Alkaline-earth-metal atoms have a long-lived electronic excited state, and when atoms in this excited state are localized in the Fermi sea of ground-state atoms by an external potential, they serve as magnetic impurities, due to the spin-exchange interaction between the excited- and the ground-state atoms. This can give rise to the Kondo effect. However, in order to achieve this effect in current atomic gas experiments, it requires the Kondo temperature to be increased to a sizable portion of the Fermi temperature. In this paper we calculate the confinement-induced resonance (CIR) for the spin-exchanging interaction between the ground and the excited states of the alkaline-earth-metal atoms and propose that the spin-exchange interaction can be strongly enhanced by utilizing the CIR. We analyze this system by the renormalization-group approach and show that near a CIR, the Kondo temperature can be significantly enhanced.
A nuclear-spin-exchange interaction exists between two ultracold fermionic alkali-earth-metal-like atoms in the electronic
1S0 state (
g state) and
3P0 state (
e state) and is an essential ingredient for the quantum simulation of the Kondo effect. We study the control of this spin-exchange interaction for two atoms simultaneously confined in a quasi-one-dimensional (quasi-1D) tube, where the
g atom is freely moving in the axial direction while the
e atom is further localized by an additional axial trap and behaves as a quasi-0D impurity. In this system, the two atoms experience effective 1D spin-exchange interactions in both even and odd partial-wave channels, whose intensities can be controlled by the characteristic lengths of the confinements via confinement-induced resonances (CIRs). In a previous work, we studied this problem with a simplified pure 1D model [Y. Cheng et al., Phys. Rev. A 96, 063605 (2017)]. In the present work, we go beyond that pure 1D approximation. We model the transverse and axial confinements by harmonic traps with finite characteristic lengths ${a}_{\ensuremath{\perp}}$ and
az, respectively, and exactly solve the quasi-1D--quasi-0D scattering problem between these two atoms. Using the solutions, we derive the effective 1D spin-exchange interaction and investigate the locations and widths of the even-odd wave CIRs for our system. It is found that when the ratio ${a}_{z}/{a}_{\ensuremath{\perp}}$ is larger, the CIRs can be induced by weaker confinements, which are easier to be realized experimentally. The comparison between our results and a recent experiment by L. Riegger et al. [Phys. Rev. Lett. 120, 143601 (2018)] shows that the two experimentally observed resonance branches of the spin-exchange effect are due to an even-wave CIR and an odd-wave CIR, respectively. Our results are advantageous for the control and description of either the effective spin-exchange interaction or other types of interactions between ultracold atoms in quasi-(1+0)-dimensional systems.
A recent experiment has observed Feshbach resonances between alkali and alkaline-earth-metal atoms. These Feshbach resonances are insensitive to the nuclear spin of alkaline-earth-metal atoms. Utilizing this feature, we propose to take this system as a candidate to perform quantum simulation of the Kondo effect. An alkali-metal atom can form a molecule with an alkaline-earth-metal atom with different nuclear spins, which plays the role of spin-exchange scattering responsible for the Kondo effect. Furthermore, we point out that the existence of three-body bound state and atom-molecule resonance due to the Efimov effect can enhance this spin-exchange scattering and therefore enhance the Kondo effect. We discuss this mechanism first with a three-body problem in free space and then demonstrate that the same mechanism still holds when the alkali-metal atom is localized by an external trap and becomes an impurity embedded in the alkaline-earth-metal atomic gases.
We study the two-body problem of ultracold fermionic alkaline-earth-metal-(like) atoms in the electronic
1S0 state (
g-state) and
3P0 state (
e-state) which are confined in a quasi-one-dimensional (quasi-1D) tube simultaneously, where in the axial direction the
g-atom experiences a 1D optical lattice and the
e-atom is localized by a harmonic potential. Due to the nuclear-spin exchange interaction between the
g- and
e-atoms, one can use such a quasi-
(1+0)D system to realize the Kondo effect. We suggest two tight-binding models for this system, for the cases that the odd-wave scattering between the
g- and
e-atoms is negligible or not, respectively. Moreover, we give a microscopic derivation for the interatomic interaction parameters of these models, by explicitly calculating the quasi-
(1+0)D low-energy scattering amplitude of the
g- and
e-atoms in this system and matching this exact result with the ones given by tight-binding models. We illustrate our results for the experimental systems of ultracold
173Yb and
171Yb atoms and show the control effect of the confinement potentials on these model parameters. Furthermore, the validity of the simple ``projection approximation'' is examined. In this approximation, one derives the interaction parameters of the tight-binding models by directly projecting the three-dimensional (3D) Huang-Yang pseudopotential on the ground state of the confinement and the lowest band of the optical lattice. This approximation is supposed to be correct when the 3D interatomic scattering length
as is much smaller than the characteristic lengths (CLs) of the confinements. However, we find that for our system this approximation already does not work when
as is only of the order of 10% of the confinement CLs. Using the exact two-atom scattering amplitude, we also calculate the spin-exchanging rate (i.e., the cross section of the spin-exchanging collision between the
g- and
e-atoms) for the recent experiment [L. Riegger et al., Phys. Rev. Lett. 120, 143601 (2018)] of
173Yb atoms in this quasi-
(1+0)D system and investigate finite-quasimomentum effect of the
g-atoms in this experiment. Our results show that this effect is very significant.
We demonstrate that laser excitations can coherently induce a novel Kondo effect in ultracold atoms in optical lattices. Using a model of alkaline-earth fermions with two orbitals, it is shown that the optically coupled two internal states are dynamically entangled to form the Kondo-singlet state, overcoming the heating effect due to the irradiation. Furthermore, a lack of SU(N) symmetry in the optical coupling provides a peculiar feature in the Kondo effect, which results in spin-selective renormalization of effective masses. We also discuss the effects of interorbital exchange interactions, and reveal that they induce novel crossover or reentrant behavior of the Kondo effect owing to control of the coupling anisotropy. The laser-induced Kondo effect is highly controllable by tuning the laser strength and the frequency, and thus offers a versatile platform to study the Kondo physics using ultracold atoms.
We propose a scheme to investigate the interplay between the Kondo-exchange interaction and the quantum spin Hall effect with ultracold fermionic alkaline-earth-metal atoms trapped in two-dimensional optical lattices using ultracold collision and laser-assisted tunneling. In the strong Kondo-coupling regime, although the loop trajectory of the mobile atom disappears, collective dynamics of an atom pair in two clock states can exhibit an unexpected spin-dependent cyclotron orbit in a plaquette, realizing the quantum spin Hall effect of the Kondo singlet. We demonstrate that the collective cyclotron dynamics of the spin-zero Kondo singlet is governed by an effective Harper-Hofstadter model in addition to second-order diagonal tunneling.