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Zeitschrift für Physikalische Chemie

Phase Separation in Ultracold Boson–Fermion Mixtures under Confinement

Z. Akdeniz, M. P. Tosi

Published Aug 1, 2003• 1 citation
Publisher

Abstract

Abstract A short review is given of recent progress in understanding the demixing transition in a mesoscopic gaseous cloud of bosonic and fermionic alkali atoms under the effect of their mutual repulsions at zero temperature. The mixture is confined inside a magnetic trap exerting external harmonic potentials on the atoms and the bosonic component is taken in a Bose-Einstein condensed state while the fermions are in a spin-polarized state. Main emphasis is placed on the role of the confinement: in a mesoscopic system (i) the phase transition becomes smooth as a function of the driving parameter, which is the boson-fermion s-wave scattering length; and (ii) various configurations of the phase-separated gaseous cloud are allowed, including some very exotic ones in an anisotropic trap. The transition inside a spherical trap leads to an egg-type structure, with the bosonic condensate being surrounded by a shell of fermions, and is best identified from a sharp upturn of the frequency of low-lying monopolar and dipolar oscillations of fermionic character. This dynamical signature of the transition appears when the overlap between the two components has already started to decrease, but is still quite appreciable. A system of specific experimental interest is the mixture of 6Li and 7Li isotopes, whose parameters could be driven towards the phase transition.

DOI
10.1524/zpch.217.8.927.20422

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Annales de Physique•Mar 1, 2003•11 citations
Abstract A short review is given of recent progress in understanding the demixing transition in a mesoscopic gaseous cloud of bosonic and fermionic alkali atoms under the effect of their mutual repulsions at zero temperature. The mixture is confined inside a magnetic trap exerting external harmonic potentials on the atoms and the bosonic component is taken in a Bose-Einstein condensed state while the fermions are in a spin-polarized state. Main emphasis is placed on the role of the confinement: in a mesoscopic system (i) the phase transition becomes smooth as a function of the driving parameter, which is the boson-fermion s-wave scattering length; and (ii) various configurations of the phase-separated gaseous cloud are allowed, including some very exotic ones in an anisotropic trap. The transition inside a spherical trap leads to an egg-type structure, with the bosonic condensate being surrounded by a shell of fermions, and is best identified from a sharp upturn of the frequency of low-lying monopolar and dipolar oscillations of fermionic character. This dynamical signature of the transition appears when the overlap between the two components has already started to decrease, but is still quite appreciable. A system of specific experimental interest is the mixture of 6Li and 7Li isotopes, whose parameters could be driven towards the phase transition.
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 drives the system towards spatial separation of its components (``demixing''), whereas boson-fermion attractions drives 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.
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.
A cooling strategy that is currently being pursued for a gas of fermionic atoms uses sympathetic cooling via s-wave collisions against a Bose-condensed gas. At increasing values of the scattering lengths, the boson-fermion cloud undergoes demixing. Locating the onset of incipient spatial separation is relevant to fermion cooling, since at that point the diminishing overlap between the two clouds will start reducing the effectiveness of the collisional transfer processes. With full demixing, the system enters a new quantum phase, where its properties are expected to be substantially modified. In this perspective, we have used a semiclassical model to evaluate spatial demixing in mesoscopic clouds of fermionic and bosonic atoms at high dilution inside cylindrical harmonic traps. The finite system size allows three different regimes for the equilibrium density profiles: a fully mixed state, a partially mixed state in which the overlap between the boson and fermion clouds decreases, and a fully demixed state wherein the two clouds have zero overlap. Simple analytical rules account for the crossovers between these regimes as functions of the physical system parameters and are supported by extensive numerical calculations. A universal phase diagram involving simple scaling parameters is valid for the transition to full demixing, inside which we identify several exotic configurations for the two phase-separated clouds in addition to the simple ones consisting of a core of bosons enveloped by fermions and vice versa.
We use a semiclassical three-fluid model to evaluate the phenomena of spatial demixing in mesoscopic clouds of fermionic and bosonic atoms at high dilution under harmonic confinement. We assume repulsive boson-boson and boson-fermion interactions and include a bosonic thermal cloud at finite temperature T.T.T. The finite system size allows three different regimes for the equilibrium density profiles at T=0:T=0:T=0: a fully mixed state, a partially mixed state in which the overlap between bosons and fermions is decreasing, and a fully demixed state where the two clouds have zero overlap. We propose simple analytical rules for the two crossovers between the three regimes as functions of the system parameters and support these rules by extensive numerical calculations. A universal ``phase diagram'' is shown to be valid for the transition to the regime of full demixing, where we identify several exotic configurations in addition to simple ones consisting of a core of bosons enveloped by fermions and vice versa. With increasing temperature some exotic configurations are transformed into more symmetric ones, until demixing is ultimately lost. For very high values of the boson-fermion repulsion we also report demixing between the fermions and the thermally excited bosons.
We study the collective modes of a confined gaseous cloud of bosons and fermions with mutual attractive interactions at zero temperature. The cloud consists of a Bose-Einstein condensate and a spin-polarized Fermi gas inside a spherical harmonic trap and the coupling between the two species is varied by increasing either the magnitude of the interspecies sss-wave scattering length or the number of bosons. The mode frequencies are obtained in the collisional regime by solving the equations of generalized hydrodynamics and are compared with the spectra calculated in the collisionless regime within a random-phase approximation. We find that, as the mixture is driven towards the collapse instability, the frequencies of the modes of fermionic origin show a blue shift which can become very significant for large numbers of bosons. Instead the modes of bosonic origin show a softening, which becomes most pronounced in the very proximity of collapse. Explicit illustrations of these trends are given for the monopolar spectra, but similar trends are found for the dipolar and quadrupolar spectra except for the surface (n=0)(n=0)(n=0) modes which are essentially unaffected by the interactions.
This thesis presents studies of quantum degenerate atomic gases of fermionic 6Li and bosonic 7Li. Degeneracy is reached by evaporative cooling of 7Li in a strongly confining magnetic trap. Since at low temperatures direct evaporative cooling is not possible for a polarized fermionic gas, 6Li is sympathetically cooled by thermal contact with 7Li. In a first series of experiments both isotopes are trapped in their low-field seeking higher hyperfine states. A Fermi degeneracy of is achieved for 105 fermions. For more than ~300 atoms, the 7Li condensate collapses, due to the attractive interatomic interaction in this state. This limits the degeneracy reached for both species. To overcome this limit, in a second series of experiments 7Li and 6Li atoms are transferred to their low field seeking lower hyperfine states, where the boson-boson interaction is repulsive but weak. The inter-isotope collisions are used to thermalize the mixture. A 7Li Bose-Einstein condensate (BEC) of 104 atoms immersed in a Fermi sea is produced. The BEC is quasi-one-dimensional and the thermal fraction can be negligible. The measured degeneracies are . The temperature is measured using the bosonic thermal fraction, which vanishes at the lowest temperatures, limiting our measurement sensitivity. In a third series of experiments, the bosons are transferred into an optical trap and their internal state is changed to , the lowest energy state. A Feshbach resonance is detected and used to produce a BEC with tunable atomic interactions. When the effective interaction between atoms is tuned to be small and attractive, we observe the formation of a matter-wave bright soliton. Propagation of the soliton without spreading over a macroscopic distance of 1.1~mm is observed.