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arXiv:1706.05623 · Physical Review A

Mass-imbalanced fermionic mixture in a harmonic trap

Betzalel Bazak

Published Aug 23, 2017• 5 citations
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Abstract

The mass-imbalanced fermionic mixture is studied, where $N\ensuremath{\le}5$ identical fermions interact resonantly with an impurity, a distinguishable atom. The shell structure is explored, and the physics of a dynamic light-impurity is shown to be different from that of the static heavy-impurity case. The energies in a harmonic trap at unitarity are calculated and extrapolated to the zero-range limit. In doing so, the scale factor of the ground state, as well as of a few excited states, is calculated. In the $2\ensuremath{\le}N\ensuremath{\le}4$ systems, pure $(N+1)$ Efimov states exist for large enough mass ratio. However, no sign for a six-body Efimov state in the $(5+1)$ system is found in the mass ratio explored, $M/m\ensuremath{\le}12$.

DOI
10.1103/physreva.96.022708

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The mass-imbalanced fermionic mixture is studied, where N\ensuremath≤5N\ensuremath{\le}5N\ensuremath≤5 identical fermions interact resonantly with an impurity, a distinguishable atom. The shell structure is explored, and the physics of a dynamic light-impurity is shown to be different from that of the static heavy-impurity case. The energies in a harmonic trap at unitarity are calculated and extrapolated to the zero-range limit. In doing so, the scale factor of the ground state, as well as of a few excited states, is calculated. In the 2\ensuremath≤N\ensuremath≤42\ensuremath{\le}N\ensuremath{\le}42\ensuremath≤N\ensuremath≤4 systems, pure (N+1)(N+1)(N+1) Efimov states exist for large enough mass ratio. However, no sign for a six-body Efimov state in the (5+1)(5+1)(5+1) system is found in the mass ratio explored, M/m\ensuremath≤12M/m\ensuremath{\le}12M/m\ensuremath≤12.
We show that four heavy fermions interacting resonantly with a lighter atom (4+1 system) become Efimovian at mass ratio 13.279(2), which is smaller than the corresponding 2+1 and 3+1 thresholds. We thus predict the five-body Efimov effect for this system in the regime where any of its subsystem is non-Efimovian. For smaller mass ratios we show the existence and calculate the energy of a universal 4+1 pentamer state, which continues the series of the 2+1 trimer predicted by Kartavtsev and Malykh and 3+1 tetramer discovered by Blume. We also show that the effective-range correction for the light-heavy interaction has a strong effect on all these states and larger effective ranges increase their tendency to bind.
Motivated by recent experimental investigations of Cs-Cs-Li Efimov resonances, this work theoretically investigates the few-body properties of $N\ensuremath{-}1$ noninteracting identical heavy bosons, which interact with a light impurity through a large sss-wave scattering length. For Cs-Cs-Cs-Li, we predict the existence of universal four-body states with energies E4(n,1){E}_{4}^{(n,1)}E4(n,1)​ and E4(n,2){E}_{4}^{(n,2)}E4(n,2)​, which are universally linked to the energy E3(n){E}_{3}^{(n)}E3(n)​ of the nnnth Efimov trimer. For infinitely large $^{133}\mathrm{Cs}\text{\ensuremath{-}}^{6}\mathrm{Li}$ and vanishing $^{133}\mathrm{Cs}\text{\ensuremath{-}}^{133}\mathrm{Cs}$ scattering lengths, we find $({E}_{4}^{(1,1)}/{E}_{3}^{(1)}{)}^{1/2}\ensuremath{\approx}1.51$ and $({E}_{4}^{(1,2)}/{E}_{3}^{(1)}{)}^{1/2}\ensuremath{\approx}1.01$. The $^{133}\mathrm{Cs}\text{\ensuremath{-}}^{6}\mathrm{Li}$ scattering lengths at which these states merge with the four-atom threshold, the dependence of these energy ratios on the mass ratio between the heavy and light atoms, and selected aspects of the generalized Efimov scenario for N>4N>4N>4 are also discussed. Possible implications of our results for ongoing cold atom experiments are presented.
We explore a few-fermion mixture consisting of two components that are repulsively interacting and confined in a one-dimensional harmonic trap. Different scenarios of population imbalance ranging from the completely imbalanced case where the physics of a single impurity in the Fermi sea is discussed to the partially imbalanced and equal population configurations are investigated. For the numerical calculations the multiconfigurational time-dependent Hartree method is employed, extending its application to few-fermion systems. Apart from numerical calculations we generalize our ansatz for a correlated pair wave function proposed recently [I. Brouzos and P. Schmelcher, Phys. Rev. Lett. 108, 045301 (2012)] for bosons to mixtures of fermions. From weak to strong coupling between the components the energies, the densities and the correlation properties of one-dimensional systems change vastly with an upper limit set by fermionization where for infinite repulsion all fermions can be mapped to identical ones. The numerical and analytical treatments are in good agreement with respect to the description of this crossover. We show that for equal populations each pair of different component atoms splits into two single peaks in the density while for partial imbalance additional peaks and plateaus arise for very strong interaction strengths. The case of a single-impurity atom shows rich behavior of the energy and density as we approach fermionization and is directly connected to recent experiments [G. Z\"urn et al., Phys. Rev. Lett. 108, 075303 (2012)].
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.
Abstract We consider a system of three particles, either three identical bosons or two identical fermions plus an impurity, within a three-dimensional isotropic trap interacting via a contact interaction. Using two approaches, one using an infinite sum of basis states for the wavefunction and the other a closed form wavefunction, we calculate the allowable energy eigenstates of the system as a function of the interaction strength, including the strongly and weakly interacting limits. For the fermionic case this is done while maintaining generality regarding particle masses. We find that the two methods of calculating the spectrum are in excellent agreement in the strongly interacting limit. However the infinite sum approach is unable to uniquely specify the energy of Efimov states, but in the strongly interacting limit there is, to a high degree of accuracy, a correspondence between the three-body parameter required by the boundary condition of the closed form approach and the summation truncation order required by the summation approach. This specification of the energies and wavefunctions forms the basis with which thermodynamic variables such as the virial coefficients or Tan contacts, or dynamic phenomena like quench dynamics can be calculated.
Dynamical properties of two-component mass-imbalanced few-fermion systems confined in a one-dimensional harmonic trap following a sudden quench of interactions are studied. It is assumed that initially the system is prepared in the non-interacting ground state and then, after a sudden quench of interactions, the unitary evolution is governed by interacting many-body Hamiltonian. By careful analysis of the evolution of the Loschmidt echo, density distributions of the components, and entanglement entropy between them, the role of mass imbalance and particle number imbalance on the system's evolution stability are investigated. All the quantities studied manifest a dramatic dependence on the number of heavy and lighter fermions in each component at a given quench strength. The results may have implications for upcoming experiments on fermionic mixtures with a well-defined and small number of particles.