Bose-Einstein Condensate Critical Temperature Research Articles

Coexistence of two kinds of superfluidity at finite temperatures in optical lattices

Bosonic lattice systems with extended interactions constitute a unique platform to study new phases of matter. This work presents an analysis of the Bose–Hubbard model with density-induced tunneling. The U(1) quantum rotor method in the path integral effective action formulation is used. This approach enables the discovery of a second kind of superfluidity in physical systems: pair superfluidity, thus adding to the phases of matter. It also sheds light on the properties of single-particle Bose–Einstein condensation (BEC) in optical lattice systems with higher inter-particle correlations. The derived effective phase Hamiltonian includes the residue of many-body correlations, providing information about phase transitions between the normal state and single-particle and pair superfluids at finite temperatures. The thermodynamical properties of the system are investigated. The impact of density-induced tunneling on single-particle BEC is also analyzed. The density-induced term supports single-particle coherence at high densities and low temperatures, improving the single BEC critical temperature. It is also responsible for dissipative effects, which are independent of the system’s thermal properties.

Bose-Einstein condensation of pions in proton–proton collisions at the Large Hadron Collider using non-extensive Tsallis statistics

The possibility of formation of Bose-Einstein Condensation (BEC) is studied in pp collisions at $$\sqrt{s} = 7$$ TeV at the Large Hadron Collider. A thermodynamically consistent non-extensive formulation of the identified hadron transverse momentum distributions is used to estimate the critical temperature required to form BEC of charged pions, which are the most abundant species in a multi-particle production process in hadronic and nuclear collisions. The obtained results have been contrasted with the systems produced in Pb-Pb collisions to have a better understanding. We observe an explicit dependency of BEC critical temperature and number of particles in the pion condensates on the non-extensive parameter q, which is a measure of degree of non-equilibrium – as q decreases, the critical temperature increases and approaches to the critical temperature obtained from Bose-Einstein statistics without non-extensivity. Studies are performed on the final state multiplicity dependence of number of particles in the pion condensates in a wide range of multiplicity covering hadronic and heavy-ion collisions, using the inputs from experimental transverse momentum spectra.

On the dynamics of finite temperature trapped Bose gases

The system that describes the dynamics of a Bose–Einstein Condensate (BEC) and the thermal cloud at finite temperature consists of a nonlinear Schrodinger (NLS) and a quantum Boltzmann (QB) equations. In such a system of trapped Bose gases at finite temperature, the QB equation corresponds to the evolution of the density distribution function of the thermal cloud and the NLS is the equation of the condensate. The quantum Boltzmann collision operator in this temperature regime is the sum of two operators C12 and C22, which describe collisions of the condensate and the non-condensate atoms and collisions between non-condensate atoms. Above the BEC critical temperature, the system is reduced to an equation containing only a collision operator similar to C22, which possesses a blow-up positive radial solution with respect to the L∞ norm (cf. [29]). On the other hand, at the very low temperature regime (only a portion of the transition temperature TBEC), the system can be simplified into an equation of C12, with a different (much higher order) transition probability, which has a unique global classical positive radial solution with weighted L1 norm (cf. [3]). In our model, we first decouple the QB, which contains C12+C22, and the NLS equations, then show a global existence and uniqueness result for classical positive radial solutions to the spatially homogeneous kinetic system. Different from the case considered in [29], due to the presence of the BEC, the collision integrals are associated to sophisticated energy manifolds rather than spheres, since the particle energy is approximated by the Bogoliubov dispersion law. Moreover, the mass of the full system is not conserved while it is conserved for the case considered in [29]. A new theory is then supplied.

Universal Behavior of the BEC Critical Temperature for a Multi-slab Ideal Bose Gas

For an ideal Bose-gas within a multi-slab periodic structure, we discuss the effect of the spatial distribution of the gas on its Bose-Einstein condensation critical temperature $T_c$, as well as on the origin of its dimensional crossover observed in the specific heat. The multi-slabs structure is generated by applying a Kronig-Penney potential to the gas in the perpendicular direction to the slabs of width $b$ and separated by a distance $a$, and allowing the particles to move freely in the other two directions. We found that $T_c$ decreases continuously as the potential barrier height increases, becoming inversely proportional to the square root of the barrier height when it is large enough. This behavior is {\it universal} as it is independent of the width and spacing of the barriers. The specific heat at constant volume shows a crossover from 3D to 2D when the height of the potential or the barrier width increase, in addition to the well known peak related to the Bose-Einstein condensation. These features are due to the trapping of the bosons by the potential barriers, and can be characterized by the energy difference between the energy bands below the potential height.

