We study measurable quantities of bosonic and fermionic mixtures on a one-dimensional ring. These few-body ensembles consist of majority atoms obeying certain statistics (Fermi or Bose) and an impurity atom in a different hyperfine state. The repulsive interactions between majority-impurity and majority-majority are varied from weak to strong. We show that the majority-impurity repulsion is mainly responsible for the loss of coherence in the strongly interacting regime. The momentum distribution follows the $\mathcal{C}/p^4$ universal behaviour for the high momentum tail, but the contact $\mathcal{C}$ is strongly dependent on the strength of the majority-impurity and in a different way on the majority-majority interactions. The static structure factor of the majority atoms exposes a low-momentum peak for strong majority-impurity repulsion, which is attributed to an effective attraction not expected for purely repulsive forces.
We introduce a density functional formalism to study the ground-state properties of strongly-correlated dipolar and ionic ultracold bosonic and fermionic gases, based on the self-consistent combination of the weak and the strong coupling limits. Contrary to conventional density functional approaches, our formalism does not require a previous calculation of the interacting homogeneous gas, and it is thus very suitable to treat systems with tunable long-range interactions. Due to its asymptotic exactness in the regime of strong correlation, the formalism works for systems in which standard mean-…
In this paper we address the ratio of the shear viscosity to entropy density $η/s$ in bosonic and fermionic superfluids. A small $η/s$ is associated with nearly perfect fluidity, and more general measures of the fluidity perfection/imperfection are of wide interest to a number of communities. We use a Kubo approach to concretely address this ratio via low temperature transport associated with the quasi-particles. Our analysis for bosonic superfluids utilizes the framework of the one-loop Bogoliubov approximation, whereas for fermionic superfluids we apply BCS theory and its BCS-BEC extension. …
We consider a mixture of two bosonic species with tunable interspecies interaction in a periodic potential and discuss the advantages of low filling factors on the detection of the pair-superfluid phase. We show how the emergence of such a phase can be put dramatically into evidence by looking at the interference pictures and density correlations after expansion and by changing the interspecies interaction from attractive to repulsive.
We develop a self-contained approach to bosonization and refermionization using the Keldysh functional integral. Starting from fermionic particles, we bosonize the system and obtain a description in terms of the Tomonaga-Luttinger liquid, with, in addition, an infinite series of interaction terms arising from the curvature of the fermionic particle spectrum. We explicitly calculate the leading interaction term and check its consistency with a different approach based on the Matsubara framework, within which we calculate the second leading interaction term, as well. Moreover, we bosonize weakly…
We discuss the master equation approach to diffusive current of bosonic or fermionic carriers in one- and two-dimensional lattices. This approach is shown to reproduce all known results of the linear response theory, including the integer quantum Hall effect for fermionic carriers. The main advantage of the approach is that it allows to calculate the current beyond the linear response regime where new effects are found. In particular, we show that the Hall current can be inverted by changing orientation of the static force (electric field) relative to the primary axes of the lattice.
We show that dipolar bosons and fermions confined in a quasi-one-dimensional ring trap exhibit a rich variety of states because their interaction is inhomogeneous. For purely repulsive interactions, with increasing strength of the dipolar coupling there is a crossover from a gas-like state to an inhomogeneous crystal-like one. For small enough angles between the dipoles and the plane of the ring, there are regions with attractive interactions, and clustered states can form.
We investigate topological phase transitions driven by interaction and identify a novel topological Mott insulator state in one-dimensional fermionic optical superlattices through numerical density matrix renormalization group (DMRG) method. Remarkably, the low-energy edge excitations change from spin-1/2 fermionic single-particle modes to spin-1 bosonic collective modes across the phase transition. Due to spin-charge separation, the low-energy theory is governed by an effective spin superexchange model, whereas the charge degree of freedom is fully gapped out. Such topological Mott state can …
We show that the dynamics of quenches in one dimension far off equilibrium can be described by power laws, but with exponents differing from the fully renormalized ones at lowest energies. Instead they depend on the initial state and its excitation energy. Furthermore, we found that for quenches to strong interactions unexpected similarities between systems in one and in infinite dimensions occur, indicating the dominance of local processes.
Motivated by recent experiments and theoretical investigations on binary mixtures, we investigate the miscible-immiscible transition at finite temperature by means of Quantum Monte Carlo. Based on the observation that the segregated phase is strongly affected by temperature, we propose to use the degree of demixing for thermometry of a binary bosonic mixture trapped in an optical lattice. We show that the proposed method is especially sensitive at low temperatures, of the order of the tunnelling amplitude, and therefore is particularly suitable in the regime where quantum magnetism is expected…
We present an exactly-solvable $p$-wave pairing model for two bosonic species. The model is solvable in any spatial dimension and shares some commonalities with the $p + ip$ Richardson-Gaudin fermionic model, such as a third order quantum phase transition. However, contrary to the fermionic case, in the bosonic model the transition separates a gapless fragmented singlet pair condensate from a pair Bose superfluid, and the exact eigenstate at the quantum critical point is a pair condensate analogous to the fermionic Moore-Read state.
By means of full exact diagonalization, we study level statistics and the structure of the eigenvectors of one-dimensional gapless bosonic and fermionic systems across the transition from integrability to quantum chaos. These systems are integrable in the presence of only nearest-neighbor terms, whereas the addition of next-nearest neighbor hopping and interaction may lead to the onset of chaos. We show that the strength of the next-nearest neighbor terms required to observe clear signatures of nonintegrability is inversely proportional to the system size. Interestingly, the transition to chao…
We present a scheme to implement a Fermi-Hubbard-like model in ultracold atoms in optical lattices and analyze the topological features of its ground state. In particular, we show that the ground state for appropriate parameters has a large overlap with a lattice version of the bosonic Laughlin state at filling factor one half. The scheme utilizes laser assisted and normal tunnelling in a checkerboard optical lattice. The requirements on temperature, interactions, and hopping strengths are similar to those needed to observe the Néel antiferromagnetic ordering in the standard Fermi-Hubbard mode…
We unravel the nonequilibrium dynamics of two fermionic impurities immersed in a one-dimensional bosonic gas following an interspecies interaction quench from weak to strong repulsions. Monitoring the temporal evolution of the single-particle density of each species we reveal the existence of four distinct dynamical regimes. For weak interspecies repulsions both species either perform a breathing motion or the impurity density splits into two parts which interact and disperse within the bosonic cloud. Turning to strong interactions we observe the formation of dark-bright states within the mean…
We extent the recently developed Multi-Layer Multi-Configuration Time-Dependent Hartree method for Bosons (ML-MCTDHB) for simulating the correlated quantum dynamics of bosonic mixtures to the fermionic sector and establish a unifying approach for the investigation of the correlated quantum dynamics of mixture of indistinguishable particles, be it fermions or bosons. Relying on a multi-layer wave-function expansion, the resulting Multi-Layer Multi-Configuration Time-Dependent Hartree method for Mixtures (ML-MCTDHX) can be adapted to efficiently resolve system-specific intra- and inter-species c…
We show that, near a Feshbach resonance, a strong p-wave resonance is present at low energy in atom-dimer scattering for $^6$Li-$^{40}$K fermionic mixtures. This resonance is due to a virtual bound state, in the atom-dimer system, which is present at this low energy. When the mass ratio between the two fermionic elements is increased, this virtual bound state goes to a known real bound state which appears when the mass ratio reaches 8.17. This resonance should affect a number of physical properties. These include the equation of state of unbalanced mixtures at very low temperature but also the…
