One-dimensional Bose-Fermi Mixture Research Articles

Influence of a static electric field on a one-dimensional Bose-Fermi mixture confined in a double-well potential

In this study, we conducted a detailed investigation into the time evolution of the probability density within a 1D double-well potential hosting a Bose-Fermi mixture. This system comprised spinless bosons and spin one-half fermions with weak repulsive contact interactions. Notably, even at very low effective coupling constants, periodic probabilities were observed, indicating correlated tunneling of both bosons and fermions, leading to complete miscibility, which disappears when an external electric field is turned on. The electric field accentuated fermion-fermion interactions due to the Pauli exclusion principle, altering both boson density and interactions and leading to spatial redistribution of particles. These findings underscore the complex interplay between interactions, external fields, and spatial distributions within confined quantum systems. Our exploration of higher interaction strengths revealed conditions under which probability density functions are decoupled. Furthermore, we observed that increased fermion interaction, driven by the electric field, led to higher tunneling frequencies for both species because of the repulsive nature of the boson-fermion interaction. Conversely, increased boson-boson interaction resulted in complete tunneling of both species, especially when boson density was high, leading to effective fermion repulsion. Expanding our analysis to scenarios involving four bosons demonstrated that higher interaction values corresponded to increased oscillation frequencies in tunneling probabilities. Finally, by manipulating interaction parameters and activating the electric field, we achieved complete tunneling of both species, further increasing oscillation frequencies and resulting in intervals characterized by overlapping probability functions.

Exploring phononlike interactions in one-dimensional Bose-Fermi mixtures

Exploring phononlike interactions in one-dimensional Bose-Fermi mixtures

Enhanced visibility of the Fulde-Ferrel-Larkin-Ovchinnikov state in one-dimensional Bose-Fermi mixtures near the immiscibility point

Based on the matrix product states method, we investigate numerically the ground state properties of one-dimensional mixtures of repulsive bosons and spin-imbalanced attractive fermions, the latter being in the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, where Cooper pairs condense at a finite momentum $k=k_{FFLO}$. We find that the visibility of such a state is dramatically enhanced as the repulsive Bose-Fermi mixture is brought close to the phase-separation point. In particular, large amplitude self-induced oscillations with wave-vector $2k_{FFLO}$ appear in both the fermion total density and the boson density profiles, leaving sharp fingerprints in the corresponding static structure factors. We show that these features remain well visible in cold atoms systems trapped longitudinally by a smooth flat-bottom potential. Hence bosons can be used to directly reveal the modulated Fermi superfluid in experiments.

Momentum reconstruction and contact of the one-dimensional Bose-Fermi mixture

We investigate the one-dimensional mixture of scalar bosons and spin polarized fermions interacting through a $\delta$-function potential. Using a thermodynamic description derived by employing a lattice embedding of the continuum model and the quantum transfer matrix method we perform a detailed analysis of the contact and quantum critical behaviour. We show that the compressibility Wilson ratio presents anomalous enhancement at the quantum critical points and that the boundaries of the quantum critical regions can be well mapped by the maxima of the specific heat. As a function of the coupling strength and temperature the contact presents nonmonotonic behavior. In the strong coupling regime the local minimum exhibited by the contact as a function of temperature is accompanied by a significant momentum reconstruction at both low and high momenta. This momentum reconstruction occurs as the system crosses the boundary between the Tomonaga-Luttinger liquid phase to the spin-incoherent regime and provides an experimental signature of the transition.

Higher first Chern numbers in one-dimensional Bose–Fermi mixtures

We propose to use a one-dimensional system consisting of identical fermions in a periodically driven lattice immersed in a Bose gas, to realise topological superfluid phases with Chern numbers larger than 1. The bosons mediate an attractive induced interaction between the fermions, and we derive a simple formula to analyse the topological properties of the resulting pairing. When the coherence length of the bosons is large compared to the lattice spacing and there is a significant next-nearest neighbour hopping for the fermions, the system can realise a superfluid with Chern number ±2. We show that this phase is stable in a large region of the phase diagram as a function of the filling fraction of the fermions and the coherence length of the bosons. Cold atomic gases offer the possibility to realise the proposed system using well-known experimental techniques.