Finite-size effects on the Bose–Einstein condensation critical temperature in a harmonic trap

We obtain second and higher order corrections to the shift of the Bose–Einstein critical temperature due to finite-size effects. The confinement is that of a harmonic trap with general anisotropy. Numerical work shows the high accuracy of our expressions. We draw attention to a subtlety involved in the consideration of experimental values of the critical temperature in connection with analytical expressions for the finite-size corrections.

Towards a theory of superconductivity based on collective Cooper pairs

Superconductivity could be seen as a Bose–Einstein condensation (BEC) of Cooper pairs. However, the creation and annihilation operators of Cooper pairs do not satisfy the bosonic commutation relations and then, the mentioned viewpoint has a weakness in its foundation. In this work, we introduce the concept of collective Cooper pairs (CCP) as linear combinations of Cooper pairs and prove their bosonic nature at the dilute limit. This bosonic nature is given rise from their diffuse character on the Cooper pairs, which permits the accumulation of many collective pairs at a single quantum state. Moreover, the superconducting ground state proposed by Bardeen, Cooper and Schrieffer (BCS) can be written in terms of these collective Cooper pairs, which means that the BCS theory is consistent with a possible BEC theory of superconductivity based on collective Cooper pairs. Finally, we calculate the energy spectra and the BEC critical temperature of CCP.

Dimensional crossover of a boson gas in multilayers

We obtain the thermodynamic properties for a non-interacting Bose gas constrained on multilayers modeled by a periodic Kronig-Penney delta potential in one direction and allowed to be free in the other two directions. We report Bose-Einstein condensation (BEC) critical temperatures, chemical potential, internal energy, specific heat, and entropy for different values of a dimensionless impenetrability $P\geqslant 0$ between layers. The BEC critical temperature $T_{c}$ coincides with the ideal gas BEC critical temperature $T_{0}$ when $P=0$ and rapidly goes to zero as $P$ increases to infinity for any finite interlayer separation. The specific heat $C_{V}$ \textit{vs} $T$ for finite $P$ and plane separation $a$ exhibits one minimum and one or two maxima in addition to the BEC, for temperatures larger than $T_{c}$ which highlights the effects due to particle confinement. Then we discuss a distinctive dimensional crossover of the system through the specific heat behavior driven by the magnitude of $P$. For $T<T_{c}$ the crossover is revealed by the change in the slope of $\log C_{V}(T)$ and when $T>T_{c}$, it is evidenced by a broad minimum in $C_{V}(T)$.

Bose-Einstein condensation of trapped polaritons in two-dimensional electron-hole systems in a high magnetic field

The Bose-Einstein condensation (BEC) of magnetoexcitonic polaritons in two-dimensional (2D) electron-hole system embedded in a semiconductor microcavity in a high magnetic field $B$ is predicted. There are two physical realizations of 2D electron-hole system under consideration: a graphene layer and quantum well (QW). A 2D gas of magnetoexcitonic polaritons is considered in a planar harmonic potential trap. Two possible physical realizations of this trapping potential are assumed: inhomogeneous local stress or harmonic electric field potential applied to excitons and a parabolic shape of the semiconductor cavity causing the trapping of microcavity photons. The effective Hamiltonian of the ideal gas of cavity polaritons in a QW and graphene in a high magnetic field and the BEC temperature as functions of magnetic field are obtained. It is shown that the effective polariton mass $M_{\rm eff}$ increases with magnetic field as $B^{1/2}$. The BEC critical temperature $T_{c}^{(0)}$ decreases as $B^{-1/4}$ and increases with the spring constant of the parabolic trap. The Rabi splitting related to the creation of a magnetoexciton in a high magnetic field in graphene and QW is obtained. It is shown that Rabi splitting in graphene can be controlled by the external magnetic field since it is proportional to $B^{-1/4}$, while in a QW the Rabi splitting does not depend on the magnetic field when it is strong.

