Boson-fermion mixtures inside an elongated cigar-shaped trap

We present mean-field calculations of the equilibrium state in a gaseous mixture of bosonic and spin-polarized fermionic atoms with repulsive or attractive interspecies interactions, confined inside a cigar-shaped trap under conditions such that the radial thickness of the two atomic clouds is approaching the magnitude of the s-wave scattering lengths. In this regime the kinetic pressure of the fermionic component is dominant. Full demixing under repulsive boson-fermion interactions can occur only when the number of fermions in the trap is below a threshold, and collapse under attractive interactions is suppressed within the range of validity of the mean-field model. Specific numerical illustrations are given for values of system parameters obtaining in 7Li-6Li clouds.Comment: 12 pages, 6 figure

Renormalization Group Analysis of a Gursey Model Inspired Field Theory II

Recently a model, which is equivalent to the scalar form of Gursey model, is shown to be a nontrivial field theoretical model when it is gauged with a SU(N) field. In this paper we study another model that is equivalent to the vector form of the Gursey model. We get a trivial theory when it is coupled with a scalar field. This result changes drastically when it is coupled with an additional SU(N) field. We find a nontrivial field theoretical model under certain conditions.Comment: 10 pages, 10 figures, revtex4, typos corrected, published versio

Collective excitations of a trapped boson-fermion mixture across demixing

We calculate the spectrum of low-lying collective excitations in a mesoscopic cloud formed by a Bose-Einstein condensate and a spin-polarized Fermi gas as a function of the boson-fermion repulsions. The cloud is under isotropic harmonic confinement and its dynamics is treated in the collisional regime by using the equations of generalized hydrodynamics with inclusion of surface effects. For large numbers of bosons we find that, as the cloud moves towards spatial separation (demixing) with increasing boson-fermion coupling, the frequencies of a set of collective modes show a softening followed by a sharp upturn. This behavior permits a clear identification of the quantum phase transition. We propose a physical interpretation for the dynamical transition point in a confined mixture, leading to a simple analytical expression for its location.Comment: revtex4, 9 pages, 8 postscript file

Transmittivity of a Bose-Einstein condensate on a lattice: interference from period doubling and the effect of disorder

We evaluate the particle current flowing in steady state through a Bose-Einstein condensate subject to a constant force in a quasi-onedimensional lattice and to attractive interactions from fermionic atoms that are localized in various configurations inside the lattice wells. The system is treated within a Bose-Hubbard tight binding model by an out-of-equilibrium Green's function approach. A new band gap opens up when the lattice period is doubled by locating the fermions in alternate wells and yields an interference pattern in the transmittivity on varying the intensity of the driving force. The positions of the transmittivity minima are determined by matching the period of Bloch oscillations and the time for tunnelling across the band gap. Massive disorder in the distribution of the fermions will wash out the interference pattern, but the same period doubling of the lattice can be experimentally realized in a four-beam set-up. We report illustrative numerical results for a mixture of 87Rb and 40K atoms in an optical lattice created by laser beams with a wavelength of 763 nm.Comment: 13 pages, 5 figure

Demixing in mesoscopic boson-fermion clouds inside cylindrical harmonic traps: quantum phase diagram and role of temperature

We use a semiclassical three-fluid thermodynamic model to evaluate the phenomena of spatial demixing in mesoscopic clouds of fermionic and bosonic atoms at high dilution under harmonic confinement, assuming repulsive boson-boson and boson-fermion interactions and including account of a bosonic thermal cloud at finite temperature T. The finite system size allows three different regimes for the equilibrium density profiles at T=0: a fully mixed state, a partially mixed state in which the overlap between the boson and fermion clouds is decreasing, and a fully demixed state where the two clouds have zero overlap. We propose simple analytical rules for the two cross-overs between the three regimes as functions of the physical system parameters and support these rules by extensive numerical calculations. A universal ``phase diagram'' expressed in terms of simple scaling parameters is shown to be valid for the transition to the regime of full demixing, inside which we identify several exotic configurations for the two phase-separated clouds in addition to simple ones consisting of a core of bosons enveloped by fermions and "vice versa". With increasing temperature the main role of the growing thermal cloud of bosons is to transform some exotic configurations into more symmetric ones, until demixing is ultimately lost. For very high values of boson-fermion repulsive coupling we also report demixing between the fermions and the thermally excited bosons.Comment: 11 pages, 8 figure

