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arXiv:1906.03573 · Physical Review A

Mass-imbalance-induced structures of binary atomic mixtures in box potentials

Bishal Parajuli, Daniel Pęcak, Chih-Chun Chien

Published Dec 9, 2019• 10 citations
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Abstract

We consider the ground states of binary atomic boson-boson and fermion-fermion mixtures confined in one-dimensional box potentials by simulating the systems using few-body models with $\ensuremath{\delta}$-function interactions and many-body models with density-density interactions. For boson-boson mixtures with strong interspecies repulsion, both models show sandwiched structures in the presence of mass imbalance but not in the equal-mass case. The structural difference between equal-mass and mass-imbalanced systems is due to the minimization of the interaction energy and the kinetic energies from the density distortion at the hard walls and at the phase-separation interface. The mass imbalance adjusts the kinetic energies and causes the lighter species to avoid the hard walls. For fermion-fermion mixtures, few-body simulations show mass-imbalance-induced structural changes in the strong-repulsion regime, while many-body simulations show two-chunk phase separation due to the strong bulk kinetic energy. For equal-mass mixtures with strong interspecies repulsion, the few-body and many-body models predict different structures because of the different treatments of kinetic and interaction energies.

DOI
10.1103/physreva.100.063623

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We consider the ground states of binary atomic boson-boson and fermion-fermion mixtures confined in one-dimensional box potentials by simulating the systems using few-body models with \ensuremathδ\ensuremath{\delta}\ensuremathδ-function interactions and many-body models with density-density interactions. For boson-boson mixtures with strong interspecies repulsion, both models show sandwiched structures in the presence of mass imbalance but not in the equal-mass case. The structural difference between equal-mass and mass-imbalanced systems is due to the minimization of the interaction energy and the kinetic energies from the density distortion at the hard walls and at the phase-separation interface. The mass imbalance adjusts the kinetic energies and causes the lighter species to avoid the hard walls. For fermion-fermion mixtures, few-body simulations show mass-imbalance-induced structural changes in the strong-repulsion regime, while many-body simulations show two-chunk phase separation due to the strong bulk kinetic energy. For equal-mass mixtures with strong interspecies repulsion, the few-body and many-body models predict different structures because of the different treatments of kinetic and interaction energies.
We study binary atomic boson-fermion mixtures confined in one dimensional box potentials by few-body theory with contact interactions and mean-field many-body theory with density-density interactions. A variety of correlations and structures arise as the inter- and intraspecies interactions are tuned. Both few-body and many-body results show that miscible phase and three-chunk phase separation are directly observable in the density profiles. Meanwhile, two-chunk phase separation can be inferred from the few-body correlations and many-body density profiles. We present phase diagrams of selected types of atomic mixtures to show where different structures survive. The few-body analysis demonstrates that two-body correlation functions can reveal information relevant to the results from many-body calculations or experiments. From the many-body density profiles in the phase-separation regime, we extract the healing lengths of both species and explain the scaling behavior by an energy-competition argument.
Abstract In this paper we study a mixed system of bosons and fermions with up to six particles in total. All particles are assumed to have the same mass. The two-body interactions are repulsive and are assumed to have equal strength in both the Bose–Bose and the Fermi–Boson channels. The particles are confined externally by a harmonic oscillator one-body potential. For the case of four particles, two identical fermions and two identical bosons, we focus on the strongly interacting regime and analyze the system using both an analytical approach and density matrix renormalization group calculations using a discrete version of the underlying continuum Hamiltonian. This provides us with insight into both the ground state and the manifold of excited states that are almost degenerate for large interaction strength. Our results show great variation in the density profiles for bosons and fermions in different states for strongly interacting mixtures. By moving to slightly larger systems, we find that the ground state of balanced mixtures of four to six particles tends to separate bosons and fermions for strong (repulsive) interactions. On the other hand, in imbalanced Bose–Fermi mixtures we find pronounced odd–even effects in systems of five particles. These few-body results suggest that question of phase separation in one-dimensional confined mixtures are very sensitive to system composition, both for the ground state and the excited states.
We study the ground-state properties and quantum dynamics of few-boson mixtures with strong interspecies repulsion in one-dimensional traps. If one species localizes at the center, e.g., due to a very large mass compared to the other component, it represents an effective barrier for the latter, and the system can be mapped onto identical bosons in a double well. For weaker localization, the barrier atoms begin to respond to the light component, leading to an induced attraction between the mobile atoms that may even outweigh their bare intraspecies repulsion. To explain the resulting effects, we derive an effective Hubbard model for the lighter species accounting for the back action of the barrier in correction terms to the lattice parameters. Also the tunneling is drastically affected: by varying the degree of localization of the ``barrier'' atoms, the dynamics of intrinsically noninteracting bosons can change from Rabi oscillations to effective pair tunneling. For identical fermions (or fermionized bosons), this leads to the tunneling of attractively bound pairs.
We present possible ground-state structures of two-component atomic Fermi gases with repulsive interactions in a thin spherical shell geometry by implementing a self-consistent Hartree-Fock approximation. The system exhibits a miscible-immiscible transition from a homogeneous mixture to two-chunk phase separation as the interaction strength crosses a critical value. While the critical value is relatively insensitive to population imbalance for equal-mass mixtures, it decreases with the mass ratio when mass imbalance is present. The interaction may be tuned by the two-body scattering length or the radius of the sphere, thereby allowing the system to cross the transition by varying different parameters. When the atoms on the sphere are rotating, three-chunk sandwich structures emerge in mass-imbalanced mixtures as a consequence of maximal angular momentum along the rotation axis. Some indications of geometric effects and possible experimental implications are also discussed.
We study repulsive two-component Bose mixtures with equal populations and confined in a finite-size box through path-integral Monte Carlo simulations.For different values of the s-wave scattering length of the interspecies potential, we calculate the local population imbalance in a region of fixed volume inside the box at different temperatures.We find two different behaviors: For phase-separated states at T = 0, thermal effects induce a diffusion process which reduces the local imbalance, whereas for miscible states at T = 0, a maximum in the local population imbalance appears at a certain temperature, below the critical one.We show that this intriguing behavior is strongly related to the bunching effect associated with the Bose-Einstein statistics of the particles in the mixture and to an unexpected behavior of the cross pair distribution function.
We consider a homogeneous Bose-Fermi mixture, with the boson-fermion interaction tuned by a Fano-Feshbach resonance, in the presence of mass and density imbalance between the two species. By using many-body diagrammatic methods, we first study the finite-temperature phase diagram for the specific case of the mass-imbalanced mixture 87{}^{87}87Rb-40{}^{40}40K for different values of the density imbalance. We then analyze the quantum phase transition associated with the disappearance at zero temperature of the boson condensate above a critical boson-fermion coupling. We find a pronounced dependence of the critical coupling on the mass ratio and a weak dependence on the density imbalance. For a vanishingly small boson density, we derive, within our approximation, the asymptotic expressions for the critical coupling in the limits of small and large mass ratios. These expressions are relevant also for the polaron-molecule transition in a Fermi mixture at small and large mass ratios. The analysis of the momentum distribution functions at sufficiently large density imbalances shows an interesting effect in the bosonic momentum distribution due to the simultaneous presence of composite fermions and unpaired fermions.