Ultranarrow optical absorption and two-phonon excitation spectroscopy of Cu2O paraexcitons in a high magnetic field

We show that in a magnetic field B the otherwise forbidden lowest exciton in Cu2O (paraexciton of Gamma(2)(+) symmetry) gives rise to a narrow absorption line of 80 neV at a temperature of 1.2 K. The B2 dependence of the field-induced oscillator strength and the low energy shift DeltaE with increasing field strength are measured. From two-phonon excitation spectroscopy measurements we derive by a merely kinematical analysis a very reliable value for the paraexciton mass. A blueshift and a broadening of the absorption line are observed for increasing excitation intensity. These observations are discussed in connection with a Bose-Einstein condensation of paraexcitons in Cu2O.     

Bose-Einstein condensation of magnons in Cs2CuCl4

We report on results of specific heat measurements on single crystals of the frustrated quasi-2D spin-1/2 antiferromagnet Cs2CuCl4 (T(N)=0.595 K) in external magnetic fields B<12 T and for temperatures T>30 mK. Decreasing B from high fields leads to the closure of the field-induced gap in the magnon spectrum at a critical field Bc approximately = 8.51 T and a magnetic phase transition is clearly seen below Bc. In the vicinity of Bc, the phase transition boundary is well described by the power law Tc(B) proportional, variant (Bc-B)(1/phi), with the measured critical exponent phi approximately =1.5. These findings are interpreted as a Bose-Einstein condensation of magnons.     

Bose-Einstein condensation of chromium

We report on the generation of a Bose-Einstein condensate in a gas of chromium atoms, which have an exceptionally large magnetic dipole moment and therefore underlie anisotropic long-range interactions. The preparation of the chromium condensate requires novel cooling strategies that are adapted to its special electronic and magnetic properties. The final step to reach quantum degeneracy is forced evaporative cooling of 52Cr atoms within a crossed optical dipole trap. At a critical temperature of T(c) approximately 700 nK, we observe Bose-Einstein condensation by the appearance of a two-component velocity distribution. We are able to produce almost pure condensates with more than 50,000 condensed 52Cr atoms.     

Bose-Einstein condensation in interacting gases

We study the occurrence of a Bose-Einstein transition in a dilute gas with repulsive interactions, starting from temperatures above the transition temperature. The formalism, based on the use of Ursell operators, allows us to evaluate the one-particle density operator with more flexibility than in mean-field theories, since it does not necessarily coincide with that of an ideal gas with adjustable parameters (chemical potential, etc.). In a first step, a simple approximation is used (Ursell-Dyson approximation), which allow us to recover results which are similar to those of the usual mean-field theories. In a second step, a more precise treatment of the correlations and velocity dependence of the populations in the system is elaborated. This introduces new physical effects, such as a change of the velocity profile just above the transition: the proportion of atoms with low velocities is higher than in an ideal gas. A consequence of this distortion is an increase of the critical temperature (at constant density) of the Bose gas, in agreement with those of recent path integral Monte-Carlo calculations for hard spheres. Received 13 November 1998     

Bose-Einstein condensation in a cavity

The effect of the physically correct boundary conditions and the nonvanishing ground state energy on Bose-Einstein condensation of quantum particles confined to a cubic volumeV=L ³ is evaluated. The transition point is shifted towards higher temperatures by the confinement, the specific heat below the onset of condensation is no longer proportional toT ^3/2, and the pressure does depend on the volume. Precise expressions for the modification of the ground state population and for the shift of the condensation temperature are derived, together with an expansion of the internal energy and of the specific heat. Numerical computations confirm the accuracy of our analytical approximations.Dedicated to Herbert Wagner, whose work on quantum Fermi liquids proved to be also very stimulating for quantum Bose liquids.     

Bose-Einstein condensation in nonequilibrium systems

The properties of quantum statistically degenerate systems of Bosons which are created by an external pump field and decay within a finite lifetime are investigated by means of a Green's function treatment. These investigations help to understand the physical properties of such condensed Bose-systems as excitons, excitonic molecules and spin aligned hydrogen atoms. As an example, recent experiments by Hulin et al. on degenerate excitons in Cu₂O are analyzed and a condensate fraction of about 5% is obtained.     

Bose-Einstein condensation of rubidium atoms

A setup for preparing the Bose-Einstein condensate of rubidium atoms has been built. The condensate consists of 10⁵–10^{6 87}Rb atoms in the hyperfine state F _g = 2 of the ground electronic state. Three key indications of condensation—a sharp increase in the phase-space density of atoms, the threshold emergence of two fractions in the cloud, and anisotropic expansion of the condensate—have been observed.     