A phase diagram for the Bose-Einstein condensation of magnons

Evidence has recently been given for the Bose-Einstein condensation (BEC) of magnons in nanostructures. This behavior occurs for nanoparticles some tens of nanometers in size (having some millions of atoms in a nanoparticle). Here we explore the effect of particle size on the BEC critical temperature and the blocking temperature. These considerations lead to a proposed phase diagram for magnetic behavior in nanoparticles, with distinct BEC, superparamagnetic, and ferromagnetic phases.

Condensation in a Disordered Infinite-Range Hopping Bose–Hubbard Model

We study Bose-Einstein Condensation (BEC) in the Infinite-Range Hopping Bose-Hubbard model for repulsive on-site particle interaction in presence of ergodic random one-site potentials with different distributions. We show that the model is exactly soluble even if the on-site interaction is random. But in contrast to the non-random case, we observe here new phenomena: instead of enhancement of BEC for perfect bosons, for constant on-site repulsion and discrete distributions of the single-site potential there is suppression of BEC at some fractional densities. We show that this suppression appears with increasing disorder. On the other hand, the BEC suppression at integer densities may disappear, if disorder increases. For a continuous distribution we prove that the BEC critical temperature decreases for small on-site repulsion while the BEC is suppressed at integer values of density for large repulsion. Again, the threshold for this repulsion gets higher, when disorder increases.

Bose-Einstein Condensation and Superfluidity of Strongly Correlated Bose Fluid in a Random Potential

It was recently observed that liquid 4He confined in porous glass lost its superfluidity at high pressures and very low temperatures, causing the quantum phase transition by the strong correlation. Motivated by this experiment, we study the behavior of a strongly correlated Bose fluid in a disordered environment, such as the Bose-Einstein condensate (BEC) and superfluid critical temperatures, by using a model of 3-dimensional Bose fluid in a random potential. For the perturbation of the repulsive interaction between particles, we introduced two-loop renormalized self energy by the self-consistent calculation, which is effective near the BEC critical temperature. Calculating the second order perturbation with respect to the random potential, we found that the BEC disappears at high densities, which is qualitatively consistent with the experimental results.

Improved optimization of perturbation theory: Applications to the oscillator energy levels and Bose-Einstein condensate critical temperature

Improving perturbation theory via a variational optimization has generally produced in higher orders an embarrassingly large set of solutions, most of them unphysical (complex). We introduce an extension of the optimized perturbation method which leads to a drastic reduction of the number of acceptable solutions. The properties of this new method are studied and it is then applied to the calculation of relevant quantities in different $\phi^4$ models, such as the anharmonic oscillator energy levels and the critical Bose-Einstein Condensation temperature shift $\Delta T_c$ recently investigated by various authors. Our present estimates of $\Delta T_c$, incorporating the most recently available six and seven loop perturbative information, are in excellent agreement with all the available lattice numerical simulations. This represents a very substantial improvement over previous treatments.

Anomalous particle-number fluctuations in a three-dimensional interacting Bose-Einstein condensate

The particle-number fluctuations originated from collective excitations are investigated for a three-dimensional, repulsively interacting Bose-Einstein condensate (BEC) confined in a harmonic trap. The contribution due to the quantum depletion of the condensate is calculated and the explicit expression of the coefficient in the formulas denoting the particle-number fluctuations is given. The results show that the particle-number fluctuations of the condensate follow the law $<\delta N_0^2> \sim N^{22/15}$ and the fluctuations vanish when temperature approaches to the BEC critical temperature.

Quasipure Bose-Einstein condensate immersed in a Fermi sea.

We report the observation of coexisting Bose-Einstein condensate (BEC) and Fermi gas in a magnetic trap. With a very small fraction of thermal atoms, the 7Li condensate is quasipure and in thermal contact with a 6Li Fermi gas. The lowest common temperature is 0.28 microK approximately 0.2(1)T(C) = 0.2(1)T(F) where T(C) is the BEC critical temperature and T(F) the Fermi temperature. The 7Li condensate has a one-dimensional character.