Spin-chain model for strongly interacting one-dimensional Bose-Fermi mixtures

Strongly interacting one-dimensional (1D) Bose--Fermi mixtures form a tunable $XXZ$ spin chain. Within the spin-chain model developed here, all properties of these systems can be calculated from states representing the ordering of the bosons and fermions within the atom chain and from the ground-state wave function of spinless noninteracting fermions. We validate the model by means of an exact diagonalization of the full few-body Hamiltonian in the strongly interacting regime. Using the model, we explore the phase diagram of the atom chain as a function of the boson-boson (BB) and boson-fermion (BF) interaction strengths and calculate the densities, momentum distributions, and trap-level occupancies for up to 17 particles. In particular, we find antiferromagnetic (AFM) and ferromagnetic (FM) order and a demixing of the bosons and fermions in certain interaction regimes. We find, however, no demixing for equally strong BB and BF interactions, in agreement with earlier calculations that combined the Bethe ansatz with a local-density approximation.

Quasiparticle decay in a one-dimensional Bose-Fermi mixture

In a one-dimensional weakly interacting Bose-Fermi mixture one branch of elementary excitations is well described by the Bogoliubov spectrum. Here we use the microscopic theory to study the decay of such quasiparticle excitations. The main scattering process which leads to their decay is the backscattering of a Bogoliubov quasiparticle off the Fermi sea, where a particle-hole pair is excited. For a low-momentum quasiparticle (phonon) of momentum $q$, we find that the decay rate scales as $q^3$ provided $q$ is smaller than the Fermi momentum $k_F$, while in the opposite case the decay behaves as $q^2$. If the ratio of the masses of fermions and bosons equals to the ratio of the boson-fermion and the boson-boson interaction strengths, the decay rate changes dramatically. It scales as $q^7$ for $q<k_F$ while we find $q^6$ scaling at $q>k_F$. For a high momentum Bogoliubov quasiparticle, we find a constant decay rate for $q<k_F$, while it scales as $1/q$ for $q>k_F$. We also find an analytic expression for the decay rate in the crossover region between low and high momenta. The decay rate is a continuous, but nonanalytic function of the momentum at $q=k_F$. In the special case when the parameters of our system correspond to the integrable model, we observe that the decay rate vanishes.

Counterflow superfluid of polaron pairs in Bose-Fermi mixtures in optical lattices

We study the quantum phases of one-dimensional Bose-Fermi mixtures in optical lattices. Assuming repulsive interparticle interactions, equal mass, and unit total filling, we calculate the ground-state phase diagram by means of both the Tomonaga-Luttinger liquid theory and time-evolving block decimation method. We demonstrate the existence of a counterflow superfluid phase of polaron pairs, which are composite particles consisting of two fermions and two bosonic holes, in a broad range of the parameter space. We find that this phase naturally emerges in ${}^{174}$Yb-${}^{173}$Yb mixtures, realized in recent experiments, at low temperatures.

Symmetry breaking of a Bose–Fermi mixture in a triple-well potential

We investigate the properties of a one-dimensional Bose–Fermi mixture in a triple-well potential with two equally populated spin components at zero temperature. Based on the coupled equations for a Bose–Fermi mixture, we illustrate the symmetry breaking of the Bose–Fermi mixture with different strengths of interspecies and intraspecies interactions that are induced by changing the particle numbers of bosons and fermions. The several novel density profiles of symmetric and asymmetric ground states in the phase diagram of the (NF,NB) plane are demonstrated. In addition, the variation of density as a function of NB at fixed NF, which clearly shows the transition among distinct types of symmetric and asymmetric ground states, is illustrated.

Quantum criticality of a one-dimensional Bose-Fermi mixture

The one-dimensional interacting Bose-Fermi mixtures, exhibiting quantum phase transitions at zero temperature, are particularly valuable for the study of quantum critical phenomena. In the present paper, we analytically study quantum phase diagram, equation of state and quantum criticality of the Bose-Fermi mixture using the thermodynamic Bethe ansatz equations. We show that thermodynamical properties display universal scaling behaviour at quantum criticality. Furthermore, quantum criticality of the Bose-Fermi mixture in an harmonic trap is also studied within the local density approximation. We thus demonstrate that the phase diagram and critical properties of the bulk system provide insights into understanding universal features of many-body critical phenomena.

