Effect of interactions on harmonically confined Bose-Fermi mixtures in optical lattices

We investigate a Bose-Fermi mixture in a three-dimensional optical lattice, trapped in a harmonic potential. Using generalized dynamical mean-field theory, which treats the Bose-Bose and Bose-Fermi interaction in a fully nonperturbative way, we show that for experimentally relevant parameters a peak in the condensate fraction close to the point of vanishing Bose-Fermi interaction is reproduced within a single-band framework. We identify two physical mechanisms contributing to this effect: the spatial redistribution of particles when the interspecies interaction is changed and the reduced phase space for strong interactions, which results in a higher temperature at fixed entropy.     

Bose-fermi mixtures in a three-dimensional optical lattice

We have studied mixtures of fermionic (40)K and bosonic (87)Rb quantum gases in a three-dimensional optical lattice. We observe that an increasing admixture of the fermionic species diminishes the phase coherence of the bosonic atoms as measured by studying both the visibility of the matter wave interference pattern and the coherence length of the bosons. Moreover, we find that the attractive interactions between bosons and fermions lead to an increase of the boson density in the lattice which we measure by studying three-body recombination in the lattice. In our data, we do not observe three-body loss of the fermionic atoms. An analysis of the thermodynamics of a noninteracting Bose-Fermi mixture in the lattice suggests a mechanism for sympathetic cooling of the fermions in the lattice.     

High-temperature atomic superfluidity in lattice Bose-Fermi mixtures

We consider atomic Bose-Fermi mixtures in optical lattices and study the superfluidity of fermionic atoms due to s-wave pairing induced by boson-fermion interactions. We prove that the induced fermion-fermion coupling is always attractive if the boson-boson on-site interaction is repulsive, and predict the existence of an enhanced BEC-BCS crossover as the strength of the lattice potential is varied. We show that for direct on-site fermion-fermion repulsion, the induced attraction can give rise to superfluidity via s-wave pairing at striking variance with the case of pure systems of fermionic atoms with direct repulsive interactions.     

Multiband spectroscopy of ultracold fermions: observation of reduced tunneling in attractive Bose-Fermi mixtures

We perform a detailed experimental study of the band excitations and tunneling properties of ultracold fermions in optical lattices. Employing a novel multiband spectroscopy for fermionic atoms, we can measure the full band structure and tunneling energy with high accuracy. In an attractive Bose-Fermi mixture we observe a significant reduction of the fermionic tunneling energy, which depends on the relative atom numbers. We attribute this to an interaction-induced increase of the lattice depth due to the self-trapping of the atoms.     

Landau-Zener tunneling of Bose-Fermi mixture in double-well

The nonlinear Landau-Zener tunneling of a Bose-Fermi mixture in a double-well potential is studied in the present paper. The effect of interaction parameters on bosonic and fermionic tunneling probability is studied for the mixture of ⁴⁰K-⁸⁷Rb. The tunneling phenomena of the system can be controled by adjusting sweeping rate, intraspecies interaction, interspecies interaction and the numbers of bosons and fermions. It is noted that there are three different regions in phase diagram: self-trapping (ST), complete tunneling (CT) and incomplete tunneling (ICT).     

Ultracold heteronuclear molecules and ferroelectric superfluids

We analyze the possibility of a ferroelectric transition in heteronuclear molecules consisting of Bose-Bose, Bose-Fermi, or Fermi-Fermi atom pairs. This transition is characterized by the appearance of a spontaneous electric polarization below a critical temperature. We discuss the existence of a ferroelectric Fermi liquid phase for Fermi molecules and the existence of a ferroelectric superfluid phase for Bose molecules characterized by the coexistence of ferroelectric and superfluid orders. Lastly, we propose an experiment to detect ferroelectric correlations through the observation of coherent dipole radiation pulses.     

Tunable Range Interactions and Multi-Roton Excitations for Bosons in a Bose-Fermi Mixture with Optical Lattices *

In this article, we discuss a method to control the long-range interactions between bosons in a three-dimensional Bose-Fermi mixture with the help of optical lattices on fermions. We find the range and the peaked momentum of the fermion-mediated interactions can be tuned by the optical lattice depth and the fermion density. If the fermion density is close to half-filling, roton excitations can be generated with weak Bose-Fermi interactions. Further, if the fermions are not exact at half-filling, multi-roton structure may emerge, implying competing density orders. Therefore, tuning the lattice depth and the fermion density in a Bose-Fermi mixture serves as an effective way to control the interaction range and resonant momentum between bosons.     

Density and stability in ultracold dilute boson-fermion mixtures

We analyze in detail recent experiments on ultracold dilute ⁸⁷Rb–⁴⁰K mixtures in Hamburg and in Florence within a mean-field theory. To this end we determine how the stationary bosonic and fermionic density profiles in this mixture depend in the Thomas-Fermi limit on the respective particle numbers. Furthermore, we investigate how the observed stability of the Bose-Fermi mixture with respect to collapse is crucially related to the value of the interspecies s-wave scattering length.     

