Critical Temperature For Bose-Einstein Condensation Research Articles

Quantum-Degenerate Mixture of Fermionic Lithium and Bosonic Rubidium Gases

We report on the observation of sympathetic cooling of a cloud of fermionic 6Li atoms which are thermally coupled to evaporatively cooled bosonic 87Rb. Using this technique we obtain a mixture of quantum-degenerate gases, where the Rb cloud is colder than the critical temperature for Bose-Einstein condensation and the Li cloud is colder than the Fermi temperature. From measurements of the thermalization velocity we estimate the interspecies s-wave triplet scattering length |amx|=20(+9)(-6)aB. We found that the presence of residual rubidium atoms in the |2, 1> and the |1, -1> Zeeman substates gives rise to important losses due to inelastic collisions.

Critical temperature of Bose-Einstein condensa-tion for weakly interacting bose gas in a poten-tial trap

The critical temperature of Bose-Einstein condensation at minimum momentum state for weakly interacting Bose gases in a power-law potential and the deviation of the critical temperature from ideal bose gas are studied. The effect of interaction on the critical temperature is ascribed to the ratiao α / λ c , where a is the scattering length for s wave and lc is de Broglie wavelength at critical temperature. As α / λ c π ) 2 , the interaction is negligible. The presented deviation of the critical temperature for three dimensional harmonic potential is well in agreement with recent measurement of critical temperature for 87 Rb bose gas trapped in a harmonic well.

Critical temperature of Bose-Einstein condensation in an external potential

Expressions for critical temperature of Bose-Einstein condensation (BEC) in an e xternal potential, which are different from published results in the literatur e, are presente d. The results reveal the relation between the critical temperature of BECgas and the external potential, and demonstrates proporti onality of critical temperature in external potential to the value T0c at which th e potential is absent. In addition, a criterion for the validity of potential is also prese nted, which is based on the comparison between the potential and the product  kT 0c. This comparison shows that only when the external potential is nearly eq ual to or larg er than kT0c, the increase of critical temperature is significant. A s the potential is much smaller than kT０c, the potential has no effects on the BEC gas.

Numerical research on critical temperature of Bose-Einstein condensation for gas with interaction in harmonic trap

In this article we study BoseEinstein condensation of the gas with interactions in a harmonic trap using a numerical method. The distribution of the energy states was given, by which the author calculated the shift of the critical temperature and made a comparison with the situation without interactions. We have obtained a positive shift of critical temperature for systems with repulsive interaction, and a negative one for systems with attractive interaction.

Ferromagnetic phase transition and Bose-Einstein condensation in spinor Bose gases

Phase transitions in spinor Bose gases with ferromagnetic (FM) couplings are studied via mean-field theory. We show that an infinitesimal value of the coupling can induce a FM phase transition at a finite temperature always above the critical temperature of Bose-Einstein condensation. This contrasts sharply with the case of Fermi gases, in which the Stoner coupling $I_s$ can not lead to a FM phase transition unless it is larger than a threshold value $I_0$. The FM coupling also increases the critical temperatures of both the ferromagnetic transition and the Bose-Einstein condensation.

Thermodynamics of a trapped Bose-Fermi mixture

By using the Hartree-Fock-Bogoliubov equations within the Popov approximation, we investigate the thermodynamic properties of a dilute binary Bose-Fermi mixture confined in an isotropic harmonic trap. For mixtures with an attractive Bose-Fermi interaction we find a sizable enhancement of the condensate fraction and of the critical temperature of Bose-Einstein condensation with respect to the predictions for a pure interacting Bose gas. Conversely, the influence of the repulsive Bose-Fermi interaction is less pronounced. The possible relevance of our results in current experiments on trapped $^{87}{\rm Rb}-^{40}${\rm K} mixtures is discussed.

Bose-Einstein Condensation in Liquid 4He in Vycor

We present neutron scattering measurements of Bose-Einstein condensation (BEC) in liquid 4He confined in Vycor. The data show clear evidence of a condensate in Vycor with a condensate fraction comparable to that of bulk superfluid 4He, approximately 7.5% at low temperature and SVP. The temperature dependence of n0(T) is also similar to that in the bulk with critical temperature for BEC, TBEC, in the range 1.80<TBEC<2.05 K. The data are not accurate enough to show whether TBEC for Vycor is the same or greater than the depressed critical temperature for superfluidity, Tc=1.95 K.

