electron gas has been investigated. It has been shown that self-localization is possible even at a weak coupling between the components of the structure, when a fluctuation of the density of excitons producing a potential well for the electron is small compared to their average density.     

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.     

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.     

Dark Lump Excitations in Bose—Einstein Condensates

We investigate the dynamics of two-dimensional matter-wave pulses in a Bose-Einstein condensate with diskshaped traps.For the case of repulsive atom-atom interactions,a Kadomtsev-Petviashvili equation with positive dipersion is derived using the method of multiple scales.The results show that it is possible to excite dark lump-like two-dimensional nonlinear excitations in the Bose-Einstein condensate.     

Theory of atomic–molecular conversion under the conditions of Bose–Einstein condensation

A set of nonlinear differential equations that describe the dynamics of atomic–molecular conversion under the action of two arbitrarily shaped Raman pulses of resonance laser radiation has been derived in the mean-field approximation. The dynamics of the system subjected to Gaussian pulses has been studied in detail. It has been shown that the time evolution of the system depends on the initial conditions.     

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 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.     

Primordial power spectrum from the Dapor–Liegener model of loop quantum cosmology

We compute the predictions for the power spectrum of scalar perturbations from a recent new proposal for the effective Hamiltonian of loop quantum cosmology. The model provides an attractive picture of the early cosmos, in which our classical Friedmann–Lemaître–Robertson–Walker universe emerges from a quantum phase where the spacetime curvature remains constant and of Planckian size. We compare the predictions for the cosmic microwave background with previous results obtained within loop quantum cosmology, and discuss the differences and similarities. The analysis provides an example of the way differences between quantization schemes can be translated to physical observables.     

Solitons in Bose–Einstein condensates

The Gross–Pitaevskii equation (GPE) describing the evolution of the Bose–Einstein condensate (BEC) order parameter for weakly interacting bosons supports dark solitons for repulsive interactions and bright solitons for attractive interactions. After a brief introduction to BEC and a general review of GPE solitons, we present our results on solitons that arise in the BEC of hard-core bosons, which is a system with strongly repulsive interactions. For a given background density, this system is found to support both a dark soliton and an antidark soliton (i.e., a bright soliton on a pedestal) for the density profile. When the background has more (less) holes than particles, the dark (antidark) soliton solution dies down as its velocity approaches the sound velocity of the system, while the antidark (dark) soliton persists all the way up to the sound velocity. This persistence is in contrast to the behaviour of the GPE dark soliton, which dies down at the Bogoliubov sound velocity. The energy–momentum dispersion relation for the solitons is shown to be similar to the exact quantum low-lying excitation spectrum found by Lieb for bosons with a delta-function interaction.     

Towards surface quantum optics with Bose–Einstein condensates in evanescent waves

We present a surface trap which enables the study of coherent interactions between ultracold atoms and evanescent waves. The trap combines a magnetic Joffe trap with a repulsive evanescent dipole potential. Exploiting the advantages of both approaches this technique improves recent surfaces traps, which are based either on magnetic or optical traps alone. On the one hand, the position of the magnetic trap can be controlled with high precision which makes it possible to move ultracold atoms to the surface of a glass prism or to withdraw the atoms from the surface in a controlled way. On the other hand, the optical potential of the evanescent wave partially compensates for strong attractive surface forces and generates a potential barrier at only a few hundred nanometers from the surface. This barrier prevents the surface potentials from limiting the trap depth of the magnetic trap. The surface trap is probed with ⁸⁷Rb Bose–Einstein condensates (BECs), which are stably positioned at distances from the surfaces below one micrometer.