Collective excitations in trapped boson-fermion mixtures: from demixing to collapse

We calculate the spectrum of low-lying collective excitations in a gaseous cloud formed by a Bose-Einstein condensate and a spin-polarized Fermi gas over a range of the boson-fermion coupling strength extending from strongly repulsive to strongly attractive. Increasing boson-fermion repulsions drive the system towards spatial separation of its components (``demixing''), whereas boson-fermion attractions drive it towards implosion (``collapse''). The dynamics of the system is treated in the experimentally relevant collisionless regime by means of a Random-Phase approximation and the behavior of a mesoscopic cloud under isotropic harmonic confinement is contrasted with that of a macroscopic mixture at given average particle densities. In the latter case the locations of both the demixing and the collapse phase transitions are sharply defined by the same stability condition, which is determined by the softening of an eigenmode of either fermionic or bosonic origin. In contrast, the transitions to either demixing or collapse in a mesoscopic cloud at fixed confinement and particle numbers are spread out over a range of boson-fermion coupling strength, and some initial decrease of the frequencies of a set of collective modes is followed by hardening as evidenced by blue shifts of most eigenmodes. The spectral hardening can serve as a signal of the impending transition and is most evident when the number of bosons in the cloud is relatively large. We propose physical interpretations for these dynamical behaviors with the help of suitably defined partial compressibilities for the gaseous cloud under confinement.Comment: 16 pages, 7 figures, revtex

Friedel oscillations in a gas of interacting one-dimensional fermionic atoms confined in a harmonic trap

Using an asymptotic phase representation of the particle density operator $\hat{\rho}(z)$ in the one-dimensional harmonic trap, the part $\delta \hat{\rho}_F(z)$ which describes the Friedel oscillations is extracted. The expectation value $$ with respect to the interacting ground state requires the calculation of the mean square average of a properly defined phase operator. This calculation is performed analytically for the Tomonaga-Luttinger model with harmonic confinement. It is found that the envelope of the Friedel oscillations at zero temperature decays with the boundary exponent $\nu = (K+1)/2$ away from the classical boundaries. This value differs from that known for open boundary conditions or strong pinning impurities. The soft boundary in the present case thus modifies the decay of Friedel oscillations. The case of two components is also discussed.Comment: Revised version to appear in Journal of Physics B: Atomic, Molecular and Optical Physic

Exact first-order density matrix for a d-dimensional harmonically confined Fermi gas at finite temperature

We present an exact closed form expression for the {\em finite temperature} first-order density matrix of a harmonically trapped ideal Fermi gas in any dimension. This constitutes a much sought after generalization of the recent results in the literature, where exact expressions have been limited to quantities derived from the {\em diagonal} first-order density matrix. We compare our exact results with the Thomas-Fermi approximation (TFA) and demonstrate numerically that the TFA provides an excellent description of the first-order density matrix in the large-N limit. As an interesting application, we derive a closed form expression for the finite temperature Hartree-Fock exchange energy of a two-dimensional parabolically confined quantum dot. We numerically test this exact result against the 2D TF exchange functional, and comment on the applicability of the local-density approximation (LDA) to the exchange energy of an inhomogeneous 2D Fermi gas.Comment: 12 pages, 3 figures included in the text, RevTeX4. Text before Eq.(25) corrected. Additional equation following Eq.(25) has been adde

Temperature dependence of density profiles for a cloud of non-interacting fermions moving inside a harmonic trap in one dimension

We extend to finite temperature a Green's function method that was previously proposed to evaluate ground-state properties of mesoscopic clouds of non-interacting fermions moving under harmonic confinement in one dimension. By calculations of the particle and kinetic energy density profiles we illustrate the role of thermal excitations in smoothing out the quantum shell structure of the cloud and in spreading the particle spill-out from quantum tunnel at the edges. We also discuss the approach of the exact density profiles to the predictions of a semiclassical model often used in the theory of confined atomic gases at finite temperature.Comment: 7 pages, 4 figure