Exact solution for the degenerate ground-state manifold of a strongly interacting one-dimensional Bose-Fermi mixture

We present the exact solution for the many-body wavefunction of a one-dimensional mixture of bosons and spin-polarized fermions with equal masses and infinitely strong repulsive interactions under external confinement. Such a model displays a large degeneracy of the ground state. Using a generalized Bose-Fermi mapping we find the solution for the whole set of ground-state wavefunctions of the degenerate manifold and we characterize them according to group-symmetry considerations. We find that the density profile and the momentum distribution depends on the symmetry of the solution. By combining the wavefunctions of the degenerate manifold with suitable symmetry and guided by the strong-coupling form of the Bethe-Ansatz solution for the homogeneous system we propose an analytic expression for the many-body wavefunction of the inhomogeneous system which well describes the ground state at finite, large and equal interactions strengths, as validated by numerical simulations.

Competition of superfluidity and density waves in one-dimensional Bose-Fermi mixtures

We study a mixture of one-dimensional bosons and spinless fermions at incommensurate filling using phenomenological bosonization and Green's functions techniques. We derive the relation between the parameters of the microscopic Hamiltonian and macroscopic observables. Galilean invariance results in extra constraints for the current current interactions. We obtain the exact exponents for the various response functions, and show that superfluid fluctuations are enhanced by the effective boson-fermion density-density interaction and suppressed by the effective boson-fermion current-current interaction. In the case of a bosonized model with purely density-density interaction, when the effective boson-fermion density-density interaction is weak enough, the superfluid exponent of the bosons has a non-monotonous variation with the ratio of the fermion velocity to the boson velocity. By contrast, density-wave exponent and the exponent for fermionic superfluidity are monotonous functions of the velocity ratio.

Hard-core Bose-Fermi mixture in one-dimensional split traps

We consider a strongly interacting one-dimensional (1D) Bose-Fermi mixture confined in a hard-wall trap or a harmonic oscillator trap with a tunable $\ensuremath{\delta}$-function barrier at the trap center. The mixture consists of a 1D Bose gas with repulsive interactions and of a 1D noninteracting spin-aligned Fermi gas, with both species interacting through hard-core interactions. Using a generalized Bose-Fermi mapping, we calculate the reduced single-particle density matrix and the momentum distribution of the gas as a function of barrier strength and the parity of particle number. The secondary peaks in the momentum distribution show remarkable correlation between particles on the two sides of the split.

Ground-state properties of a one-dimensional strongly interacting Bose-Fermi mixture in a double-well potential

We calculate the reduced single-particle density matrix (RSPDM), momentum distributions, natural orbitals and their occupancies, for a strongly interacting one-dimensional Bose-Fermi mixture in a double-well potential with a large central barrier. For mesoscopic systems, we find that the ground state properties qualitatively differ for mixtures with even number of particles (both odd-odd and even-even mixtures) in comparison to mixtures with odd particle numbers (odd-even and even-odd mixtures). For even mixtures the momentum distribution is smooth, whereas the momentum distribution of odd mixtures possesses distinct modulations; the differences are observed also in the off-diagonal correlations of the RSPDM, and in the occupancies of natural orbitals. The calculation is based on a derived formula which enables efficient calculation of the RSPDM for mesoscopic mixtures in various potentials.

Fermionization of a strongly interacting Bose-Fermi mixture in a one-dimensional harmonic trap

We consider a strongly interacting one-dimensional (1D) Bose-Fermi mixture confined in a harmonic trap. It consists of a Tonks-Girardeau (TG) gas (1D Bose gas with repulsive hard-core interactions) and of a noninteracting Fermi gas (1D spin-aligned Fermi gas), both species interacting through hard-core repulsive interactions. Using a generalized Bose-Fermi mapping, we determine the one-body density matrices, exact particle density profiles, momentum distributions, and behavior of the mixture under 1D expansion when opening the trap. In real space, bosons and fermions do not display any phase separation: the respective density profiles extend over the same region and they both present a number of peaks equal to the total number of particles in the trap. In momentum space the bosonic component has the typical narrow TG profile, while the fermionic component shows a broad distribution with fermionic oscillations at small momenta. Due to the large boson-fermion repulsive interactions, both the bosonic and the fermionic momentum distributions decay as $C{p}^{\ensuremath{-}4}$ at large momenta, like in the case of a pure bosonic TG gas. The coefficient $C$ is related to the two-body density matrix and to the bosonic concentration in the mixture. When opening the trap, both momentum distributions ``fermionize'' under expansion and turn into that of a Fermi gas with a particle number equal to the total number of particles in the mixture.