Bose-Einstein Condensation in a Two-Dimensional System with Sixty Bosons

A 60-boson system confined on a sphere has been qualitatively studied based on symmetry considerations. The low-lying spectrum is dominated by the ground rotation band based on the fullerene structure. In this band all the L = 1 to L = 5 states are found to be prohibited by symmetry. Therefore, there is a large gap lying between the ground state and the first excited state. The magnitude of this gap, which is associated with the critical temperature of Bose-Einstein condensation, has been evaluated. It is found that, the smaller the radius of the sphere of confinement, the higher the critical temperature.

Measurement of the spatial coherence of a trapped Bose gas at the phase transition

The experimental realization of Bose-Einstein condensates of dilute gases has allowed investigations of fundamental concepts in quantum mechanics at ultra-low temperatures, such as wave-like behaviour and interference phenomena. The formation of an interference pattern depends fundamentally on the phase coherence of a system; the latter may be quantified by the spatial correlation function. Phase coherence over a long range is the essential factor underlying Bose-Einstein condensation and related macroscopic quantum phenomena, such as superconductivity and superfluidity. Here we report a direct measurement of the phase coherence properties of a weakly interacting Bose gas of rubidium atoms. Effectively, we create a double slit for magnetically trapped atoms using a radio wave field with two frequency components. The correlation function of the system is determined by evaluating the interference pattern of two matter waves originating from the spatially separated 'slit' regions of the trapped gas. Above the critical temperature for Bose-Einstein condensation, the correlation function shows a rapid gaussian decay, as expected for a thermal gas. Below the critical temperature, the correlation function has a different shape: a slow decay towards a plateau is observed, indicating the long-range phase coherence of the condensate fraction.

Bose-Einstein condensation of a trapped gas inndimensions

The critical temperature for Bose-Einstein condensation, ground-state fraction, and heat capacity of an ideal gas of Bose particles that are confined by an n-dimensional generic power-law potential trap are derived. The conditions for Bose-Einstein condensation and the discontinuous conditions of the heat capacity at critical temperature are obtained. All these quantities and conditions are found to vary markedly with the dimensionality of space, characteristics of particles, and shape of the external potential. The results obtained here are universal.

Pair correlation function of an inhomogeneous interacting Bose-Einstein condensate

We calculate the pair correlation function of an interacting Bose gas in a harmonic trap directly via Path Integral Quantum Monte Carlo simulation for various temperatures and compare the numerical result with simple approximative treatments. Around the critical temperature of Bose-Einstein condensation, a description based on the Hartree-Fock approximation is found to be accurate. At low temperatures the Hartree-Fock approach fails and we use a local density approximation based on the Bogoliubov description for a homogeneous gas. This approximation agrees with the simulation results at low temperatures, where the contribution of the phonon-like modes affects the long range behavior of the correlation function. Further we discuss the relation between the pair correlation and quantities measured in recent experiments.

Coulomb Barrier Total Screening by Bose-Einstein-Condensed Deuterium in Palladium Blisters and Reaction Chains in High-Density Hysteresis

A theoretical model is proposed in order to explain, via ordinary physics, fundamental aspects of the cold fusion phenomena experimentally observed. These phenomena include unexpected high fusion reaction rates at low temperatures, the paradox of low neutron emission compared to the energy release observed, the cold fusion dependence on critical temperature, neutronic stimulation, and the constitution of nuclei with high electric charge. This theory is based on the hypothesis that a degenerate, cold plasma may be created inside lattice defects through a sudden deuteron discharge from a saturated metal lattice. The proposed method is based on the perturbative solution of Vlasov-Poisson kinetic-electric equations. A Fourier transformation of such equations proves that the plasma behaves like an ideal Bose gas of electronically screened deuterons. This approach shows that a high particle density can exist with no pressure increase above the limiting value reached at Bose-Einstein condensation (BEC) and that the electrical repulsion field between positive ions disappears below the critical temperature for BEC. Inside the voids created by defects, the behavior of the cold degenerate plasma below critical temperature suppresses the Coulomb barrier between any pair of ions, in particular those that will fuse. The absence of Coulomb barrier allows one to simply predict fusion reaction rates of the order of those found experimentally and the particle trapping in high-density condensate causing fusion chains. The main reactions involved are and . Subsequent fusions of the main reaction products lead to nuclei of greater complexity. A high neutron multiplication factor via deuteron disintegrations is calculated. Neutron bursts, temperature, and pressure excursions are also predicted. Finally, new procedures for inducing such reactions outside metal lattices are suggested.