双势阱中玻色-费米混合气体的周期调制效应

在周期调制场下, 通过对双势阱中费米子数目及相互作用参数的调节, 研究了该系统中玻色子的自俘获现象. 研究发现, 系统中费米子数目及相互作用参数都会影响玻色子的自俘获现象, 并且随着 相互作用及粒子数目的变化, 玻色子的自俘获发生临界现象. 关键词： 玻色-费米混合气体 周期调制 自俘获     

Supersolid bose-fermi mixtures in optical lattices

We study a mixture of strongly interacting bosons and spinless fermions with on-site repulsion in a three-dimensional optical lattice. For this purpose we develop and apply a generalized dynamical mean-field theory, which is exact in infinite dimensions and reliably describes the full range from weak to strong coupling. We restrict ourselves to half filling. For weak Bose-Fermi repulsion a supersolid forms, in which bosonic superfluidity coexists with charge-density wave order. For stronger interspecies repulsion the bosons become localized while the charge-density wave order persists. The system is unstable against phase separation for weak repulsion among the bosons.     

Topological properties of one-dimensional hardcore Bose-Fermi mixture

We study the topological properties of a one-dimensional （1D） hardcore Bose-Fermi mixture using the exact diagonalization method. We firstly add a hardcore boson to a fermionic system and by examining the edge states we find that the quasi-particle manifests the topological properties of the system. Then we study a mixture with 7 fermions and 1 boson. We find that the mixture also exhibits topological properties and its behaviors are similar to that of the corresponding fermionic system. We present a qualitative explanation to understand such behaviors using the mapping between a hardcore boson and a spinless fermion. These results show the existence of topological properties in a 1D hardcore Bose-Fermi mixture and may be realized using cold atoms trapped in optical lattices experimentally.     

Interaction-dependent temperature effects in Bose-Fermi mixtures in optical lattices

We present a quantitative finite temperature analysis of a recent experiment with Bose-Fermi mixtures in optical lattices, in which the dependence of the coherence of bosons on the interspecies interaction was analyzed. Our theory reproduces the characteristics of this dependence and suggests that intrinsic temperature effects play an important role in these systems. Namely, under the assumption that the ramping up of the optical lattice is an isentropic process, adiabatic temperature changes of the mixture occur that depend on the interaction between bosons and fermions. Matching the entropy of two regimes-no lattice on the one hand and deep lattices on the other-allows us to compute the temperature in the lattice and the visibility of the quasimomentum distribution of the bosonic atoms, which we compare to the experiment.     

Critical Kondo destruction and the violation of the quantum-to-classical mapping of quantum criticality

Antiferromagnetic heavy fermion metals close to their quantum critical points display a richness in their physical properties unanticipated by the traditional approach to quantum criticality, which describes the critical properties solely in terms of fluctuations of the order parameter. This has led to the question as to how the Kondo effect gets destroyed as the system undergoes a phase change. In one approach to the problem, Kondo lattice systems are studied through a self-consistent Bose-Fermi Kondo model within the extended dynamical mean field theory. The quantum phase transition of the Kondo lattice is thus mapped onto that of a sub-Ohmic Bose-Fermi Kondo model. In the present article we address some aspects of the failure of the standard order-parameter functional for the Kondo-destroying quantum critical point of the Bose-Fermi Kondo model.     

Hidden Caldeira-Leggett dissipation in a Bose-Fermi Kondo model

We show that the Bose-Fermi Kondo model (BFKM), which may find applicability both to certain dissipative mesoscopic qubit devices and to heavy-fermion systems described by the Kondo lattice model, can be mapped exactly onto the Caldeira-Leggett model. This mapping requires an ohmic bosonic bath and an Ising-type coupling between the latter and the impurity spin. This allows us to conclude unambiguously that there is an emergent Kosterlitz-Thouless quantum phase transition in the BFKM with an ohmic bosonic bath. By applying a bosonic numerical renormalization group approach, we thoroughly probe physical quantities close to the quantum phase transition.     

Soluble models of strongly interacting ultracold gas mixtures in tight waveguides

A Fermi-Bose mapping method is used to determine the exact ground states of several models of mixtures of strongly interacting ultracold gases in tight waveguides, which are generalizations of the Tonks-Girardeau (TG) gas (1D Bose gas with point hard cores) and fermionic Tonks-Girardeau (FTG) gas (1D spin-aligned Fermi gas with infinitely strong zero-range attractions). We detail the case of a Bose-Fermi mixture with TG boson-boson (BB) and boson-fermion (BF) interactions. Exact results are given for density profiles in a harmonic trap, single-particle density matrices, momentum distributions, and density-density correlations. Since the ground state is highly degenerate, we analyze the splitting of the ground manifold for large but finite BB and BF repulsions.     