Superuid and insulator of dirty Bose-Fermi mixture

One-dimensional Bose-Fermi mixture systems in a random potential are numerically investigated with focus on their superfluidity and localization properties. It is known that one-dimensional bosons and fermions behave differently in a weak random potential: Interacting bosons in a weak random potential exhibit superfluidity if the interactions are repulsive and not too strong, while interacting fermions with repulsive forces are localized in the presence of randomness. So the question is what happens if weakly interacting bosons and fermions are mixed in a random potential, which might be actually realized by the technique of trapping atoms on a random optical lattice. To answer this question we performed quantum Monte Carlo simulations of bosons and fermions on a one-dimensional lattice with random site energies. The result showed that when the boson-fermion interactions were attractive, both bosons and fermions tended to be localized. However when the boson- fermion interactions were repulsive and relatively weak, the superfluidity of bosons was enhanced and the fermions were delocalized.

Supersolids in one-dimensional Bose-Fermi mixtures

Using quantum Monte Carlo simulations, we study a mixture of bosons and fermions loaded on an optical lattice. With simple on-site repulsive interactions, this system can be driven into a solid phase. We dope this phase and, in analogy with pure bosonic systems, identify the conditions under which the bosons enter a supersolid phase, i.e., exhibit at the same time charge density-wave and superfluid order. We perform finite-size scaling analysis to confirm the presence of a supersolid phase and discuss its properties, showing that it is a collective phase that also involve phase coherence of the fermions.

Superfluid and Mott-insulator phases of one-dimensional Bose-Fermi mixtures

We study the ground state phases of Bose-Fermi mixtures in one-dimensional optical lattices with quantum Monte Carlo simulations using the canonical worm algorithm. Depending on the filling of bosons and fermions, and the on-site intra- and interspecies interaction, different kinds of incompressible and superfluid phases appear. On the compressible side, correlations between bosons and fermions can lead to a distinctive behavior of the bosonic superfluid density and the fermionic stiffness, as well as of the equal-time Green functions, which allow one to identify regions where the two species exhibit anticorrelated flow. We present here complete phase diagrams for these systems at different fillings and as a function of the interaction parameters.

Quantum Monte Carlo study of the visibility of one-dimensional Bose-Fermi mixtures

The study of ultracold optically trapped atoms has opened new vistas in the physics of correlated quantum systems. Much attention has now turned to mixtures of bosonic and fermionic atoms. A central puzzle is the disagreement between the experimental observation of a reduced bosonic visibility ${\mathcal{V}}_{b}$, and quantum Monte Carlo (QMC) calculations which show ${\mathcal{V}}_{b}$ increasing. In this paper, we present QMC simulations which evaluate the density profiles and ${\mathcal{V}}_{b}$ of mixtures of bosons and fermions in one-dimensional optical lattices. We resolve the discrepancy between theory and experiment by identifying parameter regimes where ${\mathcal{V}}_{b}$ is reduced, and where it is increased. We present a simple qualitative picture of the different response to the fermion admixture in terms of the superfluid and Mott-insulating domains before and after the fermions are included. Finally, we show that ${\mathcal{V}}_{b}$ exhibits kinks which are tied to the domain evolution present in the pure case, and also additional structure arising from the formation of boson-fermion molecules, a prediction for future experiments.

Pairing of one-dimensional Bose-Fermi mixtures with unequal masses

We have considered one-dimensional Bose-Fermi mixture with equal densities and unequal masses using numerical density matrix renormalization group. For the mass ratio of K-Rb mixture and attraction between bosons and fermions, we determined the phase diagram. For weak boson-boson interactions, there is a direct transition between two-component Luttinger liquid and collapsed phases as the boson-fermion attraction is increased. For strong enough boson-boson interactions, we find an intermediate ``paired'' phase, which is a single-component Luttinger liquid of composite particles. We investigated correlation functions of such a ``paired'' phase, studied the stability of ``paired'' phase to density imbalance, and discussed various experimental techniques which can be used to detect it.