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arXiv:1304.6303 · Physical Review A

Phase equilibrium of binary mixtures in mixed dimensions

E. Malatsetxebarria, Francesca Maria Marchetti, Miguel A. Cazalilla

Published Sep 3, 2013• 3 citations
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Abstract

We study the stability of a Bose-Fermi system loaded into an array of coupled one-dimensional (1D) ``tubes,'' where bosons and fermions experience different dimensions: Bosons are heavy and strongly localized in the 1D tubes, whereas fermions are light and can hop between the tubes. Using the ${}^{174}$Yb-${}^{6}$Li system as a reference, we obtain the equilibrium phase diagram. We find that, for both attractive and repulsive interspecies interaction, the exact treatment of 1D bosons via the Bethe ansatz implies that the transitions between pure fermion and any phase with a finite density of bosons can only be first order and never continuous, resulting in phase separation in density space. In contrast, the order of the transition between the pure boson and the mixed phase can either be second or first order depending on whether fermions are allowed to hop between the tubes or they also are strictly confined in 1D. We discuss the implications of our findings for current experiments on ${}^{174}$Yb-${}^{6}$Li mixtures as well as Fermi-Fermi mixtures of light and heavy atoms in a mixed-dimensional optical-lattice system.

DOI
10.1103/physreva.88.033604

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We study the stability of a Bose-Fermi system loaded into an array of coupled one-dimensional (1D) ``tubes,'' where bosons and fermions experience different dimensions: Bosons are heavy and strongly localized in the 1D tubes, whereas fermions are light and can hop between the tubes. Using the 174{}^{174}174Yb-6{}^{6}6Li system as a reference, we obtain the equilibrium phase diagram. We find that, for both attractive and repulsive interspecies interaction, the exact treatment of 1D bosons via the Bethe ansatz implies that the transitions between pure fermion and any phase with a finite density of bosons can only be first order and never continuous, resulting in phase separation in density space. In contrast, the order of the transition between the pure boson and the mixed phase can either be second or first order depending on whether fermions are allowed to hop between the tubes or they also are strictly confined in 1D. We discuss the implications of our findings for current experiments on 174{}^{174}174Yb-6{}^{6}6Li mixtures as well as Fermi-Fermi mixtures of light and heavy atoms in a mixed-dimensional optical-lattice system.
We consider a mixture of single-component bosonic and fermionic atoms in an array of coupled one-dimensional "tubes." For an attractive Bose-Fermi interaction, we show that the system exhibits phase separation instead of the usual collapse. Moreover, above a critical intertube hopping, all first-order instabilities disappear in both attractive and repulsive mixtures. The possibility of suppressing instabilities in this system suggests a route towards the realization of paired phases, including a superfluid of p-wave pairs unique to the coupled-tube system, and quantum critical phenomena.
We study the ground-state phase diagram of a mixture of bosonic and fermionic cold atoms confined on two- and three-dimensional optical lattices. The coupling between bosonic fluctuations and fermionic atoms can be attractive or repulsive and has similarities with electron-phonon coupling in crystals. We investigate behavior of the mixtures in the limit, where the Bogoliubov sound velocity that dictates bosonic dynamics is comparable to the Fermi velocity, hence the retardation effects are an important part of the physics. The dynamic Lindhard response function of the fermionic density to changes in the bosonic number of particles above some critical frequency can alter the sign, and consequently the interspecies interaction between particles becomes repulsive in contrast to the static limit (instantaneous and always attractive). Considering the above, we show that the structure of the phase diagrams crucially depends on the difference in masses of the bosons and fermions. We discuss the situations where integrating out the fermionic field provides an additional interaction that can decrease or increase bosonic coherence.
We consider a one-dimensional interacting Bose-Fermi mixture with equal masses of bosons and fermions, and with equal and repulsive interactions between Bose-Fermi and Bose-Bose particles. Such a system can be realized in experiments with ultracold boson and fermion isotopes in optical lattices. We use the Bethe-ansatz technique to find the ground state energy at zero temperature for any value of interaction strength and density ratio between bosons and fermions. We prove that the mixture is always stable against demixing. Combining exact solution with the local density approximation, we calculate density profiles and collective oscillation modes in a harmonic trap. In the strongly interating regime, we use exact wave functions to calculate correlation functions for bosons and fermions under periodic boundary conditions.
The mixture of the scalar bosonic and the spinless or polarized fermionic cold atoms in the one-dimensional optical lattice is studied. The system is modeled by the Bose-Fermi-Hubbard Hamiltonian, which shows different behavior from that of the Bose-Hubbard or the Fermi-Hubbard models. Because the $\text{SU}(1\ensuremath{\mid}1)$-supersymmetric Bethe ansatz solution gives an excellent approximation to this kind of mixed cold atomic systems, the ground-state properties of the system such as the densities of state in the momentum space are obtained based on the Bethe ansatz. If the number of bosons is equal to that of fermions and the filling factor is 1, it is found that there exists a critical on-site interaction Uc{U}_{c}Uc​. If U<UcU<{U}_{c}U<Uc​, the ground state of the system is in the superfluid phase, while if U>UcU>{U}_{c}U>Uc​, the ground state is in the insulating phase. The superfluid-insulator transition occurs at Uc{U}_{c}Uc​. From the analysis of the superfluid density, the value of the critical point is determined as Uc=2.79256{U}_{c}=2.79256Uc​=2.79256, which is larger than the Uc=0{U}_{c}=0Uc​=0 for the Fermi-Hubbard model and smaller than the Uc=3.28{U}_{c}=3.28Uc​=3.28 for the Bose-Hubbard model. The elementary excitations and effective Hamiltonian in the strong-coupling limit are also discussed.
The phase diagrams of low density Fermi-Fermi mixtures with equal or unequal masses and equal or unequal populations are described at zero and finite temperatures in the strong attraction limit. In this limit, the Fermi-Fermi mixture can be described by a weakly interacting Bose-Fermi mixture, where the bosons correspond to Feshbach molecules and the fermions correspond to excess atoms. First, we discuss the three and four fermion scattering processes, and use the exact boson-fermion and boson-boson scattering lengths to generate the phase diagrams in terms of the underlying fermion-fermion scattering length. In three dimensions, in addition to the normal and uniform superfluid phases, we find two stable nonuniform states corresponding to (i) phase separation between pure unpaired (excess) and pure paired fermions (molecular bosons); and (ii) phase separation between pure excess fermions and a mixture of excess fermions and molecular bosons. Lastly, we also discuss the effects of the trapping potential in the density profiles of condensed and noncondensed molecular bosons, and excess fermions at zero and finite temperatures, and discuss possible implications of our findings to experiments involving mixtures of ultracold fermions.
We study numerically and analytically the phases of a mixture of ultracold bosons and spin-polarized fermions in a one-dimensional lattice. In particular, along a symmetry plane in the parameter space, we obtain the exact boundary of the boson-demixing transition from the Bethe ansatz solution of the standard Hubbard model. For a region of parameter space, we prove the existence of boson-fermion mixed phase at all densities. This phase is a two-component Luttinger liquid for weak couplings or for incommensurate total density, otherwise it has a charge gap but retains a gapless mode of mixture composition fluctuations. We show that the static density correlations in these two regimes are markedly different.