Density and boundary effects on pion distributions in relativistic heavy-ion collisions

We compute the pion inclusive momentum distribution in a heavy-ion collision, assuming thermal equilibrium and accounting for boundary effects at the time of decoupling. We calculate the chemical potential corresponding to an average pion multiplicity in central collisions and explore the consequences of having the pion system produced close to the critical temperature for Bose-Einstein condensation.

Critical temperature of a trapped interacting Bose-Einstein gas in the local-density approximation

The Bose gas in an external potential is studied by means of the local density approximation. An analytical result is derived for the dependence of the critical temperature of Bose-Einstein condensation on the mutual interaction in a generic power-law potential.

Bose-Einstein condensation: Kinetic evolution obtained from simulated trajectories

In this paper, we present a method for simulating the kinetic evolution of a dilute gas of atoms that are cooled below the critical temperature for Bose-Einstein condensation. Our method gives insight into the formulation of physical kinetics by illustrating directly the decomposition of the distribution function into an infinite sum of single-particle trajectories. This approach is valid for the entire range of phase-space densities, although we limit the discussion here to exclude the region where the condensate fraction is close to unity and the effect of the mean field is significant. We present explicit calculations of finite number effects on equilibrium, the dynamic build-up of the ground state, and simulations of evaporative cooling.

Quantum field theory of atoms interacting with photons. II. Scattering of short laser pulses from trapped bosonic atoms.

We discuss a method for probing a system of cold bosonic atoms in a trap using intense short laser pulses. Above the critical temperature for Bose-Einstein condensation, such a system scatters very weakly. Coherent scattering occurs primarily in the forward direction within a solid angle determined by phase matching conditions for the thermal atomic distribution. Below the critical temperature, the number of scattered photons increases dramatically and the scattered light is emitted into a solid angle determined by the size of the condensate. Quantum statistics of the atoms explicitly effect the spectrum as well as the squeezing properties of the scattered light. The theory accounts for the atom-atom interactions.

Bose-Einstein condensation as symmetry breaking in curved spacetime and in spacetimes with boundaries.

A quantum field theory treatment of Bose-Einstein condensation for a charged, noninteracting scalar field in a static spacetime with a possible spatial boundary is given. An interpretation is presented in terms of symmetry breaking to give a nonconstant scalar field expectation value. The method used is a computation of the effective action in the high-temperature limit. Results are obtained for static spacetimes of general dimension. The critical temperature for Bose-Einstein condensation is obtained in terms of the lowest eigenvalue of the Laplacian with the scalar field subject to the appropriate boundary conditions. A number of applications are provided for flat spacetimes with and without boundaries, and to curved spacetimes. In special cases where the scalar field expectation value is constant, some previously known results are obtained; in other cases, new results are found.

Spin dynamics in a polarized Bose gas.

The equation of motion for the spin density of a spin-polarized Bose gas is derived for low temperatures down to ${\mathit{T}}_{\mathit{c}+}$, the critical temperature of Bose-Einstein condensation. In the classical regime, our results agree with those of Lhuillier and Lalo\"e. However, at low T, ${\mathrm{\ensuremath{\tau}}}_{\mathrm{\ensuremath{\perp}}}$ and ${\mathrm{\ensuremath{\tau}}}_{\mathrm{\ensuremath{\parallel}}}$ become qualitatively different, especially at larger polarization M, and are no longer proportional to ${\mathit{T}}^{\mathrm{\ensuremath{-}}1/2}$. Particularly, ${\mathrm{\ensuremath{\tau}}}_{\mathrm{\ensuremath{\perp}}}$ reaches a maximum at T\ensuremath{\sim}1.6${\mathit{T}}_{\mathit{c}+}$ and decreases thereafter so that intrinsic spin-wave damping in a Bose gas increases with decreasing T for T1.6${\mathit{T}}_{\mathit{c}+}$.

Bose-Einstein condensation in an external potential.

We present theoretical results for the critical temperature for Bose-Einstein condensation, condensate fraction, and heat capacity of a gas of Bose particles that are confined by a generic power-law potential trap. All three of these quantities are found to vary markedly with the shape of the potential. Both the ideal and the weakly interacting Bose gas are considered.

Bose-Einstein Condensation in Compactified Spaces

We discuss the thermodynamic potential of a charged Bose gas with the chemical potential in arbitrary dimensions. The critical temperature for Bose-Einstein condensation is investigated. In the case of the compactified background metric, it is shown that the critical temperature depends on the size of the extra spaces. The asymmetry of the "Kaluza-Klein charge" is also discussed.