Newton-Leibniz integration for ket-bra operators (III)—Application in fermionic quantum statistics

The Newton-Leibniz integration over Dirac’s ket-bra operators introduced in Ref. [Hong-yi Fan, Hai-liang Lu, Yue Fan, Ann. Phys. 321 (2006) 480-494] is generalized to Newton-Leibniz-Berezin integration over fermionic ket-bra projection operators, the corresponding technique of integration within an ordered product (IWOP) of Fermi operators is proposed which is then used to develop fermionic quantum statistics. The generalized partition function formula of multi-mode quadratic interacting fermion is derived via the fermionic coherent state representation and the IWOP technique. The two-mode fermionic squeezing operators and their group property studied by their fermionic coherent state representation as well as fermionic permutation operator are also deduced in this way. Thus Dirac’s symbolic method for Fermi system can also be developed, which exhibits Bose-Fermi supersymmetry in this aspect.     

Collisional stability of fermionic Feshbach molecules

Using a Feshbach resonance, we create ultracold fermionic molecules starting from a Bose-Fermi atom gas mixture. The resulting mixture of atoms and weakly bound molecules provides a rich system for studying few-body collisions because of the variety of atomic collision partners for molecules; either bosonic, fermionic, or distinguishable atoms. Inelastic loss of the molecules near the Feshbach resonance is dramatically affected by the quantum statistics of the colliding particles and the scattering length. In particular, we observe a molecule lifetime as long as 100 ms near the Feshbach resonance.     

Superfluidity and dimerization in a multilayered system of fermionic polar molecules

We consider a layered system of fermionic molecules with permanent dipole moments aligned perpendicular to the layers by an external field. The dipole interactions between fermions in adjacent layers are attractive and induce interlayer pairing. Because of the competition for pairing among adjacent layers, the mean-field ground state of the layered system is a dimerized superfluid, with pairing only between every other layer. We construct an effective Ising-XY lattice model that describes the interplay between dimerization and superfluid phase fluctuations. In addition to the dimerized superfluid ground state, and high-temperature normal state, at intermediate temperature, we find an unusual dimerized "pseudogap" state with only short-range phase coherence. We propose light-scattering experiments to detect dimerization.     

Tunneling control and localization for Bose-Einstein condensates in a frequency modulated optical lattice

The similarity between matter waves in periodic potential and solid-state physics processes has triggered the interest in quantum simulation using Bose-Fermi ultracold gases in optical lattices. The present work evidences the similarity between electrons moving under the application of oscillating electromagnetic fields and matter waves experiencing an optical lattice modulated by a frequency difference, equivalent to a spatially shaken periodic potential. We demonstrate that the tunneling properties of a Bose-Einstein condensate in shaken periodic potentials can be precisely controlled. We take additional crucial steps towards future applications of this method by proving that the strong shaking of the optical lattice preserves the coherence of the matter wavefunction and that the shaking parameters can be changed adiabatically, even in the presence of interactions. We induce reversibly the quantum phase transition to the Mott insulator in a driven periodic potential.     

New directions in degenerate dipolar molecules via collective association

We survey results on the creation of heteronuclear Fermi molecules by tuning a degenerate Bose-Fermi mixture into the neighborhood of an association resonance, either photoassociation or Feshbach, as well as the subsequent prospects for Cooper-like pairing between atoms and molecules. In the simplest case of only one molecular state, corresponding to either a Feshbach resonance or one-color photoassociation, the system displays Rabi oscillations and rapid adiabatic passage between a Bose-Fermi mixture of atoms and fermionic molecules. For two-color photoassociation, the system admits stimulated Raman adiabatic passage (STIRAP) from a Bose-Fermi mixture of atoms to stable Fermi molecules, even in the presence of particle-particle interactions. By tailoring the STIRAP sequence it is possible to deliberately convert only a fraction of the initial atoms, leaving a finite fraction of bosons behind to induce atom-molecule Cooper pairing via density fluctuations; unfortunately, this enhancement is insufficient to achieve a superfluid transition with present ultracold technology. We therefore propose the use of an association resonance that converts atoms and diatomic molecules (dimers) into triatomic molecules (trimers), which leads to a crossover from a Bose-Einstein condensate of trimers to atom-dimer Cooper pairs. Because heteronuclear dimers may possess a permanent electric dipole moment, this overall system presents an opportunity to investigate novel microscopic physics.Received: 16 June 2004, Published online: 21 September 2004PACS: 03.75.Ss Degenerate Fermi gases - 05.30.Fk Fermion systems and electron gas - 34.10. + x General theories and models of atomic and molecular collisions and interactions (including statistical theories, transition state, stochastic and trajectory models, etc.) - 74.20.Mn Nonconventional mechanisms (spin fluctuations, polarons and bipolarons, resonating valence bond model, anyon mechanism, marginal Fermi liquid, Luttinger liquid, etc.) - 21.10.-k Properties of nuclei; nuclear energy levels