Bose-Einstein condensation of metastable helium

We have observed a Bose-Einstein condensate in a dilute gas of 4He in the (3)2S(1) metastable state. We find a critical temperature of (4.7+/-0.5) microK and a typical number of atoms at the threshold of 8 x 10(6). The maximum number of atoms in our condensate is about 5 x 10(5). An approximate value for the scattering length a = (16+/-8) nm is measured. The mean elastic collision rate at threshold is then estimated to be about 2 x 10(4) s(-1), indicating that we are deeply in the hydrodynamic regime. The typical decay time of the condensate is 2 s, which places an upper bound on the rate constants for two-body and three-body inelastic collisions.     

Kinetics of the Bose-Einstein condensation

We study the bosonic Boltzmann-Nordheim kinetic equation, which describes the kinetic regime of weakly interacting bosons with s-wave scattering only. We consider a spatially homogeneous fluid with an isotropic momentum distribution. The issue of the dynamical formation of a Bose-Einstein condensate has been studied extensively. We supply here the completed equations of motion for the coupled system, the energy density distribution of the normal fluid and the density of the condensate. With this information the post-nucleation self-similar solution is investigated in more detail than before.     

Bose-Einstein condensation of bouncing balls

Microscopic bouncing balls, i.e., particles confined within a positive one-half-dimensional gravitational potential, display Bose-Einstein condensation (BEC) not only in the thermodynamic limit but also in the case of a finite number of particles, and the critical temperature with a finite number of particles is higher than that in the thermodynamic limit. This system is different from the one-dimensional harmonic potential one, for which the standard result indicates that the BEC is not possible unless the number of particles is finite.     

Bose-Einstein condensation of stationary-light polaritons

We propose and analyze a mechanism for Bose-Einstein condensation of stationary dark-state polaritons. Dark-state polaritons (DSPs) are formed in the interaction of light with laser-driven 3-level Lambda-type atoms and are the basis of phenomena such as electromagnetically induced transparency, ultraslow, and stored light. They have long intrinsic lifetimes and in a stationary setup, a 3D quadratic dispersion profile with variable effective mass. Since DSPs are bosons, they can undergo a Bose-Einstein condensation at a critical temperature which can be many orders of magnitude larger than that of atoms. We show that thermalization of polaritons can occur via elastic collisions mediated by a resonantly enhanced optical Kerr nonlinearity on a time scale short compared to the decay time. Finally, condensation can be observed by turning stationary into propagating polaritons and monitoring the emitted light.     

Bose-Einstein condensation in dilute atomic gases

We summarize all experimental studies of Bose-Einstein condensation (BEC) in dilute atomic gases reported thus far and discuss the experimental techniques used to produce, manipulate and observe nanokelvin samples of atoms.     

Bose-Einstein condensation in solid 4He

We present neutron scattering measurements of the atomic momentum distribution n(k) in solid helium under a pressure p=41 bar (molar volume Vm=20.01+/-0.02 cm3/mol) and at temperatures between 80 and 500 mK. The aim is to determine whether there is Bose-Einstein condensation (BEC) below the critical temperature, Tc=200 mK, where a superfluid density has been observed. Assuming BEC appears as a macroscopic occupation of the k=0 state below Tc, we find a condensate fraction of n0=(-0.10+/-1.20)% at T=80 mK and n0=(0.08+/-0.78)% at T=120 mK, consistent with zero. The shape of n(k) also does not change on crossing Tc within measurement precision.     

On Bose-Einstein condensation in any dimension

A general property of an ideal Bose gas as temperature tends to zero and when conditions of degeneracy are satisfied is to have an arbitrarily large population in the groud state (or in its neighborhood); thus, condensation occurs in any dimension D but for D ≤ 2 there is no critical temperature. Some astrophysical consequences, as well as the temperature-dependent mass case, are discussed.     

Bose-Einstein condensation in dense quark matter

We consider the problem of Bose condensation of charged pions in QCD at finite isospin chemical potential μ_I using the O(4)-symmetric linear sigma model as an effective field theory for two-flavor QCD. Using the 2PI 1/N-expansion, we determine the quasiparticle masses as well as the pion and chiral condensates as a function of the temperature and isospin chemical potential in the chiral limit and at the physical point. The calculations show that there is a competition between the condensates. At T=0, Bose condensation takes place for chemical potentials larger than μ_π. In the chiral limit, the chiral condensate vanishes for any finite value of μ_I.